Collision of an atom with a colored vacuum: the vacuum-induced Kapitza-Dirac effect

We address a somewhat naive but intriguing question of momentum transfer between a matter particle and a standing-wave mode of electromagnetic radiation. A beam of two-state atoms prepared in the upper-state enters at a slightly tilted angle from the normal direction to the axis of a single mode cavity. A similar setup with a relatively short atom-field interaction time was considered by the MIT group in their microlaser experiment, where the microlaser output was measured as a function of the atom-cavity detuning, revealing two-peak gain spectra. In our present consideration, however, the atom-cavity interaction time is appropriately set that by the time an atom leaves the interaction region, it has undergone a Rabi flip. The cavity is slightly detuned from the atomic resonance frequency that each radiation quantum released from the Rabi flip of the atoms is expected to be launched into only one of the two possible directions in which the resonance condition is met by the Doppler shift due to the transverse velocity component of the atom.