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Talbot-enhanced, maximum-visibility imaging of condensate interference

Zhai, Y., Christopher Carson, Victoria Henderson, Paul F. Griffin, Erling Riis, Aidan S. Arnold

Published Jan 19, 2018• 7 citations
OpenAlex

Abstract

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.

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Talbot-enhanced, maximum-visibility imaging of condensate interference

Y. Zhai, C. H. Carson, V. A. Henderson +3 more

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.

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Maximum Contrast Interferometry and Coherence in Bose-Einstein Condensates

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Magnetic levitation is used to obtain clear spatial interference between two Bose-Einstein condensates which are initially axially separated. Fringes with periods of up to 85 µm are observed using standard (non-tomographic) resonant absorption imaging, utilising the `magnifying' effect of a weak axial inverted parabolic potential [1]. With 160ms levitation [2], and careful choice of probe detuning, single-shot interference contrast of > 95% is observed (Fig. 1a) - close to the theoretical limit caused by CCD camera pixellation of the sinusoidal fringes. In addition, we observe dramatic variation of the fringe contrast as a function of camera focal position due to the spatial Talbot effect.

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Decoherence in matter-wave Talbot interference: A hydrodynamic probability-flow analysis

David Navia, Ángel S. Sanz

We investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.

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Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

Manfred J. Mark, Elmar Haller, Johann Georg Danzl +3 more

Abstract. We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.

•Aug 10, 2011•12 citations
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.
Magnetic levitation is used to obtain clear spatial interference between two Bose-Einstein condensates which are initially axially separated. Fringes with periods of up to 85 µm are observed using standard (non-tomographic) resonant absorption imaging, utilising the `magnifying' effect of a weak axial inverted parabolic potential [1]. With 160ms levitation [2], and careful choice of probe detuning, single-shot interference contrast of > 95% is observed (Fig. 1a) - close to the theoretical limit caused by CCD camera pixellation of the sinusoidal fringes. In addition, we observe dramatic variation of the fringe contrast as a function of camera focal position due to the spatial Talbot effect.
Talbot and Talbot-Lau effects are frequently used in lensless imaging applications with light, ultrasound, x-rays, atoms and molecules--generally in situations where refractive optical elements are non-existent or not suitable. We here show an experimental visualization of the intriguing wave patterns that are associated with near-field interferometry behind a single periodic diffraction grating under plane wave illumination and which are often referred to as Talbot carpets or quantum carpets. We also show the patterns behind two separated diffraction gratings under nearly-monochromatic but spatially incoherent illumination that illustrate the nature of Talbot-Lau carpets.
We investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.