Temporal, Matter-Wave-Dispersion Talbot Effect

Abstract

We analyze and experimentally demonstrate a new (temporal) Talbot effect, where a pulsed phase grating is applied to a cloud of cold atoms (Bose-Einstein condensate). In contrast to the usual (spatial) Talbot effect, our atoms gain kinetic energy when diffracted by the pulsed grating. The energy gain and the matter-wave-dispersion relation result in an exact (no paraxial approximation) Talbot effect where the initial wave front is reconstructed at multiples of a ``Talbot time'' ${T}_{\mathrm{T}}$. We demonstrate the Talbot effect by applying a second pulsed phase grating after a variable delay. When this second grating is applied at even (odd) multiples of ${T}_{\mathrm{T}}/2$, it doubles (cancels) the effect of the first pulsed grating.