Magnetic-grating free-induction decay and magnetic-grating echo using ultrafast excitation pulses

Abstract

The interaction of atoms with ultrafast, counterpropagating optical fields is considered. The magnetic degeneracy and hyperfine splitting of the atomic levels are included in the calculations, which are carried out for arbitrary polarizations of the incident fields. The counterpropagating fields produce spatial harmonics in the ground state density matrix (gratings) which can be monitored by backscattering of a traveling wave probe pulse. Two types of excitation schemes are analyzed. The Magnetic-Grating Free-Induction Decay (MGFID) consists of excitation with a single counterpropagating wave field, while the Magnetic-Grating Echo (MGE) involves excitation by two counterpropagating wave fields, separated in time by T. The atomic response to the probe pulse is calculated in lowest-order perturbation theory for atoms cooled below the Doppler limit of laser cooling. Both the MGFID and MGE signals consist of pulses having a duration of order of the excited state lifetime, modulated at frequencies corresponding to the various hyperfine transitions. As a function of the delay between pulses, the signals oscillate at frequencies determined by the ground state hyperfine splittings. General expressions for the MGFID and MGE signals are derived and specific results are presented for the D2 line in Na.