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Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States (2019)

Chapter: 6 Precision Frontier and Fundamental Nature of the Universe

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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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Suggested Citation:"6 Precision Frontier and Fundamental Nature of the Universe." National Academies of Sciences, Engineering, and Medicine. 2019. Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States. Washington, DC: The National Academies Press. doi: 10.17226/25613.
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6 Precision Frontier and Fundamental Nature of the Universe INTRODUCTION One hundred years ago scientists believed they understood the fundamental principles of nature: most scientific problems seemed to have been solved. Newtonian mechanics, electromagnetism and thermodynamics served the needs of world technology, and the progress in comparison with the previous century seemed staggering. Yet there were hints of new physics—atomic spectra, the photoelectric effect, and mysterious X-rays; and a few now-famous names already had said the word “quantum.” No one in 1919, or even 1959, could have imagined what quantum mechanics would bring to the world, and how much of our technology would depend on understanding the nature of atoms, light, and their interaction. In the tremendous success of quantum mechanics, general relativity, and the Standard Model of particle physics lies the danger—to think again that we understand the fundamental principles of nature. The glaring signs of new physics are here again, just as they were in 1919: the Universe of the Standard Model (SM) should have too much antimatter for us to ever come into existence and the SM particles only account for less than 5 percent of it. It is our great hope that we are standing again on the brink of the new era just before the new discoveries stemming from finding solutions to these problems. As it was with quantum mechanics, one cannot even begin to imagine what new technologies these new discoveries will bring. We now live fully in the world of the quantum. The extraordinary advances in control of quantum matter and light discussed in previous chapters have generated transformative tools for precision measurement. It is remarkable that once again it is the study of atoms and light, just as it was a 100 years ago, that enables experiments that can probe the most basic laws of nature, and that allow us to gain a fundamental understanding of the physical universe. What atomic, molecular, and optical science (AMO) brings to the table is the availability of precisely controlled ultracold atoms, vast improvements in precision time and frequency metrology, and measurement techniques such as atomic magnetometry and interferometry. These experimental frontiers are coupled with recent advances in first-principles atomic and molecular theory. Together, these tools now allow novel AMO-based tests of the fundamental laws of physics with unprecedented sensitivity. The advances in precision have been so striking in the past decade that the question naturally arises: “Do the fundamental laws of physics as we know them hold at the level of experimental precision now available?” The potential for paradigm-shifting discoveries is fueled by exceptional versatility, inventiveness, and rapid development of AMO experiments, supported by continuous technological advances described in other chapters. Thus, on the one hand AMO research, with its capability for precision measurement, is likely to transform our view of the universe—competing and in some areas overmatching what can be achieved with accelerators. For example, AMO-based searches for the electron electric dipole moment have already constrained new particles beyond the energy scale reachable by present colliders. The fantastic achievement of detecting gravitational waves was also enabled by quantum technologies. Moreover, the first prototype of a new type of gravitational wave detector based on matter waves has just been approved for construction. New searches for dark matter (DM) are ongoing using all the AMO precision tools discussed in this chapter—including atomic clocks, interferometers, and magnetometers—exploring DM candidates that cannot be discovered with other technologies. Atom interferometry has provided the best limit on some possible dark energy scenarios. On the other hand, many of the same tools being used to probe fundamental physics are also extremely useful as real-world sensors. The latter include the best clocks, magnetometers, gravitometers and gravity gradiometers, as well as inertial sensors. These are critical to industry, healthcare, and PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-1

military applications, as well as to further explorations in basic and applied sciences. Such sensors are discussed in the sections below, together with their applications, both real-world and in fundamental physics. We emphasize that it is the inherently quantum nature of all the sensors described here that enables this level of precision. Most of these sensors rely on coherent superposition and exquisite control of the quantum states. Thus precision measurement, and its correlate of sensing, are in fact part of the quantum technological revolution. This chapter begins with a consideration of unresolved fundamental problems about the nature of our universe that AMO enables one to address. Next are sections on precision measurement technologies and theory advances that are used to address these questions. This leads into sections describing specific experiments aimed at answering these questions. The chapter concludes with a discussion of future directions and opportunities. For more in-depth exploration of parts of this topic the committee refers the reader to an extensive review article, “Search for New Physics with Atoms and Molecules,” containing approximately 1,100 citations to mostly recent work. CRISIS OF MODERN FUNDAMENTAL PHYSICS We live in an exciting time for fundamental physics. All the particles predicted by the so-called Standard Model (SM) (Figure 6.1), which describes the fundamental particles that make up matter and the fundamental force carriers, have been detected. The full description was experimentally completed with the discovery of the Higgs boson at the Large Hadron Collider (LHC) at CERN in 2012. FIGURE 6.1 The Standard Model (SM) of elementary particles includes quarks, leptons, force carriers of strong, weak, and electromagnetic interactions, and the Higgs boson. The SM has been very successful in describing, as well as predicting, virtually everything seen in nuclear and particle physics. Nevertheless, as a “complete” theory it has major issues—many key features of the universe remain unexplained. SOURCE: Fermi National Accelerator Laboratory; see https://commons.wikimedia.org/wiki/File:Standard_Model_From_Fermi_Lab.jpg. Nevertheless, we now know that the SM describes only a very small fraction of the universe’s composition: from the 2015 results of the Planck Mission to study the cosmic microwave background radiation, we know that our present universe is 69 percent dark energy, 26 percent dark matter (DM), and PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-2

only 5 percent ordinary (Standard Model) matter. The DM is observed only via its gravitational interaction; its composition remains a mystery, although evidence for its existence dates back to the 1930s. Its apparent existence is confirmed by numerous studies of astronomical objects. But it does not fit within the SM. Decades of investigation have not identified the nature of DM, although many “candidates” are theoretically hypothesized. So far, we have learned only what most of it is not—namely, none of the particles of the SM. All of the AMO precision tools discussed in this chapter—atomic clocks, interferometers, and magnetometers—are now being used as DM detectors, and many DM candidates can be probed only with precision experiments. The existence of “dark energy” is inferred from studies of Type I supernovae, demonstrating that the expansion of the universe is now accelerating, something possible only if our universe contains an unknown kind of energy that effectively acts as repulsive gravity. The existence of dark matter and dark energy provides a very strong motivation to search for new particles (or their associated fields) beyond those described in the SM. Atom interferometry provides the strongest limits on some dark energy candidates. In a sense, the Standard Model is inconsistent with the very existence of our universe: it cannot account for the observed imbalance of matter and antimatter, and therefore cannot explain how matter survived the annihilation with antimatter after the Big Bang. Searches for the electric dipole moments of atoms and molecules described in this chapter test theories aimed to explain this asymmetry. Another major fundamental problem is the nature of gravity. As one can see from Figure 6.1, the SM does not include gravity. Despite many decades of effort, all attempts to unify gravity with the other fundamental interactions remains unsuccessful, and there is no understanding of why gravity is so weak in comparison with the other fundamental forces. These shortcomings of the SM have long been known. However, the rapid improvement of the precision tools of AMO physics during the past decade place us at an extraordinary point in time for physics discovery. While one can search for new particles directly with large-scale collider experiments at the high energy (TeV = 1012 eV) scale, such as those carried out at the LHC, new physics may very well be observed via low-energy precision measurements based on AMO science. In many theories that have been proposed to go beyond the Standard Model (BSM), Lorentz invariance, universality of free fall, local position invariance, constancy of fundamental constants, and the like, no longer need to hold. Thus the discovery of their violation with the kinds of techniques described in this chapter will be a first glimpse into the nature of BSM physics. In addition, AMO measurements test predictions of new physics theories—non-observation of electron EDM rules out or restricts classes of such theories, and other AMO experiments restrict possible dark matter candidates. PRECISION MEASUREMENT TECHNOLOGIES Atomic Clocks Atomic clocks were briefly described in Chapter 2. Here, the committee focuses on new prospects in clock development, as these are particularly important for probing fundamental physics questions. Systematic uncertainties of 1 × 10-18 have now been demonstrated with clocks based on both neutral atoms trapped in an optical lattice and on single trapped ions, as shown in Figure 6.2. Optical lattice clocks now demonstrate extraordinary statistical uncertainty of 5 × 10-19 in 1 hour. Atomic clocks are uniquely sensitive to a number of new physics signatures. For example, variation of the fine structure constant will cause changes in optical clock transition frequencies, with the amount of change dependent on the clock transition. Microwave clocks (as well as some novel future clocks described below) are sensitive to the variation in other constants involving ratios of particle masses. Therefore, monitoring ratios of two (different) clock frequencies over time allows one to search for the variation of fundamental constants. Light dark matter can cause oscillatory or transient changes of the fundamental constants and, therefore, clock frequencies. The presence of such signals can be extracted PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-3

from clock-comparison experiments. The advances in atomic clocks over the past decade have already enabled improved tests of the constancy of the fine-structure constant and proton to electron mass ratio, several orders of magnitude improved tests of Lorentz invariance, and new applications of clocks to dark matter detection as described in the Section later in this chapter, “Searches for New Physics Beyond the Standard Model.” Considering that the gravitational redshift is 1 × 10-19 for a 1 mm height change on Earth, it is tantalizing to think of the future scientific possibilities when we improve clock performance to, say, the 1 × 10-21 precision level, when the gravitational red shift on clock atoms separated by a mere 10 μm can be detected. Such capabilities will be invaluable for relativistic geodesy and testing quantum mechanics in curved space-time. Permission Pending FIGURE 6.2 The evolution of fractional frequency uncertainties of atomic frequency standards based on both microwave (Cs clocks) and optical transitions. SOURCE: From Rev. Mod. Phys. 90, 025008 (2018), with new (last) data point added. To reach this exciting new regime, advances in ultrastable lasers and precise control of quantum states of many atoms will be necessary. Furthermore, exciting new opportunities have emerged for the next generation of state-of-the-art precision quantum metrology, such as harnessing the interactions between atoms to create and manipulate interparticle correlations and entanglement for precision measurements of time, frequency, and space. Such work has already started with the development of a three-dimensional (3D) optical lattice with Sr atoms forming a Mott insulator. This configuration suppresses effects of atomic contact interactions, and extends interrogation times to beyond 10 s. Even with atoms pinned in a 3D lattice, long-range dipolar interactions can degrade clock precision, and give rise to an important systematic effect. Understanding and controlling both the real and imaginary parts of dipolar interactions will be crucial for the next generation of clocks. New techniques, such as using an adjustable optical lattice, or an array of optical tweezers, to configure these many atoms in a spatially ordered and stationary regime, could extend the coherence time to the limit of the Sr excited state lifetime of more than 100 seconds. In addition to further development of the current clocks, new clocks are being proposed and developed which are much more sensitive (by a factor of 100 to 10,000) to fundamental physics questions. As mentioned earlier, these promise to enable measurements such as variation of fundamental constants, as well as tests of local position invariance, and dark matter searches. These are described later in this chapter. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-4

Highly charged ions (HCIs) offer extremely narrow optical transitions that are less sensitive to some of the external perturbations as compared to current atomic clocks. These should have a high sensitivity to the variation of the fine-structure constant due to relativistic enhancement. Development of high-precision atomic clocks requires cooling, trapping, and precision control of the various atomic species. Direct laser cooling, used for neutral atoms and singly charged ions, is impossible for HCIs, which lack the necessary fast-cycling optical transitions. In 2015, a breakthrough demonstration was reported of sympathetic cooling of Ar13+ down to below 100 mK, by using a laser-cooled Be+ Coulomb crystal in a cryogenic Paul trap. In 2018, quantum logic spectroscopy of Ar13+—in which a Be+ ion, trapped together with the spectroscopy ion, provides sympathetic cooling, control, and readout of the internal state of the spectroscopy ion—was demonstrated at PTB, Germany. This new development opens the pathway toward rapid development of HCI clocks. In contrast to atomic transitions, nuclear transition frequencies are typically many orders of magnitude higher than those accessible by lasers, with the unique exception of a long-lived nuclear transition that occurs between an excited state (isomer) of the 229Th isotope and the corresponding nuclear ground state. Designing a clock based on this nuclear transition, with a wavelength of 150(3) nm, is particularly attractive due to the suppression of field-induced frequency shifts, since the nucleus interacts only via the relatively small nuclear moments and is highly isolated from the environment by the electron cloud. The existence of the isomer was definitively confirmed in 2016 by a European collaboration. Further laser spectroscopy investigation of the hyperfine structure of the isomer yielded the first nuclear properties. These recent experimental milestones have provided a solid base for progress toward the accurate measurement of a transition frequency, and realization of an actual nuclear clock. Two different types of nuclear clock designs have been proposed, one based on trapped ions and another on a solid-state system in which Th is implanted in crystals transparent to radiation in the vacuum-ultraviolet range. It has been suggested that such a nuclear clock would be enormously more sensitive (by five orders of magnitude) to the variation of the fine-structure constant and quark masses than all atomic clocks currently in operation. Preparations are under way for the development of HCI clocks and nuclear clocks. Efforts in the United States to pursue these opportunities in novel clock development are also underway. Quantum Metrology Using Correlated States The performance of many precision sensors is limited by fundamental noise properties dictated by quantum mechanics. For example, the frequency stability of atomic time standards is currently limited by so-called quantum projection noise, associated with detection of the number of atoms in a given clock output state. In this case, each atom behaves in a statistically independent way from all other atoms in the clock; in general, the sensor output is given by the statistics of an ensemble of independent, uncorrelated, particles. However, it has been known for several decades that quantum mechanics in principle allows access to significantly improved performance if a suitably quantum correlated state is used for the sensor. In this case, particles no longer behave as statistically independent entities; rather, the quantum states of particles (e.g., the two atomic states comprising an atomic clock) become statistically correlated— entangled—across the entire ensemble. In the case of photons, quantum correlations lead to the squeezed states of light discussed in Chapter 2 and again later in this chapter. Amazingly, these correlations can be achieved in such a way that they may improve the noise performance of the sensor without fundamentally altering its function. The physically allowable improvements can be dramatic. For a sensor employing N particles prepared in an appropriately correlated state, the measurement precision can improve beyond the normal N1/2 scaling. In principle, for an atomic clock with a million atoms, one may achieve a thousand- fold performance improvement beyond the standard quantum limit. Broadly speaking, the performance of any precision sensor can in principle be improved with such methods. For example, an atom interferometer gyroscope that performs at a noise level suitable for aircraft navigation can, with such methods, achieve performance levels better than the very best strategic- PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-5

grade gyroscopes used for submarine navigation. The detection noise performance—and thus the astrophysical reach—of a gravitational-wave detector can be likewise improved. It is extremely challenging to produce the states that can yield the ultimate level of performance—the so-called Heisenberg limit. However, with recent advances in methods to control the quantum mechanical states of ensembles of particles, pioneering experiments in the past decade have already indicated the possible effectiveness of this approach. Since the methods needed to build the required correlated states for sensing are intimately connected with those exploited for quantum information processing, it is anticipated that substantial progress is likely in the coming decade. With sustained investment in basic and applied research in this area, it is likely that many classes of fundamental and applied sensors (e.g., magnetometers, clocks, accelerometers, gyroscopes, gravimeters, and gravitational-wave detectors) will see very significant performance improvement by adoption of these methods. Atom Interferometric Inertial Sensors Atom interferometers exploit the quantum mechanical wave properties of matter to realize sensors and instruments analogous to optical interferometers. Progress in this field has been fueled by development of cold atomic sources, which offer precise control over the velocity, hence wavelength (via the de Broglie relation) of the interfering atomic particles. De Broglie wave interferometers for atoms were first realized in the early 1990s; the past decades have seen a significant growth in both the reach and capabilities of these instruments. For example, current atom interferometers realize atomic wave- packet separations of 0.5 m over temporal durations of 2 s by exploiting increasingly sophisticated atom/laser interactions to manipulate atomic center of mass wave-functions. These observations indicate the extraordinary level of control that can now be exerted on ensembles of atoms. They provide stunning examples of the manifestation of quantum phenomena on macroscopic human scales. Such laboratory interferometers are now finding use in tests of gravitational physics, quantum mechanics, and in searches for physics beyond the standard model, as the science reach of tests like these is intimately linked with these aspects of our fundamental understanding. On the other hand, as supporting photonics technologies have matured, early laboratory-scale proof-of-concept demonstrations of inertial force sensing capabilities have matured into a class of field-deployed sensors for gravitational fields, gravity gradients, and rotations. The performance of these sensors is now beginning to compete favorably with existing state-of- the-art sensors. Related instruments have been recently used to make new measurements of the fine structure constant through indirect observation of the momentum recoil of atomic wave-packets induced by photon scattering. Atom interferometric inertial sensors derive a performance advantage compared to existing state-of- the-art sensors from the fact that atoms are superbly isolated from spurious non-inertial forces, and from the fact that precision laser sources are used to manipulate and control atomic wave-functions. These attributes enable new classes of high-accuracy sensors. For example, commercial atom interferometric gravimeters achieve 10-9 g accuracies, and atom interferometric gyroscopes have exceptional bias and scale factor stability. The noise performance of these sensors continues to improve as well-engineered high-flux atomic sources mature, as sensor noise performance is limited by the shot noise associated with the number of atoms detected in a given observation time. In practice, noise performance for well- engineered sensors meets and can exceed the performance of sensors based on other technologies. The combined noise and accuracy attributes of atom interferometric sensors makes them uniquely suited for applications such as, for example, precision inertial navigation. In the coming decade, further advances are foreseen in the performance, integration, and size of fieldable sensors. For example, deployed gravity gradiometers with 0.01 E/Hz1/2 noise performance appear feasible. (1 E = 10-9 s-2; for reference, the gravity gradient due to the Earth’s gravitational field, as measured on the Earth’s surface is ~ 3000 E.) Such sensors have national security applications in underground structure detection; and commercial application in oil and mineral exploration, in which structures and deposits are identified through their gravitational signatures. On the other hand, the PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-6

performance of laboratory-based (versus fieldable) sensors is expected to continue to advance with improved atom optics and implementation of quantum metrology detection protocols. Lastly, space-based platforms are well-suited to atom interferometric sensors, as these sensors benefit from the long free-fall times available in this environment. Recent development of space-based cold atom platforms (NASA Cold Atom Lab) suggests the possibility of future space missions. Applications of space-based inertial sensors include gravitational geodesy and gravitational wave detection, as well as fundamental gravitational physics experiments such as tests of the equivalence principle. Gravitational Wave Detection Gravitational waves (GWs) were predicted by Einstein in 1916, as part of his General Theory of Relativity (GR). GR presented a completely new way of understanding gravity, not as a force between massive objects, but as the geometry of spacetime. In GR, massive objects cause the space around them to curve, and clocks near them to tick more slowly. When massive objects accelerate, spacetime ripples, and GWs are generated that can travel across the universe carrying information about their sources. GWs are very weak; only compact masses moving at relativistic speeds radiate GWs with appreciable strength. Even some of the most violent collisions in the universe—mergers of neutron stars and black holes in the nearby universe—cause only the slightest ripples of spacetime here on Earth. As these ripples pass through a region of spacetime, they change spacetime distances L by an amount L = h L, where h is the amplitude of the GW. The GWs from a pair of neutron stars, comprising the densest matter known, merging with each other in a nearby galaxy would change kilometers long distances between objects here on Earth by L = 10-21 × 1000 m = 10-18 m, or 1/1,000th the size of a single proton. Consequently, for many decades after Einstein’s prediction, the prospects for measuring GWs seemed grim—they were just too faint. In the 1960s, with the invention of the laser and the discovery of neutron stars and black holes, the prospects for detecting these faint waves from real astrophysical sources began to seem within reach (see Box 6.1). A passing GW can be detected by measuring the spacetime distances between freely floating objects or “test masses.” The test masses must be shielded from all external forces well enough that their motion is due to the GW. If laser light, with its exquisite precision, is to be used as the meter stick for measuring the spacing between the test mass, then the test masses must also double as mirrors. ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// BOX 6.1 Laser Interferometry for Gravitational Wave Detection The combination of mirror test masses and ultrastable lasers led to the conception of a bold experiment called LIGO—the Laser Interferometer Gravitational-wave Observatory—that sought to directly measure GWs using precision optical interferometry. LIGO was funded by the National Science Foundation (NSF) over four decades, an investment that in 2015 realized two laser interferometers that had the precision to measure changes in the distances between mirrors that were 4 km apart at the level of 10-18 m. To reach this precision, LIGO uses many techniques of precision measurement and quantum optics that were developed as part of the extensive, diverse, and growing AMO science toolkit. The imperative to continue to explore the universe with GWs, searching for new unknown objects, and gaining a deeper understanding of what we already see, is driving exploration and design of a new generation of laser interferometric GW detectors that will be capable of mapping out all merging black hole binaries in the observable universe. The design of these so-called third-generation instruments is pushing the frontiers of precision measurement, from lasers and optical technologies, to vibration control, to engineering new optical materials, to subquantum sensing techniques. This continuing development of new capabilities in precision measurement is the direct result of the interplay between the fields of AMO science and GW detection. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-7

Since the first detection in 2015 (Figure 6.1.1), LIGO and its European counterpart Virgo, have published confirmed detections of GWs from 10 binary black hole mergers and one neutron star merger, as of Summer 2019. Unlike black hole collisions, where little or no light is given off, GW emission from neutron star collisions are followed by a spectacular light show, as neutrons fuse to make heavier and heavier elements. GW measurements of the neutron star merger by LIGO and Virgo triggered a massive observational campaign by telescopes worldwide, and the emitted light was observed at many wavelengths, from radio to infrared to optical to X-rays to gamma rays. One of the great attractions of observing the universe with GWs is that they are emitted by objects that may not give off light, and so are undetectable using traditional telescopes. Even when they do emit light, as in the neutron star merger case, GWs provide complementary information that provides a much fuller understanding. These first GW discoveries are already changing our understanding of some of the most violent events in our universe. Permission Pending FIGURE 6.1.1 Historic first detection of gravitational waves. Clockwise from top left: The precision optical measurement is made by detecting the interference between two light beams in the arms of a laser interferometer; aerial views of the LIGO observatories in Washington and Louisiana; the first gravitational wave signals from colliding black holes were observed by the detectors on September 14, 2015; the 2017 Nobel prize in Physics was awarded to Rainer Weiss, Kip Thorne, and Barry Barish for “decisive contributions to the LIGO detector and the observation of gravitational waves.” The success of LIGO can be directly attributed to long-term sustained funding by NSF over decades. SOURCE: Nergis Mavalvala/LIGO. END OF BOX////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// Quantum Engineering for Gravitational Wave Detectors In Chapter 2, the committee introduced squeezed states of light—specially engineered quantum states where the noise is redistributed between the amplitude and phase properties of the light. Improving the sensitivity of laser interferometer GW detectors is an immediate and tangible application of squeezed states. Figure 6.3 shows the improvement to the noise performance of the LIGO Livingston detector when squeezed states are injected. The approximately 30 percent improvement in strain sensitivity should lead to a factor of 2 increase in the rate at which astrophysical sources may be detected. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-8

Permission Pending FIGURE 6.3 Injection of squeezed states into the LIGO detectors leads to improved sensitivity. Left panel: Squeezed states are generated with a sub-threshold optical parametric oscillator, where optical nonlinearity creates correlations between photons. The squeezed states are injected into the output (anti- symmetric) port of a LIGO interferometer; they propagate through the interferometer and exit the antisymmetric port along with the GW signal imprinted on the laser light that was incident through the symmetric port. The combined fields detected by the output photodetector can have noise lower than the shot noise limit without squeezing, as shown in the right panel. Right panel: Spectra of the noise limits of the Advanced LIGO detector at Livingston, Louisiana. The blue curve is the performance when no squeezed states are injected, and the red curve is with squeezing. Squeezing gives a roughly 30 percent improvement at frequencies with the most improvement, which should give over a factor of 2 improvement in the rate of detections for Advanced LIGO. The line features are typically of power lines, calibration lines and mechanical resonances. SOURCE: Maggie Tse/LIGO. Gravitational Wave Observatories in Space Just as the electromagnetic spectrum spans wavelengths from kilometers (radio waves) to picometers (gamma radiation), so also the GW spectrum spans 20 orders of magnitude in wavelength. Different sources radiate GWs at different wavelengths, depending on the physical processes underlying the radiation. Earth-based detectors like LIGO are sensitive to GWs of frequencies between 10 Hz and 10 kHz, typically radiated by compact objects that have a few times the mass of our Sun. Much heavier objects, such as supermassive black holes at the centers of galaxies, would radiate GWs at much lower frequencies, in the 10 to 100 mHz range. Terrestrial detectors are unable to observe GWs at these lower frequencies since vibrations on Earth are too large. Exploring the rich menagerie of GW sources at lower frequencies motivates GW detectors in space. The most advanced in design is the Laser Interferometer Space Antenna (LISA), a European space mission that NASA partners in. LISA comprises three satellites that are about 1 million kilometers apart and fly in a triangular formation, shooting laser beams from one to the other. Precise on-board clocks measure the time of arrival of laser beams to infer the spacetime distances, which would be modulated by passing GWs. Like LIGO, LISA uses a vast array of AMO tools, from ultrastable lasers and atomic clocks to quantum-noise- limited optical measurement. LISA technologies have been developed for the past three decades, culminating in an important space test called the LISA Pathfinder mission. Following the spectacular success of the Pathfinder mission, which demonstrated that the spacecraft can be controlled to meet the stringent requirements on acceleration, LISA is now slated for launch in 2034. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-9

Matter Wave Interferometry for Future Gravitational Wave Detection Laser interferometry is the most mature technology for GW detection, owing in no small part to decades of intellectual and financial investments. But it is not the only technology that can be used for GW detection. Advances in atomic physics and optical physics have provided tools that enable new classes of precision measurements, including GW detection. These tools include atom interferometry, as discussed in the previous section in the context of inertial sensing, where quantum mechanical interference of atomic de Broglie waves enables precise force measurements. The combination of atom interferometry and ultrastable lasers, which have led to a generational advance in the performance of atom-based sensors, has the potential to provide a novel method for GW detection in future decades. In the atom interferometric approach, gravitational radiation is sensed through the gravitational wave- induced phase shifts on the propagation of laser beams between two spatially separated, inertially isolated, laser-cooled atomic ensembles. Momentum recoil associated with the interactions between the laser and atomic ensembles results in the concomitant interference of atomic wavepackets. Functionally, the atomic ensembles serve as precision clocks which measure the flight time of light between the atom ensembles. In the case of space-based atom interferometric GW detectors, optical lattice clocks paired with conventional drag-free vibration isolation (e.g., in LISA Pathfinder) can also realize scientifically interesting strain sensitivity levels. For ground-based configurations (see Figure 6.4), the atomic interferometric approach provides immunity to local seismic noise, and thus may enable detection of gravitational waves in the 0.3 Hz to 10 Hz frequency band. A 100 m prototype detector (MAGIS) is currently being built to evaluate the efficacy of this approach. This instrument also provides new detection modalities for ultralight dark matter. Related instruments are under development in France (MIGA) and China (ZAIGA). The GW spectrum between 0.03 Hz and 10 Hz appears to be scientifically rich. The lower end of this range would allow observation of white dwarf binary mergers, while the higher frequency region (~1 Hz) is potentially a valuable region for searching for cosmological sources. Moreover, black hole or neutron star binaries may be observed in different frequency bands during their in-spiral, merger, and ring-down phases. Observations by LISA at tens of mHz, and future mid-band detectors operating at higher frequencies, could give predictions of the time and location of a merger event at tens of Hz in LIGO, which in turn would allow narrow-field high-sensitivity optical, X-ray, gamma ray, and other telescopes to point to observe the prompt emission during the actual merger. Since the sources generally emit for a long time in this mid-frequency band, they can be localized on the sky even by a single-baseline detector, since the detector will change orientation and position significantly during the time spent observing a single source. This can potential lead to new, powerful cosmological probes. Permission Pending PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-10

FIGURE 6.4 Top and right panels: MAGIS-100 atom interferometer currently under construction at Fermilab. Lower left panel: anticipated strain sensitivities of the detector as a function of gravitational wave frequency. The upper and lower atom sources are separated by 100 m. This apparatus serves as a prototype for possible space-based and longer baseline ground-based detectors (MAGIS-km). GGN indicates the anticipated level of terrestrial gravity gradient noise based on published noise models. SOURCE: Courtesy of Jason Hogan, Stanford University. Altogether, LIGO/Virgo and their descendent experiments, such as LISA, and future atom interferometry-based GW detectors, have the potential to cover a large part of the GW spectrum. As a result, we should be able to map out astrophysical sources that include mergers of supermassive black holes, of white dwarf binaries, of neutron stars, of stellar-mass black holes, as well as supernova explosions, and yet undiscovered cosmic phenomena. As GW detectors get more sensitive, scientists can learn about the properties of these still largely mysterious sources, which in turn can increase understanding of how the universe we see came about, how stars live and die, what is the structure of neutron stars and black holes, how galaxies form, and much more. In addition to astrophysical discoveries, GW detections also serve to teach us more about the fundamental nature of gravity, such as the speed and dispersion of GWs, the mass and spin of the graviton, whether gravitational waves permanently alter the spacetime of a region through which they have passed, and more. The precision of the measurements also makes GW detectors unique testbeds for probing the quantum limits to measurement. All in all, GW detectors use a range of AMO technologies that push the quantum limits of precision measurement to observe the dark and warped universe, while also probing the fundamental nature of gravity and quantum mechanics. Another connection between AMO-related science and GW observations is the role of laboratory survey spectroscopy in characterizing sources. Kilonovae—the products of neutron star mergers—are predicted to be the factories in which heavy elements (with atomic number Z ≥ 44) of the periodic table such as gold, platinum, and the actinide and lanthanide series are produced through rapid-neutron capture nucleosynthesis processes. Indeed, this appears to be borne out by optical and infrared spectra measured by telescopes in the hours following the first observation of the first merging neutron stars observed by GW detectors. To fully understand the observations, opacities are needed for low-ionization stages of heavy elements, which requires high-resolution spectral information best obtained by combining laboratory spectroscopic measurements with AMO theory. Significant advances are required in both AMO theoretical and experimental methods in order to maximize our scientific understanding of these newly discovered objects. Magnetometry Measurement of magnetic fields has a long history. Work at the “precision frontier” in magnetometry not only impacts a variety of application domains but also loops back and impacts fundamental questions of physics itself. Some of the obvious areas of impact include mapping and understanding geological and geoplanetary magnetic fields, as well as magnetic fields in space both planetary and interplanetary. Other applications include the measurement of biomagnetic fields to deepen understanding in life sciences and for uses in medicine. The sensitive measurement of these fields enables noninvasive studies of the time dependence and spatial distribution of biocurrents, and has largely focused in people on the heart and brain. This includes direct field detection as well as detection of nuclear magnetic resonance (NMR) or magnetic resonance imaging (MRI) signals, for use in novel configurations such as “remote” NMR (where, e.g., the sample and the magnetometer can be spatially separated). Measurement of brain fields (magnetoencephalography) is widely used for functional brain studies—for example, localizing sensory response. Still other applications of magnetometry include detecting man-made objects, ranging from the mundane, like finding coins on a beach, to national security applications, like locating enemy tanks or submarines. In particular, for the scope of this chapter, sensitive measurement of magnetic fields plays a PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-11

crucial role in the testing of fundamental symmetries. For example, magnetometers are employed in setting limits on the electric dipole moments (EDM), on particular forms of violation of Lorentz invariance, and on spin-dependent forces that might be mediated by axions. Different aspects of the measurement are important for various applications. One obvious aspect is sensitivity—namely, how small a field or difference in field is discernible. In other applications, one might perhaps trade off some sensitivity for spatial resolution. How small a domain must one be able to image? For example, macroscopic is good enough for seeing a coin or a submarine, but for these applications high sensitivity is critical so that one does not miss anything; while a neuron in a biological system, or a defect in a material requires a considerably smaller sensor head to discriminate the structure (see Figure 6.5 for the trade-off between resolution and sensitivity). Although one still desires as much sensitivity as possible, typically one gets several orders of magnitude less sensitivity in the microscopic approaches. On the other hand, one can work in a shielded environment for these kinds of measurements, unlike, for example, detecting submarines in the noisy environment of Earth. Still another trade-off is simplicity. For decades, Superconducting Quantum Interference Device (SQUID) magnetometers had been the standard for sensitivity, as they can reach close to femtotesla (1 fT = 10-15 T) level discrimination, and even provide good resolution, but they must be cooled to cryogenic temperatures. The technologies involved in cooling are generally costly, bulky, and complex. Many of the atomic magnetometers the committee discusses here do not require such cooling. Another trade-off is sensitivity versus need for shielding. A SQUID magnetometer (and others discussed) must be shielded or actively compensated to measure a small field variation superimposed on large background fields. Magnetometers with the greatest sensitivity or spatial resolution for the types of application mentioned above are based either on SQUIDs or on AMO-related technologies. Given the added cost and complexity of cryogenic operation of SQUIDs, and that the sensitivity of AMO-based approaches is as good or better, for more and more applications the state of the art is AMO magnetometry. Figure 6.5 shows the sensitivity versus spatial resolution trade-off of various classes of magnetometers for comparison. One of the leading classes of AMO-based magnetometers are optically pumped magnetometers (OPMs) containing thermal atoms. These can employ electron paramagnetic resonance (EPR) or nuclear magnetic resonance (NMR) of atoms, generally contained in a glass vapor cell. One uses lasers to optically pump the vapor and prepare the atoms in a strongly polarized state. The gas vapor is usually of rubidium or cesium because the pumping frequencies match up very well with wavelengths available from semiconductor lasers, which can be made very small. (Helium-4 magnetometers are also widely used—for example, in space applications—because of their relative simplicity and reliability.) One then measures the Larmor precession frequency, which is proportional to the total magnetic field. This allows DC magnetic field measurements with femtotesla-level resolution. The precession frequency of the atomic spins can be monitored through the transmission of light perpendicular to the axis of precession. The precession can also be monitored through nonlinear magneto-optical rotation. Sources of loss of sensitivity are from collisions with the glass walls of the cells, and due to spin-exchange collisions with other atoms. Both can be overcome (e.g., with coatings such as paraffin on the glass walls, or going to lower densities or adding buffer gasses to reduce interparticle collisions). These steps increase the coherence time (which effectively translates to interrogation time), but do not entirely solve the problem. For example, reducing the density also reduces the overall sensitivity. Coatings, while they can be efficient, are still a “black art” and are not well understood (and thus are often not even reproducible); even ones that work very well can be thwarted with small areas of impurity. In state-of-the-art vapor cell magnetometers, very high sensitivity is achieved when decoherence due to spin-exchange collisions is suppressed—that is, by working in the spin-exchange relaxation free (SERF) regime. However, working in this regime requires working in a very low ambient magnetic field environment, very close to zero field. SERF and other zero-field OPMs can be used only in a magnetically shielded environment in which the background field is nearly zero, and the background magnetic noise is very low. A standard way to solve the problem of ambient magnetic field noise is the implementation of gradiometers, where the PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-12

magnetic field in two locations is measured and subtracted. Thus, when taking all the appropriate measures, SERF and OPM magnetometers reach sensitivities lower than 1 fT/Hz1/2. FIGURE 6.5 This figure shows schematically, for a variety of approaches for the measurement of magnetic fields, the trade-space of two significant metrics—namely, the resolution at which one can resolve an object versus the sensitivity with which one can detect its magnetic field. The points in the diagram show the approximate required spatial resolution versus needed magnetic sensitivity in order to detect a single proton, a single electron, a biological cell by NMR, a neuron, and to do a (brain) magneto- encephalograph (MEG). The well-known Superconducting Quantum Interference Devices (SQUIDs) were long the gold standard for magnetometers, and still have important uses. However, AMO-based approaches outdo SQUIDs now, both in field sensitivity and in resolution. The different approaches shown are discussed in the text. All have additional trade-space metrics, including various needs for isolation from the environment, such as cooling, shielding from stray fields, need for operation at zero field, and the like. Magnetic Resonance Force Microscopy (MRFM) is a form of atomic force microscopy (AFM). SOURCE: Adapted from Ron Walsworth, Harvard University. Microscopic approaches to magnetometry are very different from the vapor cell OPM approaches. These provide much higher spatial resolution, although at the expense of sensitivity (again, see Figure 6.5). One example is related to the atomic force microscope (AFM). Such a magnetic force microscope (MFM) has reached the ability to measure the magnetic moment of a single electron. Another example of a microscopic approach uses nitrogen vacancy (NV) diamond color centers, which are described in Chapter 2. They greatly exceed the spatial resolution of OPMs and even exceed the resolution of SQUIDs. Also, unlike SQUIDs, they work well with room-temperature samples. The NV-diamonds are either embedded in the sample itself, or put at the end of a tip of an AFM. To measure magnetic field, one optically measures the effect of the Zeeman shift on the NV ground-state spin levels. However, a downside of NV-diamond vis-à-vis atomic vapor cells is that unlike atoms, NVs are in general not identical (e.g., they can occur in different lattice placements or chemical environments), and therefore a collection of NVs will typically have broadening, further contributing to lower field sensitivities. Alternatively, one may use single or small numbers of NVs, but this reduces the possible signal. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-13

Nevertheless, many exciting applications are emerging using NV-diamond, including noninvasive sensing and imaging of biomagnetism in living cells and whole animals with submicron resolution; mapping of magnetic materials within primitive meteorites and early Earth rocks with micron resolution, which is already providing advances in the understanding of the formation of the solar system and Earth’s geodynamo; and imaging patterns of nanoscale magnetic fields in a wide variety of advanced materials, allowing development of smart materials. Somewhere in between for both sensitivity and spatial resolution, are trapped cold atoms and even Bose-Einstein condensates (BECs) that are created, trapped, and optically placed in close proximity to a desired target. The spatial resolution is somewhat better than with SQUIDs, but not at the NV-diamond or AFM level. Sensitivity does not reach the atomic vapor cell level, largely due to the much lower number of atoms in a BEC than in a vapor cell, despite the gain from the longer spin-coherence times. One method of detection is based on measuring density modulations—the spatially varying density measures the potential energy, which reflects the local magnetic-field. Spinor BECs are also employed, with detection based on relative populations in the different spinor states and Larmor precession among them. The most recent incarnation of a BEC-based magnetometer is the Scanning Quantum Cryogenic Atom Microscope (SQCAMscope), which is a quantum-noise-limited scanning probe magnetometer that has both high field sensitivity and micron-scale resolution. It employs a magnetically levitated atomic BEC. One can also use cold atoms for gradient magnetometry. Two modes of operation give good results here. First, one can employ two clouds of atoms, simultaneously probing two regions of space through Raman interrogation (measuring frequency difference) to yield a magnetic field gradient. Second, one can use an atom interferometer in which one uses superposition states of two different magnetic hyperfine states that evolve differently in a magnetic field, and when recombined lead to gradient dependent fringe intensity. Cold atom-based approaches lead to sensitivities that are typically in the pT/Hz1/2 regime. From a practical point of view, however, cold atom approaches require at least a glass cell if not a vacuum chamber if one is using BECs. In the end, the approach one uses will depend on many factors, including whether one needs high spatial resolution or high field sensitivity, the complexity of the apparatus one can deal with, including cryogenics, and whether one can work in the zero field regime or not. As described at the beginning of this Section, there are many applications of magnetometry, that range from national defense, to geology, planetary science, astrophysics, across the life sciences and medicine, to fundamental questions at the foundations of physics itself. This breadth of applications and approaches highlights the role of magnetometry as one of the AMO-based tools that enable precision measurement, both as an enabler for studies of fundamental physics and as sensors in applications in other areas of basic and applied science, and for industrial and military use. Some of these are discussed below in the context of searches for Beyond Standard Model physics, and others in Chapter 7 as impacts on other areas. THE ROLE OF THEORY AND RECENT THEORY PROGRESS Close collaboration of theory and experiment, which is an important feature of the AMO field, is particularly important for precision measurement and fundamental physics studies. Theory has many crucial roles in these investigations, from the proposal stage to the final analysis. For example, theory is necessary to  Develop new ideas: what other fundamental physics questions can be answered by probing atoms and molecules with precision AMO tools?  Propose new experiments and select systems with the largest sensitivity to new physics effects of interest.  Calculate atomic properties of the systems required for the planning and implementation of the experimental proposals and evaluation of systematic uncertainties. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-14

 Carry out calculations needed to interpret the experiments in terms of new physics effects or set limits on possible new physics.  Propose new tools for precision measurements—for example, to develop proposals for new clocks that are particularly sensitive to fundamental physics. There have been exceptional advances in the accuracy of atomic and molecular structure theory in the past few years, both due to development of new methods, and to significant increases in computational resources. For example, recently developed relativistic atomic coupled-cluster codes that include single, double, and triple excitations have greatly improved accuracy for heavy atoms such as Cs, reaching 0.15- 0.35 percent accuracy for transition matrix elements and hyperfine constants in this atom. Such extraordinary accuracy was required for the analysis of Cs parity violation experiments in terms of new physics as described in the section below, “Parity Violation—AMO Tests of Weak Interaction.” Other advanced codes have also allowed sub-percent prediction of many properties of alkaline-earth atoms and similar systems. They are used for evaluation of blackbody radiation shifts and other systematic uncertainties in optical atomic clocks; design of highly charged ion clocks; analysis of experiments for new physics searches; creation of new state-insensitive cooling and trapping schemes for studies of degenerate quantum gases; and atom and light shift modeling used to understand and control alkaline atoms held with optical tweezers, in optical lattices for quantum simulation, and for many other applications. Moreover, the development of several ab initio relativistic methods of increasing accuracy allows for strategies to accurately estimate uncertainties of theoretical predictions where no experimental data is available. The development of these approaches, which include electronic correlations to a much higher degree than was previously possible, allows one to make precision theory predictions not only in alkali metal and alkaline-earth metals but in more complicated systems as well. In turn, new experiments provide benchmark results for testing the theory. Further method developments and new code designs now in progress will allow efficient parallel computing on very large-scale computational facilities, with the goal of accurate predictions of atomic properties in even more complicated open-shell systems. Advances in molecular theory have allowed one to calculate effective electric fields with better than 10 percent accuracy in ThO and HfF+; this is needed for extraction of the limits on the electron EDM (eEDM) from experiments. New atomic structure community codes (CI+MBPT and AMBiT) were recently documented and released for public use. Developing flexible and robust software in computational atomic and molecular physics was a topic of a 2018 NSF-funded workshop at the Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP). The workshop identified and prioritized outstanding problems in AMO science that would benefit from a concerted community effort in developing new software tools and algorithms, leading to more rapid progress, as well as identified the best approaches and plans to address these problems. It is worth noting that collaborations between high-energy and particle theory and AMO precision measurement research has become increasingly active and important recently. Considering the discovery potential, such collaborations should be encouraged and strengthened, for example with joint research funding. SEARCHES FOR NEW PHYSICS BEYOND THE STANDARD MODEL Searches for Permanent Electric Dipole Moments Remarkably, table-top-scale experiments using methods of AMO physics can be sensitive to new forces and particles, similar to those sought at the largest particle colliders. Here the committee describes an important example, namely searches for a permanent electric dipole moment (EDM) along the quantized spin axis of any particle. For example, an electron EDM (eEDM) could result from a tiny PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-15

deformation of the electron’s charge distribution, away from perfectly spherical. AMO experiments probe such effects in both electron and nuclear sectors as described in this chapter. An electron (and every other fundamental particle) carries with it, at all times, a tiny cloud of “virtual” particles that includes every type of particle that exists in nature, including those yet to be discovered. The cloud acts to modify the properties of the electron as seen by an observer from afar, including the shape of the charge distribution. The quantum uncertainty principle ensures that the more massive the particle, the smaller its effect on this cloud. The existence of new heavy, TeV energy scale particles suggested by supersymmetry and other theories, would results in EDMs within the range of current experiments. EDMs are intrinsically linked to violations of discrete symmetries: there is an EDM only when time- reversal (T) symmetry is broken—that is, if things are different when the flow of time is reversed. This can be visualized as follows. If a particle (such as an electron) had an EDM, it would be oriented parallel or antiparallel to the particle spin. A movie of such a particle, if run backward, would be different from the original, since the spin would reverse direction while the charge distribution would remain unchanged—implying an asymmetry under T. The Standard Model (SM) of particle physics includes particles that carry T-violating forces, but their effect on EDMs is indirect and leads to tiny predicted values. For example, in the SM the eEDM is predicted to be about a billion times smaller than can currently be detected. However, it is known that nature must include new T-violating forces. Such forces are required to explain how the universe came to be made almost entirely of matter, although equal amounts of matter and antimatter would have been created in the SM description of the Big Bang. The T-violating forces in the SM are much too weak to explain the cosmologically observed imbalance between matter and antimatter. Solving this long-standing puzzle requires nature to include new, much stronger, sources of T-symmetry violation. Happily, many well-motivated extensions to the SM introduce new sources of T-violation. The new forces and new particles in these theories typically induce EDMs more directly than in the SM. Because of this, much larger EDMs often appear in these theories, although the new particles they predict are much more massive than known particles. For example, in theories where new particles have masses corresponding to energies above the TeV scale—that is, 10 times larger than the mass of the Higgs boson—the size of predicted EDMs is typically within the limits current AMO experiments could detect. Since this exceeds the scale directly accessible to current and near-future particle colliders, these AMO- based EDM experiments have a high potential for discovering new particles and forces not accessible in any other way. AMO experiments can detect several types of T-violating effects, including EDMs of the electron, proton, and neutron, T-violating electron-nucleon and purely hadronic (nucleon-nucleon) interactions. Therefore, it is essential to conduct experiments in a variety of systems to probe for different effects. Paramagnetic systems (containing unpaired electron spins) are most sensitive to the eEDM and to one type of electron-nucleus interaction; while diamagnetic systems (with closed electron shells, but nonzero nuclear spin) are mostly sensitive to purely hadronic (nucleon-nucleon) interactions, and to other types of electron-nucleon interactions. In different theoretical models, EDMs are more likely to appear in one or the other of these systems. In typical EDM search experiments, the particle’s spins are first polarized, so their EDMs point in a known direction. Next, a strong electric field exerts a torque on the EDM, causing the spin axis to rotate. After applying this E-field for as long as possible, the final direction of the axis is measured. Last, the E- field direction is reversed, to isolate the effect due to the EDM. A succession of experiments over decades has sought to detect an EDM in a paramagnetic system. These experiments are usually interpreted in terms of the eEDM. In the past decade, revolutionary advances in sensitivity have been made by embedding electrons inside polar molecules, where the intramolecular E-field acting on the EDM can be roughly a thousand times larger than in other systems. The most sensitive eEDM experiment to date, known as ACME, is featured in Box 6.2. Electron EDM results from ACME and other experiments with Tl, YbF, and HfF+ molecular ions are shown in Figure 6.6. The future reach of eEDM experiments, and constraints on new physics theories, are PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-16

shown. New experiments are under way or planned with ACME and with HfF+, and by incorporating laser cooling and/or trapping in experiments with YbF and other molecular species. //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// BOX 6.2 The ACME Search for the Electron’s Electric Dipole Moment To search for the eEDM, ACME uses electrons in ThO molecules. In addition to an extremely large intramolecular E-field, ThO has many advantageous properties. The structure of its energy levels makes it possible to easily reverse its internal E-field, not only by reversing the laboratory field that polarizes the molecules but also by preparing different internal quantum states. ThO also hold two electrons with unpaired spins: one feels a particularly large internal E-field while the other serves to cancel the magnetic moment of the first. These properties make it possible to reject many potentially large errors that could mimic the EDM signal. In ACME, a cryogenically cooled beam of ThO is prepared and interrogated by a suite of tunable lasers. Detection is achieved by measuring fluorescence, whose intensity depends on the angle between the final electron spin and the laser polarization. This method has yielded statistics sufficient for a factor of 100 improved sensitivity to the EDM over the past decade. While no EDM has been observed yet, ACME places an upper bound on its size at |de| < 1.1 × 10-29e cm with 90 percent confidence, where e is the elementary charge. It also sets the best limit on one type of T-violating electron-nucleon interaction. This sensitivity is sufficient to have detected the existence of particles with T-violating interactions, whose rest mass energy is as high as 3, 50, or even 100 TeV (depending on the specific theoretical model). In many cases, this far exceeds the range of particle masses that can be produced directly at CERN’s Large Hadron Collider. The scale of ACME is larger than most AMO-based experiments, although it is still tiny compared to particle colliders: it fits in two laboratory rooms on a university campus, and is performed by a small team of faculty, students, and postdocs. This small collaboration of a dozen or so scientists has enabled unusually rapid progress in bounding the eEDM, combined with unprecedented understanding and control of possible systematic errors. A new generation of ACME is being developed, with the aim of another order of magnitude increase in sensitivity within a few years. END OF BOX///////////////////////////////////////////////////////////////////////////////////////////////////////////////////// PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-17

FIGURE 6.6 Searching for new fundamental particles via the electron’s electric dipole moment (eEDM). The horizontal axis shows possible values for the eEDM; gray regions show how limits have improved in the past 30 years, with the year of the experiment shown on the vertical axis. Colored regions are predictions from various theories of particle physics. The standard model of particle theory predicts a value ~9 orders of magnitude smaller than the current best bound from the ACME experiment. However, many theories that include new particles naturally predict an EDM within reach of ongoing or proposed experiments (hatched region). Note that theoretical predictions (colored regions) have evolved (green regions) in response to the absence of new particles detected at the Large Hadron Collider (LHC), direct dark matter searches, and EDM experiments. AMO-based searches for EDMs are one of the few known methods to detect evidence of new particles whose mass exceeds the reach of the LHC, within the next 1- 2 decades. SOURCE: David DeMille, Yale University. The atomic 199Hg EDM search is the most sensitive EDM experiment with a diamagnetic system. 199 Hg has closed electron shells with zero electronic spin, but a nonzero nuclear spin I=1/2; therefore, its EDM must point along the nuclear spin axis. The 199Hg experiment sets a limit on the neutron EDM, dn < 1.6 × 10−26 e cm, which is more stringent by a factor of 2 than the best limit from direct measurements with free neutrons. It also sets the best limits on certain T-violating interactions between quarks inside the nucleus, and between electrons and the nucleus. Other experiments with diamagnetic systems have been carried out with 129Xe and 225Ra atoms, and 205TlF molecules; these provide important constraints on the multitude of underlying T-violating interactions that could lead to EDMs in diamagnetic systems. Large enhancements of the observable diamagnetic EDM signatures are found in polar molecules such as TlF or deformed nuclei such as 225Ra. Experiments based on these systems hold promise to increase the energy reach for probing new T-violating physics by an order of magnitude or more in the near future. For example, a new experiment (CeNTREX) is being constructed to improve the diamagnetic EDM limits PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-18

using a cryogenic beam of TlF molecules, while 225Ra experiment is also being upgraded to further advance its sensitivity. It is entirely plausible that EDM experiments, using AMO methods and room-scale apparatus, could provide the first new evidence for physics beyond the Standard Model. This would be a revolutionary discovery in particle physics, and would establish a clear benchmark for the energy needed to produce new particles in any future particle collider. Dark Matter, Variation of Fundamental Constants, and Fifth Force Searches The nature of dark matter (DM) is one of the most outstanding puzzles in physics today. To date, experimental efforts to detect DM have largely focused on weakly interacting massive particles (WIMPs), with masses between 10 and 1,000 GeV, and has required detectors in deep underground laboratories. Despite decades of significant effort, and rapid improvements of experimental sensitivities in recent years, no conclusive signs of WIMPs have been observed. While the WIMP is theoretically well motivated, many other DM candidates inhabit a vast parameter space, all the way down to 10−24 eV, ranging from ultralight axions and axion-like particles, to more complex dark sectors that lead to composite DM “clumps.” While particle detectors work by measuring energy deposition, precision measurement techniques are well suited for detecting light mass DM candidates that act as coherent entities on the scale of individual detectors or their networks. Recent advances in optical and atom interferometry, magnetometry, and atomic clocks have stimulated a plethora of new experimental proposals for DM searches with table-top precision experiments on Earth’s surface rather than underground. The key idea behind these proposals is that light DM particles have large mode occupation numbers and exhibit coherence, behaving like a wave. (DM candidates in this light mass range have to be bosonic, as the Fermi velocity exceeds the galactic escape velocity for such DM.) Many such light (below ~1eV) DM candidates have been proposed, and their effects on SM particles include the following: 1. Cause precession of nuclear and electron spins; 2. Drive currents in electromagnetic systems; 3. Induce equivalence principle-violating accelerations of matter; and 4. Modulate the values of the fundamental constants of nature, inducing changes in atomic transition frequencies and the local gravitational field. As a result, all of the AMO precision tools discussed in this chapter—atomic clocks, interferometers, and magnetometers—can be used as DM detectors. The experiments are guided by clues from other fields of physics, suggesting mysteries that can be solved by introducing new DM candidates with particular properties. Searching for the theoretically best motivated light DM candidates gives the highest discovery potential. SM extensions offer a plenitude of ultralight DM candidates characterized by their spin and intrinsic parity (scalar, pseudoscalar, vector, and axial vector). The axion (pseudoscalar) is among the most well- motivated light mass DM candidates. It was introduced in quantum chromodynamics (QCD, a quantum field theory of the strong interactions between quarks, mediated by gluons) to solve the so-called strong CP problem: according to formulation of QCD the CP-violation should occur in the strong interactions but it is not observed as shown by the lack of EDMs in diamagnetic atoms and neutrons. Axions can couple to electromagnetism, can induce EDMs for nucleons via interaction with the gluon field, and can cause precession of electron and nucleon spins. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-19

Axion and Axion-like Particle Searches Pseudoscalar particles such as axions and axion-like particles (ALPs) can be produced by the interaction of two photons via a process known as the Primakoff effect. This process can go in either direction, i.e., in reverse an axion or ALP in a magnetic field can produce a photon (i.e., one of the two photons is supplied by the magnetic field). The ADMX experiment exploits the strong coupling of the QCD axion to the electromagnetic field in a microwave cavity, to convert axions to microwave photons in the presence of a strong magnetic field. The resonant frequency of the cavity can be tuned so that it matches the frequency of the microwave photons produced by this interaction. A new experiment, HAYSTAC, which extends the ADMX experiment to search for higher mass axions, using correspondingly higher frequency microwave cavities, has recently reported first results. Another major microwave cavity experimental program is under way in South Korea. A new broadband axion DM experiment, MADMAX, based on axion-photon conversion at the transition between different dielectric media, is under development in Germany. A new experiment is now under way to search for lighter QCD axions and ALPs using different couplings from those exploited in ADMX/HAYSTAC, complementing these searches. The cosmic axion spin precession experiment (CASPEr) exploits both the axion-gluon coupling, which generates oscillating EDMs of nuclei (CASPEr electric), and the coupling of the axion to nuclear spins (CASPEr wind). CASPEr uses nuclear magnetic resonance (NMR) techniques for detecting spin precession caused by background axion DM. CASPEr electric has the potential to reach sensitivity to QCD axions over a five orders of magnitude in mass range (all well below ADMX), and search a significant fraction of unexplored parameter space for ALPs up to masses of ≈10−7 eV. The aim of the axion resonant interaction detection experiment (ARIADNE), is to use NMR techniques to detect new interactions that can be caused by axions (see the “Fifth Force Searches” section below). The upper end of the axion mass range to be explored by ARIADNE is particularly difficult for all other DM detection experiments to access, and so ARIADNE has the potential to fill an important gap in the axion parameter space. Spin-1 DM particles are commonly referred to as dark or hidden photons. Hidden-photon DM can be described as a weakly coupled “hidden electric field,” oscillating at the hidden-photon Compton frequency (determined by its mass). It was recently proposed that both hidden photons and axion/ALPs can be searched for using tunable, resonant LC circuits. Proposals for broadband detection with LC circuits are based on the axion-photon coupling that effectively modifies Maxwell’s equations—dark matter axions and ALPs generate an oscillating current density in the presence of a magnetic field. In some new physics models, the initial random distribution of the scalar field in the early universe leads to the formation of domain-wall networks as the universe expands and cools. This and other mechanisms can lead to “clumpy” DM objects. The “global network of optical magnetometers to search for exotic physics” (GNOME) collaboration is searching for transient signals due to the passage of Earth through compact DM objects, such as these domain walls or DM “stars,” that couple to atomic spins (similar to the ALP wind coupling searched for by CASPEr). While a single magnetometer system could detect such transient events, effective vetoing of false positive events requires an array of magnetometers. Variation of Fundamental Constants and Dark Matter Searches with Clocks A fundamental constant is determined experimentally and cannot be predicted by current theories. The fine-structure constant α, which characterizes the strength of the electromagnetic interaction between elementary particles, and the ratio of proton and electron masses μ = mp/me, are examples of such fundamental constants. While the very definition of the label “constants” implies that these are fixed quantities, many proposed theories beyond the SM predict that they vary in time and space. As noted above, light DM can be the source of the variation of fundamental constants. If the fundamental constants are space-time dependent, so are atomic and molecular spectra, allowing one to probe their variations PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-20

from the present day to a distant past by observing light from very distance sources. Studies of quasar absorption spectra indicate that the fine-structure constant may vary on a cosmological space-time scale, but this result is controversial. The variation of the fundamental constants would also change the atomic clock tick rate, with the degree of variation depending on the atomic species of the clock. Therefore, monitoring ratios of clock frequencies over time allows one to test the constancy of fundamental constants in the laboratory. This effort has been pursued by many metrology laboratories. The combined world limits to the variation of α and μ are given in the Figure 6.7. FIGURE 6.7 Constraints on temporal variations of the fine-structure constant α and μ (proton-to-electron mass ratio) from comparisons of atomic transition frequencies. Filled stripes mark the 1 standard deviation σ uncertainty regions of individual measurements, and the central blank region is bounded by the standard uncertainty ellipse resulting from the combination of all data. SOURCE: Reprinted figure with permission from N. Huntemann, B. Lipphardt, Chr. Tamm, V. Gerginov, S. Weyers, and E. Peik, Improved limit on a temporal variation of mp/me from comparisons of Yb+ and Cs atomic clocks, Physical Review Letters 113:210802, 2014, https://doi.org/10.1103/PhysRevLett.113.210802; copyright 2014 by the American Physical Society. The atomic clock searches initially focused on the “slow-drift” model of fundamental constant variation. Recently, it was shown that ultralight scalar dark matter can cause oscillatory and transient variation of fundamental constants, leading to new directions of such clock-comparison experiments. As noted above, such light mass DM permeating our Galaxy exhibits coherence, behaving like a wave. Its coupling to the Standard Model particles in atomic clocks leads to oscillations of fundamental constants and, therefore, to oscillations in clock transition frequencies, causing persistent time-varying signals that are localized in frequency determined by the DM mass. Such an oscillation signal would be detectable with atomic clocks for a large range of DM masses and interaction strengths, but would be too faint to probe with any other devices. To detect these oscillating signals, one performs measurements of ratios of clock frequencies, with minimum dead time, continuing measurements while the dark matter field remains coherent. Transforming the results of the time sequence measurements into the frequency domain allows one to extract the dark matter signal, or set limits on DM masses and interaction strengths. The first dedicated searches for such oscillating effects are ongoing in several clock laboratories. In addition to the oscillatory changes, transient changes in fundamental constants may be induced by dark matter objects with large spatial extent, such as stable topological defects. Such transient signals can be observed by networks of clocks, manifesting as “glitches” propagating through the clock network. The first constraints on the coupling of such DM to Standard Model particles was just reported with the first Earth-scale quantum sensor network based on optical atomic clocks aimed at DM detection. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-21

Fifth Force Searches Presently, we know of four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak force. These forces are characterized by their range and by their particular coupling to matter and fields. Remarkable advances in AMO measurement techniques over the last decade, coupled with new ideas emerging from theoretical particle physics, have reinvigorated AMO precision searches for forces beyond these four. For example, DM may have new interactions, whose discovery would lead to a much wider range of possible experiments for detection of the DM. An example is the ARIADNE experiment mentioned above. It is entirely possible that sufficiently feeble forces have escaped detection up to this point, and would be impossible to find with collider experiments. Startling discoveries are sometimes hiding just beyond the horizon of our measurement capability. If a new force exists, how might it affect atoms and molecules? A way to answer this question is by quantifying all possible new forces between electrons, protons, and neutrons by “exotic physics coupling constants,” establishing a common framework for interpreting different types of experiments. In this methodology, an experiment searches for a new force; if no signal is detected one establishes a constraint on one or more of the coupling constants for a length scale relevant to this experiment. In other words, experimentalists explore new regions of “coupling constant vs. length scale” parameter space to determine if new forces exist, and particle theorists can interpret these results in terms of specific theories. Nearly all of the AMO community’s most sophisticated experimental tools have been applied to precision searches for new forces, and have pushed the frontier of knowledge by many orders of magnitude in both coupling strength and range:  Precision spectroscopy of atoms and molecules has constrained new atomic- and molecular- scale forces, including between matter and antimatter.  Measurements using NV centers in diamond have constrained new forces between electrons.  State-of-the-art atomic magnetometers have constrained a wide variety of spin-dependent forces over ranges between a cm to the radius of Earth.  Atom interferometry has been used to search for new forces related to possible explanations of dark energy.  Experiments with trapped and cooled atoms and ions have used quantum entanglement to constrain new forces between electrons.  Torsion balances and cantilevers have proven to be some of the most sensitive tools with which to search both for new forces and violations of Einstein’s equivalence principle. There are a variety of exciting new experimental methods in development that promise to explore a far more extensive range of parameter space: novel NMR techniques, state-of-the-art optical atomic clocks, and opto-mechanical experiments with micron-scale objects, such as trapped and cooled microspheres and ferromagnetic needles. These all promise orders-of-magnitude improvement in sensitivity to new forces. These are but a few examples of the wide variety of creative experiments in this vibrant field of research. Developments in the next decade offer the possibility of not only more stringent constraints on new forces, but also, perhaps, revolutionary discoveries. Dark Matter and New Force Searches with Future Gravitational Wave Detectors Proposed atom interferometric GW detectors are sensitive to new physics which perturbs atomic trajectories or an atom’s internal energy levels. For example, DM can lead to time-dependent signals in these detectors, enabling a unique probe of its existence. In particular, these time-dependent signals can be caused by ultralight DM candidates. Well-motivated theories indicate that the mass range from 10-22 eV to 10-3 eV is particularly interesting, and atom interferometry is a promising approach for searches at PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-22

the lowest part of this mass range. Potential dark matter candidates within this range include the relaxions, which are particularly interesting since they appear in a recently suggested alternative solution of the hierarchy problem (via dynamical relaxation), without introducing any new physics at the TeV scale that LHC could have observed. In addition to these DM searches, new fundamental particles may also be discovered by searching for new forces as described above. These new forces can be sourced by Earth, and if they are sufficiently long range, they may lead to differential free-fall accelerations between different elements/isotopes. A comparison between atomic sensors made out of different elements/isotopes could reveal the existence of such forces, which in MAGIS-100 can be realized by comparing two co-falling isotopes of Sr. Parity Violation—AMO Tests of Weak Interaction Parity symmetry, P, changes the sign of the position vector, which corresponds to mirror reflection and 180-degree rotation. While electrodynamics is invariant under parity transformation, the weak interactions are not. At first glance, it would appear impossible to observe such a small effect in atoms, resulting from weak interactions between the atomic constituents. However, it was realized that parity violation effects are enhanced in heavy atoms as the nuclear charge cubed, leading to a series of atomic parity violation experiments in heavy atoms. Parity violation in atoms leads to a nonzero amplitude for atomic transitions otherwise forbidden by parity selection rules—for example, between the 6s and 7s states in cesium, which are of the same parity. The goals of high-precision atomic parity violation (APV) studies are to search for new physics beyond the SM by accurate determination of the “weak charge,” to compare it with SM predictions, and to probe hadronic parity violation. APV is also uniquely sensitive to some dark matter candidates. The analysis of a Cs APV experiment, made possible by recent advances in high-precision theory, provided the most accurate to-date test of the low-energy electroweak sector of the SM, and constrained a variety of scenarios for physics beyond the SM. Combined with the results of high-energy, large-scale collider experiments, Cs APV studies confirmed the 3 percent dependence of the electroweak force on the momentum transfer over an energy range spanning four orders of magnitude, as illustrated by Figure 6.8. The limits on extra TeV-scale Z bosons set by APV in 2009 were only recently improved upon at the LHC. APV is also uniquely sensitive to some DM models, and sets limits on a possible 50 MeV dark boson shown in Figure 6.8. The Cs experiment was also used to probe weak hadronic interactions. This analysis yielded values of weak meson-nucleon couplings in disagreement with nuclear physics constraints, but was complicated by the difficulty of the required nuclear calculations. More experiments on other atoms or molecules are required to solve this long-standing puzzle. Experiments with Yb (Mainz, Germany, already reported first results), Dy (also Mainz), Ra+ (Santa Barbara), Cs (Purdue), Fr (TRIUMF, Vancouver), and molecules (Yale) are currently under way. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-23

FIGURE 6.8 Running of the weak mixing angle (quantifying the electroweak force) with momentum transfer Q. The solid red curve is the SM prediction. The table-top Cs APV result is supplemented with data from large-scale particle physics experiments whose data points are labelled. The colored area comes from one of the “new physics” scenarios: a dark boson of mass 50 MeV. SOURCE: Reprinted figure with permission from M.S. Safronova, D. Budker, D. DeMille, D.F. Jackson Kimball, A. Derevianko, and C.W. Clark, Search for new physics with atoms and molecules, Reviews of Modern Physics 90:025008, 2018, https://doi.org/10.1103/RevModPhys.90.025008; copyright 2018 by the American Physical Society, which was adapted from H. Davoudiasl, H.-S. Lee, and W.J. Marciano, Muon g – 2, rare kaon decays, and parity violation from dark bosons, Physical Review D 89:095006, 2014. Testing Quantum Electrodynamics—The Most Precise Test of Any Physical Theory to Date Quantum electrodynamics (QED) is a quantum field theory that describes electromagnetic interactions. Precision tests of QED are carried out by comparing experimental results with theoretical predictions, with truly exceptional precision reached by both theory and experiment. There have been numerous achievements in QED tests of free particle properties such as the anomalous magnetic moment of the electron, and of bound-state QED properties such as the Lamb shift. The bound tests encompass a wide variety of simple atoms and molecules, molecular ions, highly charged ions, and exotic atoms such as positronium, antiprotonic He, and so on. Only a few examples are highlighted. Measurement of the Fine-Structure Constant The fine-structure constant α, which determines the strength of the electromagnetic interaction between elementary particles, enters as an expansion parameter in QED. At present, there are two extremely accurate determinations of α. One measurement involves determination of the electron magnetic-moment anomaly ae (i.e., deviation from the free-electron Dirac equation value of ae = 0) carried out with a single electron that was suspended for months at a time in a cylindrical Penning trap. The ratio of electron spin-flip frequency to the cyclotron frequency in the trap determines ae. The resulting value of α, obtained by combining the experimental results with theoretical calculations including QED to the fifth order (involving >10,000 Feynman diagrams), with muonic and hadronic effects, is α =1/137.035 999 084(51) at 3.7 × 10−10 accuracy. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-24

Using a completely different method, the value of α is also obtained from a precision measurement of the ratio of the Planck constant h to the mass of an atom M using atoms in a matter-wave interferometer, measuring the recoil kinetic energy transferred to or from an atom after scattering a photon. The most precise such experiment was carried out with a cloud of Cs atoms, yielding 1/α = 1/137.035 999 046(27) at 2.0 × 10−10 accuracy. This value does not depend on QED calculations, and the agreement between the two experiments both validates the theoretical QED calculation of ae in terms of α and provides the most accurate test of quantum electrodynamics (and any physical theory) to date. Work to improve both of the experiments by an order of magnitude is under way. These measurements can also be used to probe a possible substructure within the electron, and search for potential new dark matter particles. The Proton Radius Puzzle The root mean square (r.m.s.) charge radius of the proton can be extracted from the atomic hydrogen spectrum, with the help of QED calculations, and from electron scattering experiments. A different type of experiment, using the spectroscopy measurement of muonic hydrogen (which has the atom’s electron replaced by the 207 times heavier muon) was intended to improve upon these measurements. Instead, it led to the proton radius puzzle: the highly precise rp = 0.84087(39) fm extracted from the 2S-2P Lamb shift in muonic hydrogen is in significant disagreement with the result rp = 0.8758(77) fm deduced from spectroscopy with ordinary hydrogen and the electron scattering experiments. This discrepancy has prompted speculations that it may hint at new physics. Two further hydrogen spectroscopy measurements that were intended to unravel this mystery exacerbated it further, one yielding the proton radius value in agreement with the muonic hydrogen result and another supporting the previous hydrogen results. More measurements are in progress to resolve this perplexing puzzle. Precision Tests of Fundamental Interactions and Determination of Fundamental Constants Using Highly Charged Ions The comparison of experimental measurements with SM theory calculations for the magnetic moment or g-factor of the bound electron in hydrogen-like ions allows further tests of QED. In this vein, the most accurate value of the electron mass, with a relative precision at the 10‑11 level, is obtained by a comparison of state-of-the-art bound-state QED calculations and precise measurements of the g-factor of the single bound electron in a trapped 12C5+ ion, done at Mainz (Figure 6.9). FIGURE 6.9 A simplified sketch of a highly charged ion in a Penning trap (cut-away view). A determination of the magnetic moment (g-factor) of the bound electron allows for stringent tests of quantum electrodynamics in strong fields, as well as for the determination of fundamental constants like the mass of the electron or the fine structure constant α. SOURCE: Courtesy of Sven Sturm. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-25

Highly charged ions allow to test bound-state QED in the strong-field regime (Zα close to unity, with Z being the nuclear charge), explored by X-ray spectroscopy for Lamb-shift measurements, by laser spectroscopy for hyperfine and fine structure, and by microwave spectroscopy of magnetic substates for bound-electron g-factor determinations. These experiments are carried out by removing most of the electrons from a heavy atom to achieve a strong-field regime. A careful comparison of results from ions in different charge states would allow for disentangling nuclear structure and QED effects to a high degree. The highest accuracy is reached with cooled highly charged ions stored in precision traps from electron-beam ion trap (EBIT) sources, or from accelerator facilities such as the ESR heavy ion storage ring at the GSI accelerator facility in Germany. There is a competitive new experimental effort to measure the fine-structure constant as well as nuclear and isotopic effects, based on extracting heavy highly charged ions up to hydrogen-like lead 208 Pb81+ from the EBIT and injecting them into the ALPHATRAP Penning-trap setup. This way, unique measurements become feasible, such as the determination of the isotopic effect in heavy highly charged ions, which gives direct and unobstructed access to nuclear effects, as well as the measurement of specifically weighted g-factor differences of hydrogen- and lithium-like heavy HCI. The latter allows cancelling nuclear effects and testing QED to high precision, as well as further pinning down of the fine structure constant. We note the need to develop competitive HCI experiments in the United States, with many opportunities provided by new developments in the control of HCIs. Tests of CPT and Lorentz Symmetry Tests of CPT Current laws of physics are believed to be invariant under CPT (the combined charge-parity-time) inversion, but symmetry breaking may arise in physics beyond the SM, such as in string theories. CPT invariance ensures the same magnetic moments and masses of particles and their corresponding antiparticles; comparisons of particle/antiparticle properties tests CPT symmetry. There has been recent breakthrough progress in these tests: The ALPHA experiment at CERN performed a laser-spectroscopic measurement of the 1S-2S transition frequency of antihydrogen, which was a long-standing goal of the antihydrogen experiments. Comparison of this result with the 1S-2S frequency in ordinary hydrogen provided a test of CPT invariance at a relative precision of 2 ×10−10. An observation of the hyperfine spectrum of antihydrogen was also reported. The Baryon-Antibaryon Symmetry Experiment (BASE) reported exceptionally precise, part per billion, comparisons of antiproton and proton magnetic moments, with single trapped particles, using an advanced cryogenic multi-Penning trap system. In the future, the BASE collaboration proposes to use quantum-logic techniques to further advance CPT tests, by sympathetically cooling and probing the (anti)proton using a coupling to an atomic “qubit” ion trapped in its vicinity via the Coulomb interaction. This technique has the potential to enable proton and antiproton magnetic moment measurements at the parts per trillion level. The very recent CPT tests described above mark a turning point from proof-of- principle experiments to high-precision metrology CPT comparisons, with prospects for significant improvements in the near future. Tests of Lorentz Symmetry Local Lorentz invariance (LLI) is a cornerstone of modern physics. It tells us that the outcome of any local nongravitational experiment is independent of the orientation and the velocity of the (freely falling) apparatus. AMO experiments may be interpreted as Lorentz-invariance tests for the photon, electron, proton, and neutron, and their combinations, with photon contributions appearing in all atomic experiments. Atomic LLI Violation (LV) experiments in the electron-photon sector exploit the different sensitivity of various energy levels to the hypothetical Lorentz violation. The quantization axis is set by PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-26

the direction of the magnetic field, and the energy difference of two atomic levels with different LV sensitivities is monitored during Earth’s rotation and motion around the Sun. In 2015, an experiment with 40 Ca+ trapped ions demonstrated the use of quantum information techniques (a decoherence-free subspace of a two-ion superposition) to minimize the noise due to magnetic field fluctuations, improving previous limits by a factor of 100 (Figure 6.10). In 2018, an experiment with two ytterbium (Yb) ions clocks improved that result by another factor of 100. Once again, precision measurement tools, specifically quantum-information-based sensors, demonstrate the remarkable potential to test fundamental physics postulates. The best tests of LLI for nucleons or photons were carried out with Cs clocks, atomic magnetometers, and rotating optical and microwave resonators. FIGURE 6.10 40Ca+ LV experiment. As Earth rotates, the orientation of the magnetic field and, consequently, that of the electron wave packet (as shown in the inset in terms of probability envelopes) changes with respect to the Sun’s rest frame. The states of the superposition are affected differently by the potential LLI violation, resulting in phase evolution of the wave packet with Earth rotation. SOURCE: Reprinted by permission from Springer Nature: T. Pruttivarasin, M. Ramm, S.G. Porsev, I.I. Tupitsyn, M.S. Safronova, M.A. Hohensee, and H. Häffner, Michelson–Morley analogue for electrons using trapped ions to test Lorentz symmetry, Nature 517:592-595, 2015, https://doi.org/10.1038/nature14091. FUNDAMENTAL CONSTANTS AND MEASUREMENT STANDARDS AMO methods feature centrally in defining with the greatest precision possible quantities that are of enormous technical and economic importance, such as units of distance (the meter), of time (the second), and mass (the kilogram). On November 16, 2018, the 26th meeting of the General Conference of Weights and Measures consisting of 59 member states unanimously voted to redefine the International System of Units (SI) to be based on exactly defined values of fundamental constants and invariants of nature as described in Box 6.3. The new SI officially went into effect on World Metrology Day, May 20, 2019, which means that now anyone, anywhere can realize the SI units in terms of these values combined with appropriate measurements and equations derived from the laws of nature as we presently understand them. ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// BOX 6.3 The Redefinition of the SI Units PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-27

The redefinition of the SI units was made possible through the ability to relate two independent experimental methods at the required accuracy and consistency; these are combined in the new SI to realize the kilogram. One method uses the determination of the Planck constant via a Kibble balance (see Figure 6.3.1), and the other uses the determination of the Avogadro constant via the X-ray crystal density method. The required comparison of these totally different methods was achievable only through the improved experimental tools and techniques of AMO physics that enable the precise determination of the fine structure constant, the Rydberg constant, and the mass of the electron. For example, improvements in atomic recoil measurements using Raman transitions and Bloch oscillations in optical lattices, Penning trapping techniques, quantum jump spectroscopy, quantum nondemolition coupling measurements, and higher order calculations of QED theory have led to a reduction of the fine structure constant uncertainty by two orders of magnitude over the past 30 years. Today, these and other newly developed techniques, and the more accurate values of the fundamental constants provided by the new SI, are being used to further advance our understanding of the physical world. This includes the investigation of inconsistent results, such as the proton radius puzzle and the determination of the muon magnetic anomaly. FIGURE 6.3.1 The NIST-4 Kibble balance, where the weight of a test mass is offset by a force produced when an electrical current is run through a coil of wire immersed in a surrounding magnetic field. As of May 20, 2019, it uses the defining fundamental constants that form the foundation of the International System of Units (SI) to realize the kilogram. The science team consists of, from left to right in front, Frank Seifert, David Newell, Jon Pratt, Darine Haddad, and Shisong Li. In back, Stephan Schlamminger (left) and Leon Chao (right). SOURCE: National Institute of Standards and Technology, “Watt Balance Team,” https://www.nist.gov/image/wattbalancegroupapril2016-2500pxresizedjpg; courtesy of J. Lee/NIST. END OF BOX////////////////////////////////////////////////////////////////////////////////////////// PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-28

SUMMARY, DISCOVERY POTENTIAL, AND GRAND CHALLENGES Summary The last decade brought forth a plethora of new table-top AMO experiments aimed at discovery of new physics. While this field existed in the past, the scale of the effort and discovery potential increased so dramatically that it is considered a new emergent interdisciplinary field. This progress is expected to accelerate in the next decade, with the development of new technologies and plentiful ideas for new searches. There are several important factors leading these new developments, including the following: 1. Exceptional, by many orders of magnitude, improvement in the development of AMO tools, such as atomic clocks, matter-wave interferometers, magnetometers, cold molecules, and so on. In many cases, completely new measurement technologies have been developed—for example, development of optical (in place of microwave) clocks, nitrogen vacancy centers in diamond for magnetic field measurements, atomic interferometers for many types of precision measurements, gravitational wave detectors, and so on. 2. Advances in quantum information and related technologies led to improved control of quantum systems, and enabled techniques to protect from some kinds of measurement noise, allowing one to measure at or beyond the standard quantum noise limit. 3. Significant AMO theory advances now allow rapid predictions of systems with the highest sensitivity to perform the most sensitive new physics searches, and to analyze these experiments. The theory also predicts the unknown properties needed for detailed experimental proposals, allowing one to save years of experimental work. 4. Rapid progress of dedicated AMO precision experiments—for example ACME—improved eEDM limits by two orders of magnitude, probing new physics at 3-30 TeV. This is beyond the LHC’s reach. Many orders of magnitude improvement were recently demonstrated in many other new physics searches described in this chapter, including dark matter searches. 5. The absence of new “beyond-the-Standard-Model” particles being discovered at the LHC strongly restricted the parameter space of supersymmetry and other theories that expect TeV scale physics. These theories had been exceptionally promising since they provided solutions to several outstanding problems: new sources of CP violation, dark matter candidates, and solving the hierarchy problem. Similarly, the large-scale detectors for Weakly Interacting Massive Particles (WIMPs) failed to detect them after decades of effort. With lack of experimental confirmation well within the expected mass range, the possibility that supersymmetric particles/WIMPs do not exist at the few TeV scale requires pursuing other solutions to the outstanding fundamental problems. This led to a plethora of new ideas, in particular in the area of dark matter searches, many of which can be realized only in AMO table-top experiments. The possibility that there is no new physics up to the 100 TeV scale is also now considered, in which case no new particles could be detected by future colliders that can be potentially built in this century. This gives increased importance to AMO experiments probing physics at the very-high-energy scale via low-energy signals. 6. The discovery of gravitational waves from merging black holes and neutron stars using terrestrial laser interferometers has provided new opportunities for understanding the internal properties and cosmic populations of these objects. The potential for discovering new, unknown gravitational wave sources, and ultimately mapping out the gravitational wave sky over many wavelengths, is driving the design of novel next-generation gravitational wave detectors that include laser interferometers as well as atomic sensors. It is also possible that violations of general relativity may be discovered from these gravitational wave sources, possibly providing insights into a quantum theory of gravity. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-29

Discovery Potential AMO searches for new physics can probe physics not accessible by colliders and other high-energy technologies. For example, search for EDMs can potentially probe physics at the 100 TeV scale, well beyond the collider-accessible energy range. Searches for violation of Lorentz invariance, CPT violation, and so on, probe physics at much higher scales. Light mass (below 1 eV) dark matter candidates have to be probed at low energies. The committee strongly emphasizes that most AMO experiments are table-top, and are by far less expensive than conventional high-energy searches, leading to plethora of new physics ideas that can be explored at the same time. Considering the discovery potential of these AMO experiments, they provide a highly competitive and cost-effective pathway toward the discovery of new physics. Grand Challenges 1. Development of new measurement approaches and tools in the framework of quantum- information science, specifically aimed at new physics searches in the other grand challenges. 2. Discovery of EDMs, or definitive ruling out of EDMs, at the levels predicted by new physics theories. This would be a revolutionary discovery in particle physics, and would establish a clear benchmark for the energy needed to produce new particles in any future particle collider. 3. Detection of dark matter. Fully utilize the capability of precision AMO experiments (clocks, interferometers, magnetometers, and other AMO tools) to directly detect dark matter or corresponding new force signals. One specific goal is to either detect or rule out the QCD axion in the entire allowable mass range. 4. Detection of new physics signals arising from a much higher energy scale, one not accessible by foreseeable future colliders. Pursue order-of-magnitude improvements in searches for variation of fundamental constants, violations of Lorentz symmetry, of the equivalence principle, of CPT invariance, and other such tests, as well as provide much improved tests of QED. 5. Develop advanced technologies for laser interferometer gravitational wave detectors that have the sensitivity to map out the visible universe. At the same time, demonstrate promising alternative technologies for the use of atomic sensors to probe gravitational physics, including proof of principle large-scale systems for gravitational wave detection. Findings and Recommendations Finding: Rapid advances in the precision and capabilities of AMO technologies have dramatically increased the potential of AMO-based techniques to discover new physics beyond the standard model. The present lack of a federal funding program dedicated specifically to supporting such research at the intersection of high -energy physics and AMO is a limiting factor in fully utilizing the plethora of opportunities for new discoveries. Finding: Supporting and promoting much stronger joint efforts between AMO physics, particle physics, gravitational physics, astrophysics, and cosmology is necessary to promote creative ideas and new opportunities for grand challenge discoveries with AMO-based science. Finding: The United States is falling behind in deploying a diverse set of AMO precision measurement platforms and integrating tools into dedicated devices to maximize discovery potential. Finding: International collaborations are needed for full realization of AMO-based science discovery potential. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-30

Key Recommendation: The Department of Energy’s High-Energy Physics, Nuclear Physics, and Basic Energy Sciences programs should fund research on quantum sensing and beyond- the-standard-model fundamental physics questions through atomic, molecular, and optical science-based projects. Recommendation: Federal funding agencies should modify funding structures to allow for theoretical and experimental collaborations aimed at atomic, molecular, and optical science- based searches for new physics and development of diverse set of atomic, molecular, and optical precision measurement platforms including larger (more than five principal investigators) and long-term (10-year) projects. Recommendation: Funding agencies should establish funding structures for continued support for collaborative efforts of atomic, molecular, and optical theory and experiment with particle physics and other fields, including joint projects, joint summer schools, dedicated annual conferences, and so on. Recommendation: U.S. federal agencies should establish mechanisms to co-fund international collaborations in precision searches for new physics with other worldwide funding agencies. PREPUBLICATION COPY – SUBJECT TO FURTHER EDITORIAL CORRECTION 6-31

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The field of atomic, molecular, and optical (AMO) science underpins many technologies and continues to progress at an exciting pace for both scientific discoveries and technological innovations. AMO physics studies the fundamental building blocks of functioning matter to help advance the understanding of the universe. It is a foundational discipline within the physical sciences, relating to atoms and their constituents, to molecules, and to light at the quantum level. AMO physics combines fundamental research with practical application, coupling fundamental scientific discovery to rapidly evolving technological advances, innovation and commercialization. Due to the wide-reaching intellectual, societal, and economical impact of AMO, it is important to review recent advances and future opportunities in AMO physics.

Manipulating Quantum Systems: An Assessment of Atomic, Molecular, and Optical Physics in the United States assesses opportunities in AMO science and technology over the coming decade. Key topics in this report include tools made of light; emerging phenomena from few- to many-body systems; the foundations of quantum information science and technologies; quantum dynamics in the time and frequency domains; precision and the nature of the universe, and the broader impact of AMO science.

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