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Register a new userTalbot--Lau effect beyond the point-particle approximation
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Recent progress in matter-wave interferometry aims to directly probe the quantum properties of matter on ever increasing scales. However, in order to perform interferometric experiments with massive mesoscopic objects, taking into account the constraints on the experimental set-ups, the point-like particle approximation needs to be cast aside. In this work, we consider near-field interferometry based on the Talbot effects with a single optical grating for large spherical particles beyond the point-particle approximation. We account for the suppression of the coherent grating effect and, at the same time, the enhancement of the decoherence effects due to scattering and absorption of grating photons.
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We present a theoretical framework to describe the effects of decoherence on matter waves in Talbot-Lau interferometry. Using a Wigner description of the stationary beam the loss of interference contrast can be calculated in closed form. The formulation includes both the decohering coupling to the environment and the coherent interaction with the grating walls. It facilitates the quantitative distinction of genuine quantum interference from the expectations of classical mechanics. We provide realistic microscopic descriptions of the experimentally relevant interactions in terms of the bulk properties of the particles and show that the treatment is equivalent to solving the corresponding master equation in paraxial approximation.
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.
We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in non-inertial frames and in other relativistic quantum information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximation in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.
A freely propagating optical field having a periodic transverse spatial profile undergoes periodic axial revivals - a well-known phenomenon known as the Talbot effect or self-imaging. We show here that introducing tight spatio-temporal spectral correlations into an ultrafast pulsed optical field with a periodic transverse spatial profile eliminates all axial dynamics in physical space while revealing a novel space-time Talbot effect that can be observed only when carrying out time-resolved measurements. Indeed, time-diffraction is observed whereupon the temporal profile of the field envelope at a fixed axial plane corresponds to a segment of the spatial propagation profile of a monochromatic field sharing the initial spatial profile and observed at the same axial plane. Time-averaging, which is intrinsic to observing the intensity, altogether veils this effect.
The self-imaging, or Talbot Effect, that occurs with the propagation of periodically structured waves has enabled several unique applications in optical metrology, image processing, data transmission, and matter-wave interferometry. In this work, we report on the first demonstration of a Talbot Effect with single photons prepared in a lattice of orbital angular momentum (OAM) states. We observe that upon propagation, the wavefronts of the single photons manifest self-imaging whereby the OAM lattice intensity profile is recovered. Furthermore, we show that the intensity at fractional Talbot distances is indicative of a periodic helical phase structure corresponding to a lattice of OAM states. This phenomenon is a powerful addition to the toolbox of orbital angular momentum and spin-orbit techniques that have already enabled many recent developments in quantum optics.
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