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arXiv:cond-mat/0307224 · Physical Review A

Bragg spectroscopy with an accelerating Bose-Einstein condensate

R. Geursen, N. R. Thomas, A. C. Wilson

Published Oct 9, 2003• 7 citations
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Abstract

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose-Einstein condensate undergoes circular micromotion in a magnetic time-averaged orbiting potential trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.

DOI
10.1103/physreva.68.043611

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We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose-Einstein condensate undergoes circular micromotion in a magnetic time-averaged orbiting potential trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.
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We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K.T=0 \mathrm{K}.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 vvv 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.
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