Quantum chaos in atom optics: Using phase noise to model continuous momentum and position measurement

We study the effect of noise on the quantum nonlinear motion of a two-level atom in a laser standing wave. This system has recently been shown to exhibit dynamic localization in the atomic momentum. Noise is introduced through the phase of the standing wave, and has one of two forms: Weiner noise or Ornstein-Uhlenbeck noise. Using the theory of stochastic Hamiltonians we derive a master equation to describe the quantum mechanical evolution of the momentum statistics. We show that the Weiner noise process is then equivalent to a continuous measurement of the momentum of the atom, and the Ornstein-Uhlenbeck process describes a measurement of the position of the atom up to the period of the optical potential. We study the effect of noise when the classical dynamics shows global chaos.