Direct imaging of periodic sub-wavelength patterns generated by optical phase masks

We demonstrated {\em direct} imaging of interference fringes of total atomic density with period $\lambda /4$ and $\lambda /2$ for optical wavelength $\lambda$ that have been produced in de Broglie wave atom interferometer. The imaging was done by means of an ``optical mask" technique\footnote{A.~Turlapov, A.~Tonyushkin, and T.~Sleator, PRA {\bf 68}, 023408 (2003).}, which allowed us to observe sub-wavelength periodic patterns with a resolution of up to $\lambda /16$. In addition, the dependence of the fringe pattern on the recoil phase and pulse areas reveals quantum dynamics in the atomic center-of-mass motion. The behavior of the fringe patterns near the interference times distinguishes the effects of phase gratings from those of amplitude gratings.\footnote{A.~Tonyushkin, and T.~Sleator, arXiv:physics/0512016 (2005).}