Filtered Talbot lens: Producing $\lambda /2n$-periodic atomic patterns with standing wave fields having period $\lambda $

We propose a scheme to create high-contrast, periodic atom density distributions having period $\lambda /2n$ using the Talbot effect, where $$ is the wave length of the optical fields that scatter the atoms and $n$ is a positive integer. This {\em filtered Talbot lens} is comprised of two standing-wave optical fields. An atomic beam propagates perpendicular to the fields. The first field, which is far-detuned from the atomic transition frequency, acts as an array of lenses that focuses the atoms. The second field, positioned at the atom optical focus of the first, is resonant with the atomic transition frequency and acts as an amplitude mask, leaving unperturbed only those atoms that pass through its nodes. At distances following the interaction with the second field that are equal to an integral fraction of the Talbot length, atomic density gratings having period $\lambda /2n$ are formed.