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arXiv:cond-mat/0106462

Surface modes and critical velocity in trapped Bose-condensates

A. E. Muryshev, Peter O. Fedichev

Published Jun 22, 2001• 0 citations
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Abstract

We propose the novel mechanism leading to superfluidity breakdown in dilute Bose-condensed gases. We discuss the properties and highlight the role played by surface excitations in trapped condensates. We show that the critical velocity measured in recent experiments is nothing else but the critical velocity associated with the spontaneous creation of surface modes. The latter turns out to be larger than that found by the analysis of a superflow stability with respect to vortex nucleation.

DOI
10.48550/arxiv.cond-mat/0106462

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We propose the novel mechanism leading to superfluidity breakdown in dilute Bose-condensed gases. We discuss the properties and highlight the role played by surface excitations in trapped condensates. We show that the critical velocity measured in recent experiments is nothing else but the critical velocity associated with the spontaneous creation of surface modes. The latter turns out to be larger than that found by the analysis of a superflow stability with respect to vortex nucleation.
The surface mode spectrum is computed self-consistently for dilute Bose-Einstein condensates, providing the temperature dependence of the surface-mode-induced vortex nucleation frequency. Both the thermodynamic critical frequency for vortex stability and the nucleation frequency implied by the surface excitations increase as the critical condensation temperature is approached from below. The multipolarity of the destabilizing surface excitation decreases with increasing temperature. The computed finite-temperature critical frequencies support the experimental observations and the zero-temperature calculations for vortex nucleation.
We use classical field simulations of the homogeneous Bose gas to study the breakdown of superflow due to vortex nucleation past a cylindrical obstacle at finite temperature. Thermal fluctuations modify the vortex nucleation from the obstacle, turning antiparallel vortex lines (which would be nucleated at zero temperature) into wiggly lines, vortex rings, and even vortex tangles. We find that the critical velocity for vortex nucleation decreases with increasing temperature and scales with the speed of sound of the condensate, becoming zero at the critical temperature for condensation.
The surface mode spectrum is computed self-consistently for dilute Bose-Einstein condensates, providing the temperature dependence of the surface mode induced vortex nucleation frequency. Both the thermodynamic critical frequency for vortex stability and the nucleation frequency implied by the surface excitations increase as the critical condensation temperature is approached from below. The multipolarity of the destabilizing surface excitation decreases with increasing temperature. The computed finite-temperature critical frequencies support the experimental observations and the zero-temperature calculations for vortex nucleation.
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 analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular, we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.