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Physical Review Letters

Temporal, Matter-Wave-Dispersion Talbot Effect

L. Deng, E. W. Hagley, Johannes Hecker Denschlag, J. E. Simsarian, Mark Edwards, Charles W. Clark, Kristian Helmerson, S. L. Rolston, William D. Phillips

Published Dec 27, 1999• 218 citations

Abstract

We analyze and experimentally demonstrate a new (temporal) Talbot effect, where a pulsed phase grating is applied to a cloud of cold atoms (Bose-Einstein condensate). In contrast to the usual (spatial) Talbot effect, our atoms gain kinetic energy when diffracted by the pulsed grating. The energy gain and the matter-wave-dispersion relation result in an exact (no paraxial approximation) Talbot effect where the initial wave front is reconstructed at multiples of a ``Talbot time'' ${T}_{\mathrm{T}}$. We demonstrate the Talbot effect by applying a second pulsed phase grating after a variable delay. When this second grating is applied at even (odd) multiples of ${T}_{\mathrm{T}}/2$, it doubles (cancels) the effect of the first pulsed grating.

DOI: 10.1103/physrevlett.83.5407

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We analyze and experimentally demonstrate a new (temporal) Talbot effect, where a pulsed phase grating is applied to a cloud of cold atoms (Bose-Einstein condensate). In contrast to the usual (spatial) Talbot effect, our atoms gain kinetic energy when diffracted by the pulsed grating. The energy gain and the matter-wave-dispersion relation result in an exact (no paraxial approximation) Talbot effect where the initial wave front is reconstructed at multiples of a ``Talbot time''

{T}_{\mathrm{T}}

. We demonstrate the Talbot effect by applying a second pulsed phase grating after a variable delay. When this second grating is applied at even (odd) multiples of

{T}_{\mathrm{T}}/2

, it doubles (cancels) the effect of the first pulsed grating.

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.

We study the diffraction phase of different orders via the Dyson expansion series, for ultracold atomic gases scattered by a standing-wave pulse. As these diffraction phases are not observable in a single-pulse scattering process, a temporal Talbot-Lau interferometer consisting of two standing-wave pulses is demonstrated experimentally with a Bose-Einstein condensate to explore this physical effect. The role of the diffraction phases is clearly shown by the second standing-wave pulse in the relative population of different momentum states. Our experiments demonstrate obvious effects beyond the Raman-Nath method, while they agree well with our theory by including the diffraction phases. In particular, the observed asymmetry in the dependence of the relative population on the interval between two standing-wave pulses reflects the diffraction phase differences. The role of interatomic interaction in the Talbot-Lau interferometer is also discussed.

We study 87 Rb 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 87 Rb BEC is observed by applying a pair of pulsed standing waves (as pulsed phase gratings) with the separation of a variable delay.

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.