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arXiv:cond-mat/9812217 · Physical Review Letters

Optical Excitations in a Nonideal Bose Gas

Mehmet Özgür Oktel, Leonid S Levitov

Published Jul 5, 1999• 41 citations
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Abstract

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.

DOI
10.1103/physrevlett.83.6

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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.
Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An out-of-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.
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 2S2S2S 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.
The excitation spectrum for symmetric two-component Bose-Einstein condensate (BECs) in optical lattices is obtained, with emphasis on its quantitative dependence on intercomponent interaction parameter. The resulting two branches of the excitation spectrum have a linear spectrum asymptotically in the low momentum limit, which is expected as a behavior of superfluid. The critical superfluid velocity, depending on the intercomponent interaction parameter, is then obtained, which is quite different from the result obtained in other reference. A requirement of real excitation spectrum also results in a condition on the interaction parameters, which coincides with the phase separation condition. Hence in real spectrum excitation, it is proposed that there should be two branches of superfluid with different critical superfluid velocities, while in the complex spectrum it is predicted that there should be phase separation in the two-branch superfluid system. The excitation spectrum for an asymmetric two-component BEC system is also presented and analyzed.
We study the dynamics of a two-component Bose-Einstein condensate (BEC) of 174 Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description.
We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schr\"odinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In this manner we take into account both collisions between noncondensate-noncondensate and condensate-noncondensate atoms. We solve the linear response of these equations, using a time-dependent Gaussian trial function for the condensate wave function and a truncated power expansion for the deviation function of the thermal cloud. As a result, our calculation turns out to be characterized by two dimensionless parameters proportional to the noncondensate-noncondensate and condensate-noncondensate mean collision times. We find in general quite good agreement with experiment, both for the frequencies and damping of the collective modes.