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arXiv:cond-mat/0007246 · Physical Review A

Dissipative dynamics of vortex arrays in anisotropic traps

O. N. Zhuravlev, A. E. Muryshev, Peter O. Fedichev

Published Oct 1, 2001• 14 citations
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Abstract

We discuss the dissipative dynamics of vortex arrays in trapped Bose-condensed gases and discuss the lifetime of the vortices as a function of trap anisotropy and temperature. In particular, we distinguish two regimes of dissipative dynamics, depending on the relative strength of the mutual friction between the vortices and the thermal component, and the friction of the thermal particles on the trap anisotropy. We study the effects of heating of the thermal cloud by the escaping vortices on the dynamics of the system.

DOI
10.1103/physreva.64.053601

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We discuss the dissipative dynamics of vortex arrays in trapped Bose-condensed gases and discuss the lifetime of the vortices as a function of trap anisotropy and temperature. In particular, we distinguish two regimes of dissipative dynamics, depending on the relative strength of the mutual friction between the vortices and the thermal component, and the friction of the thermal particles on the trap anisotropy. We study the effects of heating of the thermal cloud by the escaping vortices on the dynamics of the system.
We develop a theory of equilibrium properties and dissipative dynamics of large vortex arrays in trapped Bose-condensed gases. We prove that, in spite of the spatial inhomogeneity of the condensate density profile in trapped gases, the equilibrium configuration corresponds to a vortex array of uniform density. We show that in a static trap the interaction of the vortex array with thermal excitations leads to a nonexponential decay of the vortex structure, and the characteristic lifetime depends on the initial density of vortices. Drawing an analogy with physics of pulsars, we propose an experiment that employs the decay induced heating of the thermal cloud as a tool for a nondestructive study of the vortex dynamics.
We discuss dissipative dynamics of a vortex state in a trapped Bose-condensed gas at finite temperature and draw a scenario of decay of this state in a static trap. The interaction of the vortex with the thermal cloud transfers energy from the vortex to the cloud and induces the motion of the vortex core to the border of the condensate. Once the vortex reaches the border, it immediately decays through the creation of excitations. We calculate the characteristic lifetime of a vortex state and address the question of how the dissipative dynamics of vortices can be studied experimentally.
We have performed numerical simulations of various vortex configurations in a trapped BoseEinstein condensate by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple model of interaction between the condensate and the finite temperature thermal cloud that surrounds it. In that interaction the non-condensed thermal cloud acts as a source of dissipation with a damping effect of excitations. In the case ora single vortex and a vortex - anti vortex pair, we have found that the path of the vortices depends on the initial position, the initial separation distance if the case of two vortices and dissipation. This motion is periodic and it was found that sound waves are created by vortex motion; the intensity was stronger when the initial vortex separation distance was smaller. We have calculated the sound energy as the difference between the kinetic energy and the vortex energy. With no dissipation the vortices followed the same path with a slight oscillation due to the sound waves. We found that the smaller the initial vortex separation distance do is, the larger the sound production. The period, frequency, translation speed, sound energy and vortex energy were measured for different initial separation distances do and for different dissipation parameters 'Y. In the case of motion of one vortex, the connection between the dissipation 'Y and the friction coefficients, a and a' was studied as well. To create a simple turbulent state, we put eight pairs of vortex - anti vortex at random positions in the condensate with initial separation distance do =1.8 between them. 'Ve have studied the decay rate of the total energy, kinetic energy, quantum energy, trap energy and the z - component of the angular momentum together with the increase rate of the internal energy. Finally, we finished our investigation by putting randomly vortex - anti vortex pairs and studied the decrease of the number of vortices with time t. We found that the decrease is exponential.
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.
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.
We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.