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arXiv:physics/9908002 · Physical Review A

1S−2S spectrum of a hydrogen Bose-Einstein condensate

T. C. Killian

Published Feb 15, 2000• 20 citations
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Abstract

We calculate the two-photon $1S\ensuremath{-}2S$ spectrum of an atomic hydrogen Bose-Einstein condensate in the regime where the cold collision frequency shift dominates the line shape. Wentzel-Kramers-Brillouin and static phase approximations are made to find the intensities for transitions from the condensate to motional eigenstates for $2S$ atoms. The excited-state wave functions are found using a mean field potential, which includes the effects of collisions with condensate atoms. Results agree well with experimental data. This formalism can be used to find condensate spectra for a wide range of excitation schemes.

DOI
10.1103/physreva.61.033611

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We present results of calculations on Bose-Einstein-condensed 87Rb{}^{87}\mathrm{Rb}87Rb atoms subjected to a moving standing-wave light potential of the form ${V}_{L}{(z,t)=V}_{0}(t)\mathrm{cos}(qz\ensuremath{-}\ensuremath{\omega}t).$ We calculate the mean-field dynamics (the order parameter) of the condensate and determine the resulting condensate momentum in the z direction, ${P}_{z}(q,\ensuremath{\omega}{,V}_{0}{,t}_{p}),$ where V0{V}_{0}V0​ is the peak optical potential strength and tp{t}_{p}tp​ is the pulse duration. Although the local-density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wave vector q of the light potential, for small q, short duration pulses, or for not-so-low intensities, the local-density perturbative description of the excitation spectrum breaks down badly, as shown by our results.
Optical excitations in a Bose gas are demonstrated to be sensitive to many-body effects. At low temperature the momentum relaxation is provided by momentum exchange collisions, rather than by elastic collisions. A collective excitation mode forms, which in a nondegenerate gas is manifest in a collision shift and dramatic narrowing of spectral lines. In the Bose-Einstein condensate state, each spectral line splits into two components. The doubling of the optical excitations results from the physics analogous to that of the second sound. We present a theory of the line doubling, and calculate optical absorption spectrum for a uniform density system.