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abstract: '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 $\varsigma={\rm Tr}(\hat \rho^2)$ that distinguishes decoherence effects from dephasing effects.'
author:
- 'Saijun 