Modifications to the chaotic dynamics of laser-cooled atoms due to spontaneous emission

We study the dynamics of laser-cooled two-level atoms in a time-dependent standing wave. In the absence of spontaneous emission, our model reduces to the much studied quantum standard mapping. For a sample of atoms initially cooled to the Doppler limit, the momentum variance increases linearly with interaction time. A sample of atoms initially cooled to the recoil limit will display momentum diffusion at a rate that is determined by two numbers: the classical chaos parameter and a dimensionless Planck parameter. This diffusion ceases after the quantum-mechanical break time. Spontaneous emission will modify the diffusion rate of both Doppler- and recoil-cooled atoms. We show that one component of the new diffusion constant is due to spontaneous recoil and that there is a correction to the deterministic diffusion rate due to the destruction of correlations in the stroboscopic position. Spontaneous emission will destroy the dynamic localization of atoms cooled to the recoil limit. The new momentum diffusion constant can be related to the quasistationary state-decoherence rate.