Abstract

A special case of mailer wave diffraction of a two level atom al a non resonant, high Q cavity field mode is analysed with respect, to the produced correlation between the held statistics and the atomic center of mass motion [1-4]. The interaction can be described by the Jaynes-Cummings model including a position-dependent Rabi frequency Ωf(r). Ensuring by a large detuning δthat no energy exchange occurs between the atom anti the field mode, the atom de Broglie wave experiences only a position dependent phase shill, which modifies the entering wavefront. If one confines the transverse extent of the initial wavefront by an aperture of width Ato a linear regime of the phase shift, the cavity field acts as a prism for the matter wave. However, the refractive angle depends on the quantum state of the mode, namely the photon number nstored in the cavity. The internal state of the two-level atom, eor g,also influences the direction of the deflection. The refractive angles can be expressed as $\alpha \left(n,g\right)=ne\frac{k}{k_{\text{at}}}\text{and}\alpha \left(n,e\right)=-\left(n+1\right)e\frac{k}{k_{\text{at}}}\text{where}e={\Omega }^2{t}_{\text{at}}/\delta$containing the passage time t_at, kis the wave number of the field and k_at, is that of the atom wave. It is shown, that provided ekA= j× 2πwhere j =1,2,…, the partial waves associated with different photon numbers, that propagates into the above-given directions, are distinguishable, even discernably detectable.

© 1996 IEEE