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arXiv:1009.0759 · Physical Review A

Momentum-space engineering of gaseous Bose-Einstein condensates

Mark Edwards, Brandon Benton, Jeffrey Heward, Charles W. Clark

Published Dec 10, 2010• 26 citations
arXivHTMLPDF

Abstract

We show how the momentum distribution of gaseous Bose-Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity was demonstrated in an earlier experiment [L. Deng et al., Phys. Rev. Lett. 83, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.

DOI
10.1103/physreva.82.063613

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We show how the momentum distribution of gaseous Bose-Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity was demonstrated in an earlier experiment [L. Deng et al., Phys. Rev. Lett. 83, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of NNN pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.
Summary form only given. In a recent experiment, performed at the National Institute of Standards and Technology (NIST), a Mach-Zender type matter-wave interferometer was demonstrated using a sequence of laser pulses applied to a gaseous Bose-Einstein condensate. Matter-wave interferometers are essential tools for probing optically manipulated Bose-Einstein condensates (BECs) and the use of a sequence of laser pulses should enable experimenters to implement a variety of interferometer types tailored for particular applications.
A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low-momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum, and energy conservation (i.e., phase matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.
We study the coherence properties of an atom laser, which operates by extracting atoms from a gaseous Bose-Einstein condensate via a two-photon Raman process, by analysing a recent experiment (Hagley et al 1999 Phys. Rev. Lett. 83 3112). We obtain good agreement with the experimental data by solving the time-dependent Gross-Pitaevskii equation in three dimensions both numerically and with a Thomas-Fermi model. The coherence is strongly affected by the space-dependent phase developed by the condensate when the trapping potential is turned off.