Arc field states, photon statistics probes and quantum lenses: Field evolution and atomic motion in a dispersive interaction model

Abstract

We study the interaction of a quantized single-mode standing-wave cavity field with a two-level atom de Broglie wave. For the sake of simplicity we consider the field to be far detuned and the atom to be moving in the Raman-Nath regime. We show that the Wigner function of the field is a superposition of the Wigner functions for the coherent states aligned on an arc in phase space. The back action of the measurement of the atomic internal state leads to the modification of the diagonal as well as of the offdiagonal elements of the field density matrix.