Dispersive optical bistability in cold atomic vapours

We present an analysis of dispersive optical bistability in a system of cold atoms enclosed in a bidirectional ring cavity. This analysis is carried out using a system of equations which extend the so-called Maxwell-Bloch model to self-consistently include atomic centre-of-mass motion. When the atomic sample is sufficiently cold and dense, the atomic centre-of-mass motion causes the low pump transmission state to become unstable when the pump is blue-shifted with respect to the atomic resonance. This recoil-induced instability results in the exponential growth of the radiation field counterpropagating to the pump and an atomic density grating. The density grating strongly influences the dispersive properties of the atomic sample and causes the pump transmission to jump from the low transmission state to the high transmission state. It is expected that these effects should be observable in a cold (T < 30μ K), dense (n ∼ 1011 cm-3) sample of Rb, enclosed in a high quality ring cavity (R ≈ 99%).