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Bulletin of the American Physical Society

Pattern Formations for Optical Switching Using Cold Atoms as a Nonlinear Medium

Bonnie L. Schmittberger, Joel A. Greenberg, Daniel J. Gauthier

Published Jun 17, 2011• 0 citations
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We study a pattern-forming instability in a laser-driven optically thick cloud of cold two-level atoms with a planar feedback mirror. We develop a theoretical model, enabling a full analysis of transverse patterns in a medium with saturable nonlinearity, taking into account diffraction within the medium, and both the transmission and reflection gratings. The focus of the analysis is on the combined treatment of nonlinear propagation in a diffractively and optically thick medium and the boundary condition given by feedback. We demonstrate explicitly how diffraction within the medium breaks the degeneracy of Talbot modes inherent in thin-slice models. We predict the existence of envelope curves bounding all possible pattern-formation thresholds and illustrate their interaction with threshold curves by experimental observation of a sudden transition between length scales as mirror displacement is varied.
The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we describe our experimental observation of pattern formation in cold atoms, which occurs using less than 1 μW of applied power. We show that the optical patterns and the self-organized atomic structures undergo continuous symmetry breaking, which is characteristic of nonequilibrium phenomena in a multimode system. To theoretically describe pattern formation in cold atoms, we present a self-consistent model that allows for tight atomic bunching in the applied optical lattice. We derive the nonlinear refractive index of a gas of multilevel atoms in an optical lattice, and we derive the threshold conditions under which pattern formation occurs. We show that by using small detunings and sub-Doppler temperatures, one achieves intensity thresholds for pattern formation that are reduced by two orders of magnitude compared to warm atoms.
Cold atomic clouds constitute highly resonant nonlinear optical media, whose refractive index can easily be tuned via the light frequency. When subjected to a retroreflected laser beam and under appropriate conditions, the cloud undergoes spontaneous symmetry breaking, and spatial patterns develop in the transverse cross section of the beam. We investigate the impact of the sign of the light detuning from the atomic resonance on these patterns, thus directly comparing pattern formation for self-focusing and self-defocusing nonlinearities. Our observations emphasize the need for a ``diffractively thick'' medium description of the light-cloud interaction in which diffraction and nonlinear propagation inside the sample are taken into account.