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arXiv:cond-mat/9906033 · Journal of Physics B Atomic Molecular and Optical Physics

Coherence properties of an atom laser

Marek Trippenbach, Y. B. Band, Mark Edwards, M. R. Doery, Paul S. Julienne, E. W. Hagley, L. Deng, Mikio Kozuma, Kristian Helmerson, S. L. Rolston, William D. Phillips

Published Dec 13, 1999• 32 citations
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Abstract

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.

DOI
10.1088/0953-4075/33/1/305

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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.
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An atom laser based on RF-outcoupling can be operated in a coherently pulsed way by using two radio frequencies. Such a two-mode atom laser can be described by coupled Gross-Pitaevskii equations which are valid for very low temperatures (T≈0). We have derived analytic expressions for the output rate and the visibility of the pulsed atomic beam in the weak coupling regime. A comparison between the analytical and numerical results shows a good agreement. This proves our assumption that the outcoupling process may be seen as the coherent outcoupling of two independent atomic beams. Though our model is only one-dimensional, we expect also a good agreement with the full 3D situation of experiment; the estimate for the value of the output rate might be only in the right order of magnitude16. Summarizing, the manipulation of trapped Bose condensates with electromagnetic waves opens a wide new area for the field of coherent atom optics.
The dynamics of quantum fluctuations of weakly coupled Bose–Einstein condensates (BECs) can be described by an effective Bose–Josephson Hamiltonian. By requiring that the mean-field approximation on this effective Hamiltonian reproduces the low energy dynamics of the Gross–Pitaevskii equation, we obtain parameters for the effective Hamiltonian. This approach is particularly suitable when the BECs are in the Thomas–Fermi regime. Considering the problem of the splitting of a trapped BEC into two BEC fragments, our results for the dynamics of the depletion, collapses and revivals of the phase coherence are in good agreement with a recent numerical microscopic calculation from Streltsov et al (2007 Phys. Rev. Lett. 99 030402). In addition, the excitation energy of the lowest symmetric mode, which is the first relevant mode for the symmetric splitting process, is reproduced with reasonable accuracy all the way from the mean-field Josephson regime to the Fock regime.