Phase modulation of atom waves: theory and experiment using the atom optics analogue of the Kerr effect

We have produced a phase modulation of a matter wave by applying a time-dependent perturbation. In the present study, the perturbation is the Stark effect produced by an electric field and, as this effect is quadratic in the applied field, this is the atom optics equivalent of the Kerr effect. In the present paper, we first develop an exact theory of phase modulation and we find results in agreement with a semiclassical calculation assuming a localized wavepacket. We then describe briefly our experimental setup which uses an atom interferometer to detect the phase modulations produced on its two arms which are spatially separated. The interferometer signal exhibits periodic oscillations, at the frequency of the modulation and its harmonics, when the same modulation frequency is applied on the two arms, and at the difference frequency and its harmonics when two different frequencies are used. All the experimental results are in very good agreement with theory.