We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
We study theoretically the dimensional crossover from a three-dimensional elongated condensate to a one-dimensional condensate as the transverse degrees of freedom get frozen by tight confinement, in the limit of small density fluctuations, i.e. for a strongly degenerate gas. We compute analytically the radially integrated density profile at low temperatures using a local density approximation, and study the behavior of phase fluctuations with the transverse confinement. Previous studies of phase fluctuations in trapped gases have either focused on the 3D elongated regimes or on the 1D regime. The present approach recovers these previous results and is able to interpolate between them. We show in particular that in this strongly degenerate limit the shape of the spatial correlation function is insensitive to the transverse regime of confinement, pointing out to an almost universal behavior of phase fluctuations in elongated traps.
We discuss the collective modes in a harmonically trapped, highly-elongated Bose condensed gas. The transverse breathing mode exhibits a number of interesting features, such as the insensitivity of the condensate mode frequency to the interaction strength, and the closeness of the frequency to that of the non-condensed thermal cloud in the collisionless limit. Using finite temperature simulations, we show that these features are responsible for the very small damping rate observed experimentally. Our results for the temperature dependence of the damping rate and frequency shift are in excellent agreement with experiment. We also demonstrate that the unusually small damping rate does not arise for the
m=2 mode or for more isotropic trap potentials, suggesting further possible experimental tests of our theory.
We study Bose-Einstein condensation (BEC) for a non-interacting gas in a very anisotropic trap. Therefore, at enough small temperatures some degrees of freedom "freeze", thus reducing the "effective" dimensionality of the system. We mainly focus in quasi-bidimensional traps characterized by a surface S in the (x, y) plane. We consider two confining mechanisms in the z direction: harmonic and rigid wall potentials. There are not forces parallel to S, excepting the rigid wall at the edges. The most relevant results are: (a) The condensate smoothly sets at T ∼ script O sign(Tc/ log N), where Tc is the tridimensional condensation temperature. (b) When BEC is present, also the low-lying excited states have a macroscopic occupation; this effect is also present in a quasi-onedimensional harmonic "cigar-shape" trap. (c) The condensation process is sensitive to the shape of S.
We study superfluidity of a cigar-shaped Bose-Einstein condensate by stirring it with a Gaussian potential oscillating back and forth along the axial dimension of the condensate, motivated by experiments of Raman et al. [Phys. Rev. Lett. 83, 2502 (1999)]. Using classical-field simulations and perturbation theory, we examine the induced heating rate, based on the total energy of the system, as a function of the stirring velocity
v. We identify the onset of dissipation by a sharply increasing heating rate above a velocity
vc, which we define as the critical velocity. We show that
vc is influenced by the oscillating motion, the strength of the stirrer, the temperature, and the inhomogeneous density of the cloud. This results in a vanishing
vc for the parameters similar to the experiments, which is inconsistent with the measurement of nonzero
vc. However, if the heating rate is based on the thermal fraction after a
100ms equilibration time, our simulation recovers the experimental observations. We demonstrate that this discrepancy is due to the slow relaxation of the stirred cloud and dipole mode excitation of the cloud.
We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature
T. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on
T. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of
T. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.