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Journal of Optics B Quantum and Semiclassical Optics

Reshaping of atomic waves with two-dimensional optical crystals

S. Meneghini, Igor Jex, W. P. Schleich, Valery P. Yakovlev

Published Apr 5, 2002• 0 citations
Publisher

Abstract

We study the dynamics of atomic waves in a two-dimensional light crystal formed by two crossed standing laser fields. The longitudinal modulation of the crystal with the Doppler frequency significantly influences the transversal spatial modulation of the atomic wave. Near the doppleron resonance the atomic density shows a fractional space period. In this case a normally incident wave gives rise to an almost perfect conversion into the first momentum components and the light crystal acts as a highly efficient beamsplitter. The crossing angle, determining the Doppler frequency, is the easy-to-control parameter of the system.

DOI
10.1088/1464-4266/4/3/301

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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.
We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.
We study the dynamics of atomic waves in longitudinally modulated light crystals using an effective complex potential with time (space) dependent detuning. In the weak coupling regime we predict a sharp asymmetry of the scattering probability near the Bragg angle. In the strong coupling case we introduce the concept of a light crystal with "complex kick." We have found that the initially blue detuned crystal is much more transparent for atomic waves. Moreover, the probability distribution of the outgoing wave shows carpetlike interference structure.
Atoms in light crystals formed by a standing light wave are a model system to study the propagation of matter waves in periodic potentials. The encountered phenomena can be described by dynamical diffraction theory which has been extensively studied for x-ray, electron, and neutron scattering from solid state crystals. In this paper we show that an atomic de Broglie wave traversing a standing light wave allows investigation of predictions of dynamical diffraction theory which were previously experimentally not accessible. We present standard diffraction efficiency characterizations for pure absorptive and pure refractive crystals. Additionally we were able to measure directly the total atomic wave field formed inside a refractive and an absorptive crystal and to confirm the predicted absolute position of the atomic wave field with respect to the lattice planes. By superposing two standing light waves of different frequency we tailored a new kind of crystal potential where Friedel's law about usual diffraction symmetries is maximally violated.
We show that properly detuning the carrier frequency of each of the criss-cross bichromatic waves from the transition frequency of the atom, it is possible to form a two-dimensional trap for atoms if the intensity of the waves is sufficiently large. For zero and near zero initial phases of waves, and also for πππ and near πππ phase shift between criss-cross waves a dynamic spatial structure of square cells with the side λ/2λ/\sqrt{2}λ/2​ is formed. Numerical simulations are carried out for sodium atoms.