FIGURE B.1 Ground-state energy levels of atomic hydrogen as a function of magnetic H′. The transition used for the frequency standard is (0,0) – (1,0), which depends on magnetic field only in second order.

relaxation time from an excited state depends on the atomic structure and the energy of the state and varies from nanoseconds for moderate state energies and highly allowed transitions to seconds for what are called forbidden transitions. These transitions are in the optical, infrared, and ultraviolet ranges. Those with long relaxation times are useful for isolated atom optical frequency standards. The frequency linewidth Δv associated with a transition is of the order 1/(πT), where T is the relaxation time.

The relaxation time for transitions between ground-state levels is typically years for isolated atoms, so the relaxation can be neglected for isolated atom microwave standards. However, in gas cell microwave standards or other standards in which atomic collisions occur, collisions shorten the relaxation time and determine the linewidth. In isolated atom microwave standards, the linewidth is roughly proportional to the reciprocal of the interaction time of the electromagnetic field with the atoms. This can be understood from Fourier transform relationships.

The quality factor of a resonance is Ql= v/Δvl, where Δvl is the linewidth determined by collisions, interaction time, or the natural linewidth, whichever gives the largest linewidth. The achievable accuracy (small numbers are desired here) of an isolated atom frequency standard (essentially no collisions) is proportional to 1/Ql, so a high-frequency v and a small-linewidth Δvl are desired. This is what makes the optical standards attractive. Their accuracy can be orders of magnitude better than microwave standards.

With regard to the interaction with the electromagnetic field, atomic transitions to a higher energy state absorb a quantum of energy hv, called a photon, from the field. Transitions to a lower energy state add a photon to the field. This is simply conservation of energy.

Typically, there is a small, homogeneous, static magnetic field in the interaction region to provide what is called a quantization axis and also to separate magnetic-field-dependent states from those used for the frequency standard. The frequency standard states usually have only a small, second-order dependence on magnetic field.

A technique is provided to detect either the transition probability of the atom or the change in the electromagnetic field and convert it to an electrical signal. This allows the atomic resonance to be used



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