2007/10/29 by Saijun Wu, Wu, Saijun, Pierre S. Striehl +4
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum, superfluid, helium dynamics #physics.atom-ph
paper · pdf · doi:10.48550/arxiv.0710.5479
38 pages, 17 figures
openalex publication_date 2007/10/29 · arxiv created 2007/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.