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Journal of Experimental and Theoretical Physics Letters

Bragg Diffraction in Atomic Systems in Quantum Degeneracy Conditions

V. M. Porozova, V. A. Pivovarov, L. V. Gerasimov, Dmitriy V. Kupriyanov

Published Nov 1, 2018• 4 citations
Publisher

Abstract

Studies of the scattering of light on systems of identical atoms under conditions of their quantum degeneracy have been reviewed. The formation of a periodic spatial structure caused by the interference of material waves is responsible for coherent resonance scattering similar to Bragg diffraction on regular spatial inhomogeneities. The interference of macroscopic material waves that is observed in experiments with a Bose–Einstein condensate forms a dielectric medium in the region of optical transparency of the sample that has the properties of a photonic crystal. Common characteristics and differences between the scattering of light on atomic systems under quantum degeneracy conditions and scattering on one-dimensional atomic lattices where the positions of atoms are described by classical statistics have been discussed.

DOI
10.1134/s0021364018220137

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We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
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Atoms interacting with standing light waves are a model system for the propagation of waves in static and time varying periodic media. We present here experiments studying the coherent motion of atomic deBroglie waves in periodic potentials made from on and off resonant light. We observe anomalous transmission of atoms through resonant standing light waves and experimentally confirm that atoms fulfilling the Bragg condition form a standing matter wave pattern. We furthermore demonstrate how Bragg diffraction of atomic matter waves at a time-modulated thick standing light wave can be used to coherently shift the deBroglie frequency of the diffracted atoms. Our frequency shifter for atomic matter waves is similar to an acousto-optic frequency shifter for photons.
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