Approaching classicality in quantum accelerator modes through decoherence

We describe measurements of the mean energy of an ensemble of laser-cooled atoms in an atom optical system in which the cold atoms, falling freely under gravity, receive approximate $\delta$-kicks from a pulsed standing wave of laser light. We call this system a $\mathrm{“}\delta$-kicked accelerator.” Additionally, we can counteract the effect of gravity by appropriate shifting of the position of the standing wave, which restores the dynamics of the standard $\delta$-kicked rotor. The presence of gravity $(\delta$-kicked accelerator) yields quantum phenomena, quantum accelerator modes, which are markedly different from those in the case for which gravity is absent $(\delta$-kicked rotor). Quantum accelerator modes result in a much higher rate of increase in the mean energy of the system than is found in its classical analog. When gravity is counteracted, the system exhibits the suppression of the momentum diffusion characteristic of dynamical localization. The effect of noise is examined and a comparison is made with simulations of both quantum-mechanical and classical versions of the system. We find that the introduction of noise results in the restoration of several signatures of classical behavior, although significant quantum features remain.