Tunneling Resonances and Coherence in an Optical Lattice

The center-of-mass quantization of atoms trapped in a gray optical lattice is observed to manifest itself in the steady-state properties of the atoms. Modulations in the lifetime and macroscopic magnetization as a function of an applied $\mathbf{B}$ field are attributed to quantum mechanical tunneling resonances and are shown to exist only under conditions which afford spatial coherence of the trapped atoms over several lattice wells and coherence times that exceed the tunneling period.