Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

P. B. Blakie, R. J. Ballagh, and C. W. Gardiner
Phys. Rev. A 65, 033602 – Published 4 February 2002
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Abstract

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K. We demonstrate that within the linear-response regime, both a quantum-field-theory treatment and a mean-field Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a mean-field formalism. We analyze the behavior of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (mean field, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the mean-field treatment, and can be interpreted in terms of the interference of the u and v quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear-response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.

  • Received 30 August 2001

DOI:https://doi.org/10.1103/PhysRevA.65.033602

©2002 American Physical Society

Authors & Affiliations

P. B. Blakie* and R. J. Ballagh

  • Department of Physics, University of Otago, Dunedin, New Zealand

C. W. Gardiner

  • School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand

  • *Electronic address: bblakie@physics.otago.ac.nz

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Vol. 65, Iss. 3 — March 2002

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