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

TL;DR

This paper introduces a Weyl function-based diagrammatic method to analyze matter-wave coherence and Talbot-Lau effects in interferometers, accommodating complex initial states and multidimensional gratings, enhancing understanding of coherence conservation.

Contribution

The paper presents a novel Weyl function approach with a displacement diagram technique for analyzing matter-wave interference in complex potentials and initial conditions.

Findings

Analyzes 2D Talbot-Lau effect with the new method.

Shows how quadratic potentials shift echo times and phases.

Demonstrates the technique's applicability to arbitrary gratings.

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 that distinguishes decoherence effects from dephasing effects.