Observation of coherence revival and fidelity saturation in a delta-kicked rotor potential

We experimentally investigate the effect of atomic $delta$-kicked rotor potentials on the mutual coherence between wavepackets in an atom interferometer. The differential action of the kicked rotor degrades the mutual coherence, leading to a reduction of the interferometry fringe visibility; however, when the repetition rate of the kicked rotor is at or near the quantum resonance, we observe revival of matter-wave coherence as the number of kicks increases, resulting in non-vanishing coherence in the large kick number limit. This coherence saturation effect reflects a saturation of fidelity decay due to momentum displacements in deep quantum regime. The saturation effect is accompanied with an invariant distribution of matter-wave coherence under the kicked rotor perturbations.

A Weyl function approach to matter-wave coherence and Talbot-Lau effects

Weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials. In this work we use Weyl functions to study the ``Talbot-Lau effect in a time-domain matter-wave interferometer. A ``displacement diagram is introduced to analyze and calculate the matter-wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo. Unlike previous treatments, this new approach allows the atomic ensemble to have an arbitrary initial phase-space distribution, and the standing wave grating vectors to span three dimensions. Several examples are discussed to illustrate the convenience of the diagrammatic technique including the following: a two-dimensional Talbot-Lau effect, the shift in the echo time and the recoil phase for the interferometer perturbed by a quadratic potential; and the realization of a time-domain ``Lau effect using a pulsed harmonic potential. The diagrammatic technique is applicable to diffraction gratings with arbitrary grating transmission functions. We conclude the paper with a general discussion on the Weyl function representations of matter-wave coherence, and relate the conservation of matter-wave coherence with the conservation of purity that distinguishes decoherence effects from dephasing effects.