Periodic structures generated in a cloud of cold atoms

We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength $\lambda .$ We have detected structures of period $\lambda /2\mathrm{}$ and $\lambda /4.\mathrm{}$ Calculations indicate that these density gratings have period $\lambda /2N$ for integer N. While the structures with the period $\lambda /2\mathrm{}$ are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorter-period gratings get converted into the structures with period $\lambda /2,$ readily detected in real time. Applications related to lithography are discussed.