High resolution amplitude and phase gratings in atom optics

An atom-field geometry is chosen in which an atomic beam traverses a field interaction zone consisting of three fields, one having frequency $\Omega =c/\lambda$ propagating in the $\hat{z}$ direction and the other two having frequencies $\Omega +\delta_{1}$ and $\Omega +\delta_{2}$ propagating in the -$\hat{z}$ direction. For $n_{1}\delta_{1}+n_{2}\delta_{2}=0$ and $|\delta_{1}| T,|\delta_{2}| T\gg 1$, where $n_{1}$ and $n_{2}$ are positive integers and $T$ is the pulse duration in the atomic rest frame, the atom-field interaction results in the creation of atom amplitude and phase gratings having period $$. In this manner, one can use optical fields having wavelength $\lambda$ to produce atom gratings having periodicity much less than $\lambda$.