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Journal of Physics Conference Series

Temperature dependence of critical velocity in a Bose gas in a moving optical lattice

Emiko Arahata, Tetsuro Nikuni

Published Feb 1, 2009• 1 citation
Publisher

Abstract

We study the critical velocity of a Bose-condensed gas in a moving one-dimensional (1D) optical lattice potential at finite temperatures. Using a quasi-1D model of the Gross-Pitaeavskii equation and the Bogoliubov equations, we explicitly include effects of thermal excitations in the radial direction. Within the Popov approximation, we calculate the temperature dependence of the Bogoliubov excitations with varying lattice velocity. From the condition of the negative excitation energy, we obtain the critical velocity as a function of the lattice depth and the temperature. We find that the critical velocity decreases rapidly with increasing the temperature; this result is consistent with the experimental observations. Moreover, the critical velocity shows a rapid decrease with increasing lattice depth. This tendency is much more significant than in the previous works ignoring the effect of thermal excitations in the radial direction.

DOI
10.1088/1742-6596/150/3/032006

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We study the critical velocity of a Bose-condensed gas in a moving one-dimensional (1D) optical lattice potential at finite temperatures. Using a quasi-1D model of the Gross-Pitaeavskii equation and the Bogoliubov equations, we explicitly include effects of thermal excitations in the radial direction. Within the Popov approximation, we calculate the temperature dependence of the Bogoliubov excitations with varying lattice velocity. From the condition of the negative excitation energy, we obtain the critical velocity as a function of the lattice depth and the temperature. We find that the critical velocity decreases rapidly with increasing the temperature; this result is consistent with the experimental observations. Moreover, the critical velocity shows a rapid decrease with increasing lattice depth. This tendency is much more significant than in the previous works ignoring the effect of thermal excitations in the radial direction.
We study the critical velocity of a Bose-condensed gas in a moving one-dimensional optical lattice potential at finite temperatures. Solving the Gross-Pitaevskii equation and the Bogoliubov equations, within the Popov approximation, we calculate the Bogoliubov excitations with varying lattice velocity. From the condition of the negative excitation energy, we determine the critical velocity as a function of the lattice depth and the temperature. We find that the critical velocity decreases rapidly with increasing temperature; this result is consistent with the experimental observations. Moreover, the critical velocity shows a rapid decrease with increasing lattice depth. This tendency is much more significant than in the previous works ignoring the effect of thermal excitations in the radial direction.
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 investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.
We investigate Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at finite temperatures. Using a one-dimensional tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain condensate velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence of the critical velocities reveals the microscopic mechanism of the Landau instability. This instability mechanism shows that a thermal cloud plays a crucial role in the breakdown of superfluids, since the thermal cloud is a vital source of Landau damping. We also examine the possibility of simultaneous disappearance of all damping processes.
We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms nc0(T){n}^{\mathrm{c}0}(T)nc0(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid 4He^{4}\mathrm{He}4He. This leads to the disappearance of all damping processes in a DDD-dimensional simple cubic optical lattice when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6DJ$, where UUU is the on-site interaction, and JJJ is the hopping matrix element.
We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a nonmonotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures TTT, we demonstrate that the coefficient in T2{T}^{2}T2 expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in detail. At T=0T=0T=0 we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.