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arXiv:physics/9903020 · Physical Review A

Talbot oscillations and periodic focusing in a one-dimensional condensate

Alberto G. Rojo, J. L. Cohen, P. R. Berman

Published Aug 1, 1999• 27 citations
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Abstract

An exact theory for the density of a one-dimensional Bose-Einstein condensate with hard-core particle interactions is developed in second quantization and applied to the scattering of the condensate by a spatially periodic impulse potential. The boson problem is mapped onto a system of free fermions obeying the Pauli exclusion principle to facilitate the calculation. The density exhibits a spatial focusing of the probability density as well as a periodic self-imaging in time, or Talbot effect. Furthermore, the transition from single-particle to many-body effects can be measured by observing the decay of the modulated condensate density pattern in time. The connection of these results to classical and atom optical phase gratings is made explicit.

DOI
10.1103/physreva.60.1482

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An exact theory for the density of a one-dimensional Bose-Einstein condensate with hard-core particle interactions is developed in second quantization and applied to the scattering of the condensate by a spatially periodic impulse potential. The boson problem is mapped onto a system of free fermions obeying the Pauli exclusion principle to facilitate the calculation. The density exhibits a spatial focusing of the probability density as well as a periodic self-imaging in time, or Talbot effect. Furthermore, the transition from single-particle to many-body effects can be measured by observing the decay of the modulated condensate density pattern in time. The connection of these results to classical and atom optical phase gratings is made explicit.
We report the experimental observation of two-dimensional Talbot effect when a resonance plane wave interacts with a two-dimensional atomic density grating generated by standing wave manipulation of ultracold Bose gases. Clear self-images of the grating and sub-images with reversed phase or fractal patterns are observed. By calculating the autocorrelation functions of the images, the behavior of periodic Talbot images is studied. The Talbot effect with two-dimensional atomic density grating expands the applications of the Talbot effect in a wide variety of research fields.
We propose a laser field configuration that acts as a quasiperiodic atom optical diffraction grating. Exact analytical results for the atomic center-of-mass wave function in the Fresnel region after the grating reveal a quasiperiodic density pattern, a semiclassical focusing effect, and a quasiperiodic self-imaging of the atomic wave function analogous to a Talbot effect. The high-contrast quasiperiodic pattern that forms at the focal plane survives both transverse and longitudinal velocity averaging. The quasi-Talbot effect should be observable using atoms from Bose-Einstein condensates.
We study 87Rb Bose-Einstein condensation (BEC) loading into the pulse of the one-dimensional (1D) optical lattice experimentally. The lattice is turned on abruptly, held constant for a variable time, and then turned off abruptly. The measurement of the depth of the optical lattice is obtained by Kapitza-Dirac scattering. The temporal matter-wave-dispersion Talbot effect with 87Rb BEC is observed by applying a pair of pulsed standing waves (as pulsed phase gratings) with the separation of a variable delay.
Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a ‘carpet’ of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose-Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry, however we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light – yielding Talbot-enhanced single-shot interference visibility of > 135% compared to the ideal visibility for resonant light.
Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a `carpet' of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose-Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry, however we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light -- yielding Talbot-enhanced single-shot interference visibility of >135% compared to the ideal visibility for resonant light.
The Talbot interferometer, as a periodic reproduction of momentum distribution in the time domain, finds significant applications in multiple research. The interparticle interactions during the diffraction and interference process introduce numerous many-body physics problems, leading to unconventional interference characteristics. This work investigates both experimentally and theoretically the influence of interaction in a Talbot interferometer with a 6Li2^{6}\mathrm{Li}_{2}6Li2​ molecular Bose-Einstein condensate in a one-dimensional optical lattice, with interaction strength directly tunable via magnetic Feshbach resonance. A clear dependence of the period and amplitude of signal revivals on the interaction strength can be observed. While interactions increase the decay rate of the signal and advance the revivals, we find that over a wide range of interactions, the Talbot interferometer remains highly effective over a certain evolutionary timescale, including the case of fractional Talbot interference. This work provides insight into the interplay between interaction and the coherence properties of a temporal Talbot interference in optical lattices, paving the way for research into quantum interference in strongly interacting systems.