Bistability phase diagrams for light-driven atomic arrays  

Extended arrays of few-level atoms show a variety of interesting effects when driven continuously by light. One example is optical bistability, a nonlinear phenomenon analogous to spontaneous symmetry breaking, wherein multiple distinct scattering patterns are possible for the incident light. Past works have explored nonlinear effects such as this in the dense limit (atom separations much smaller than incident wavelength), while others have shown that collective linear effects are still possible at much lower atom densities. Here we bridge these studies by mapping out the occurrence of bistability as a function of atom separation and other parameters such as laser detuning, for a variety of level structures. We find that while separation is by far the most important parameter in determining whether bistability (or multistability) will manifest, the level structure has a significant influence as well --- ladder, lambda, and V structures for three-level atoms have bistability "phase diagrams" which are qualitatively different both from each other and from that of two-level atoms.