λ /4, λ /8, and higher order atom gratings via Raman transitions

A method is proposed for producing atom gratings having period $\lambda /4$ and $\lambda /8$ using optical fields having wavelength $\lambda $. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\em another} Raman field having propagation vector -2 k, one, in effect, creates a standing wave Raman field \label{91}%which whose ``intensity'' varies as $\cos (4 k\cdot r).$ When atoms move through this standing wave field, atom gratings having period $\lambda /4$ are produced, with the added possibility that the total ground state population in a given ground state manifold can have $\lambda /8$ periodicity. The conditions required to produce such gratings are derived. Moreover, it is shown that even higher order gratings having periodicity smaller than $\lambda /8$ can be produced using a multicolor field geometry involving three (two-photon) Raman fields. Although most calculations are carried out in the Raman-Nath approximation, the use of Raman fields to create reduced period optical lattices is also discussed.