MAGNETIC GRATING FREE INDUCTION DECAY AND MAGNETIC GRATING ECHO

A theory of the magnetic grating free induction decay (MGFID) and the magnetic grating echo (MGE) is presented. In the MGFID, a pulse of cou nterpropagating waves creates a spatially modulated coherence between magnetic sublevels of the same or different ground-state hyperfine lev els. This coherence is probed at some later time by a traveling-wave p ulse. In the MGE, a second pulse of counterpropaging fields is applied at time T following the initial pulse. An echo or rephasing of the gr ound-state coherence appears at a time T following the second pulse an d can be probed by a traveling-wave pulse. The MGE can monitor ground- state transients for time scales equal to some effective ground-state lifetime; as such, it can be used effectively as an interferometric pr obe of velocity changes in cold as well as thermal atoms. The calculat ions are carried out in a perturbative limit in the amplitudes of the applied fields, but fields of arbitrary polarization and atoms having arbitrary manifolds of fine and hyperfine levels are considered. It is assumed that the pulses vary slowly on a time scale compared with min [atom-field detuning]-1, (excited-state decay rate)-1]; this allows fo r spectral resolution of the scattered probe field on a frequency scal e equal to the excited-state decay rate, independent of the Doppler wi dths associated with the optical transitions.