Optical Bistability and Collective Behavior of Atoms trapped in a High-Q Ring Cavity

We study the collective motion of atoms confined in an optical lattice operating inside a high finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the line width of the cavity resonance, the otherwise tiny retro-action of the atoms upon the light field becomes a significant feature of the system, giving rise to dispersive optical bistability of the intra-cavity field. A solution of the complete set of classical equations of motion confirms these finding, however additional non-adiabatic phenomena are predicted, as for example self-induced radial breathing oscillations. We compare these results with experiments involving laser-cooled 85Rb atoms trapped in an optical lattice inside a ring cavity with a finesse of 180000. Temperature measurements conducted for moderate values of the atom-cavity interaction demonstrate that intensity-noise induced heating is kept at a very low level, a prerequisite for our further experiments. When we operate at large values of the atom--cavity interaction we observe bistability and breathing oscillations in excellent agreement with our theoretical predictions.