Longitudinal quantum interferometry

We describe an interferometric method to uncover the quantum state eld. The information needed to retrieve the corresponding Fock coefficients is impr inted on the quantized longitudinal motion of atoms that have interacted wi th the cavity held. In particular, we show that a set of four atomic moment um distributions can be analyzed easily to reconstruct used to explain the various regimes of output coupling BECs using radiation sources. We present specific calculations of the rates of output coupling as a function of the number of Bose atoms in the condensate and the frequency, detuning, and in tensity of the radio-frequency field. [S1050-2947(99)00805-7].