Quantum Dynamics for the Control of Atomic State by a Quantized Optical   Ring Cavity
  A generalized approach of the Born-Oppenheimer approximation is developed to analytically deal with the influence exercised by the spatial motion of atom's mass-center on a two-level atom in an optical ring cavity with a quantized single-mode electromagnetic field. The explicit expressions of tunneling rate are obtained for various cases, such as that with initial coherent state and thermal equilibrium state at finite temperature. Therefore, the studies for Doppler and recoil effects of the spatial motion on the scheme controlling atomic tunneling should be reconsidered in terms of the initial momentum of atom's mass center. 
Chang-Pu Sun (ITP, Northeast Normal University, China)