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arXiv:1509.02236 · Physical Review A

Thermal friction on quantum vortices in a Bose-Einstein condensate

Geol Moon, Woo Jin Kwon, Hyunjik Lee, Yong-il Shin

Published Nov 20, 2015• 41 citations
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Abstract

We investigate the dissipative dynamics of a corotating vortex pair in a highly oblate axisymmetric Bose-Einstein condensate trapped in a harmonic potential. The initial vortex state is prepared by creating a doubly charged vortex at the center of the condensate and letting it dissociate into two singly charged vortices. The separation of the vortex pair gradually increases over time and its increasing rate becomes higher with increasing the sample temperature $T$. The evolution of the vortex state is well described with a dissipative point vortex model including longitudinal friction on the vortex motion. For condensates of sodium atoms having a chemical potential of $\ensuremath{\mu}\ensuremath{\approx}{k}_{B}\ifmmode\times\else\texttimes\fi{}120$ nK, we find that the dimensionless friction coefficient $\ensuremath{\alpha}$ increases from 0.01 to 0.03 over the temperature range of $200\text{nK}<T<450$ nK.

DOI
10.1103/physreva.92.051601

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We investigate the dissipative dynamics of a corotating vortex pair in a highly oblate axisymmetric Bose-Einstein condensate trapped in a harmonic potential. The initial vortex state is prepared by creating a doubly charged vortex at the center of the condensate and letting it dissociate into two singly charged vortices. The separation of the vortex pair gradually increases over time and its increasing rate becomes higher with increasing the sample temperature TTT. The evolution of the vortex state is well described with a dissipative point vortex model including longitudinal friction on the vortex motion. For condensates of sodium atoms having a chemical potential of \ensuremathμ\ensuremath≈kB\ifmmode×\else\texttimes\fi120\ensuremath{\mu}\ensuremath{\approx}{k}_{B}\ifmmode\times\else\texttimes\fi{}120\ensuremathμ\ensuremath≈kB​\ifmmode×\else\texttimes\fi120 nK, we find that the dimensionless friction coefficient \ensuremathα\ensuremath{\alpha}\ensuremathα increases from 0.01 to 0.03 over the temperature range of 200nK<T<450200\text{nK}<T<450200nK<T<450 nK.
In recent experiments, the relaxation dynamics of highly oblate, turbulent Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay rates in various sample conditions [Phys. Rev. A 90, 063627 (2014)] and, separately, the thermal friction coefficient $\ensuremath{\alpha}$ for vortex motion was measured from the long-time evolution of a corotating vortex pair in a BEC [Phys. Rev. A 92, 051601(R) (2015)]. We present a comparative analysis of the experimental results, and find that the vortex decay rate $\mathrm{\ensuremath{\Gamma}}$ is almost linearly proportional to $\ensuremath{\alpha}$. We perform numerical simulations of the time evolution of a turbulent BEC using a point-vortex model equipped with longitudinal friction and vortex-antivortex pair annihilation, and observe that the linear dependence of $\mathrm{\ensuremath{\Gamma}}$ on $\ensuremath{\alpha}$ is quantitatively accounted for in the dissipative point-vortex model. The numerical simulations reveal that thermal friction in the experiment was too strong to allow for the emergence of a vortex-clustered state out of decaying turbulence.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.
We study the dynamics of a single and a corotating vortex pair in a dipolar Bose–Einstein condensate in the framework of a dissipative Gross–Pitaevskii equation. This simple model enables us to simulate the effect of finite temperature on the vortex dynamics. We study the effect of dipolar interactions on the dynamics of a single vortex in the presence of phenomenological dissipation. In the case of a corotating vortex pair, initial asymmetry in the locations of the vortices can lead to different decay rates for the constituent vortices, as is the case for the condensates interacting via pure contact interactions. We observe that the anisotropic interaction between the component vortices manifests itself as the perceptible difference in the trajectories traversed by the vortices in the condensate at finite temperatures.
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 study the dynamics of a vortex in an atomic Bose-condensed gas at finite temperature within the Zaremba-Nikuni-Griffin formalism. In a harmonically trapped pancake-shaped condensate, an off-centered vortex is known to decay by spiraling out toward the edge of the condensate. We quantify the dependence of this decay on temperature, atomic collisions, and thermal cloud rotation. Near the trap center where the density varies slowly, we show that our numerical results agree with the predictions of the Hall-Vinen phenomenological friction force model used to describe quantized vorticity in superfluid systems. Our result thus clarifies the microscopic origin of the friction and provides an ab initio determination of its value.
We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices, and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential decay of the vortex number is quantitatively well described by a rate equation consisting of one-body and two-body decay terms. In our measurement, we find that the local two-body decay rate is closely proportional to ${T}^{2}/\ensuremath{\mu}$, where TTT is the temperature and $\ensuremath{\mu}$ is the chemical potential.