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arXiv:cond-mat/0606398 · Physical Review A

Landau damping: Instability mechanism of superfluid Bose gases moving in optical lattices

Kiyohito Iigaya, Satoru Konabe, Ippei Danshita, Tetsuro Nikuni

Published Nov 13, 2006• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.74.053611

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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 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.
Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between condensate and noncondensate atoms. It is shown that the Landau criterion of the superfluidity for the uniform system is modified due to the presence of the periodic optical lattice potential. 1.
Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion,'' analogous to phonons in superfluid 4He^{4}\mathrm{He}4He. This leads to the disappearance of all damping processes when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6J$, where UUU is the on-site interaction, JJJ is the hopping matrix element, and nc0(T){n}^{\mathrm{c}0}(T)nc0(T) is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.
[[abstract]]We study the instabilities, Landau and dynamical instabilities, that are two mechanisms responsible for the breakdown of superfluidity in Bose-Einstein condensates interacting with a one-dimensional optical lattice. An effective-mass Gross-Pitaevskii equation was used to calculate the excitation spectrum and the condensate density of Bose-Einstein condensates in a weak periodic potential. After the condensate velocities greater than the speed of sound, we observe a decreasing of the condensate density, which is the onset of Landau instability. The condensate is dissipated, but not completely, from colliding with the thermal atom cloud. For even higher velocities of the condensate, we find a fast decreasing of the condensate density until full removal of the condensate. The regime of totally removing of the condensate is happened at the inverse effective mass of the condensate becoming zero or negative, where the condensate is on the dynamical instability.
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.
With very few exceptions (such as the centre-of-mass dipole mode), collective oscillations in trapped superfluid Bose gases are damped. In the “collisionless” region the damping is second order in the interaction strength. There are three possible components. One is Beliaev damping, which is due to the decay of a single excitation into two excitations; this can occur even at T = 0. In addition, there is Landau damping, which is due to a collective mode scattering from thermally excited excitations. This process only occurs at finite temperatures but quickly becomes the dominant damping mechanism as the temperature increases. Both Landau and Beliaev damping arise naturally from the imaginary part of the Beliaev second-order self-energies, as given in (5.40) in the case of a uniform Bose gas. Finally there is the damping that arises from the C 22 and C 12 collision processes; this is discussed in Chapters 8, 12 and 19. In Chapter 12 we calculated the damping of various condensate modes at finite temperatures using direct numerical simulations of the ZNG equations. These numerical results were generally in very good agreement with the available experimental data. From a theoretical perspective, one advantage of the simulations is that the Landau damping contribution can be isolated simply by setting the C 12 and C 22 collision terms to zero. After providing an introduction to Landau damping in uniform Bose gases in Section 13.1, we present in Section 13.2 a detailed discussion of Landau damping based on a general formula in terms of Bogoliubov–Popov excitations. This discussion makes it clear that the Landau damping of condensate oscillations arises from the interaction with a thermal cloud of excitations.