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arXiv:1703.02750

Vortex dynamics in lattice Bose gases in a synthesized magnetic field with a random noise and a dissipation: Study by the stochastic Gross-Pitaevskii equation

Ryosuke Kato, Yoshihito Kuno, Ikuo Ichinose

Published Mar 8, 2017• 0 citations
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Abstract

In this paper, we investigate vortex dynamics in a two-dimensional Bose-Hubbard model coupled with a weak artificial magnetic field, a random white noise and a dissipation. Origin of the noise and dissipation is considered as thermal fluctuations of atoms that do not participate the Bose-Einstein condensation (BEC). Solving a stochastic Gross-Pitaevskii equation to this system, we show that the interplay of the magnetic field and the white noise generates vortices in the bulk of the BEC and stable steady states of vortices form after a transition period. We calculate the incompressible part of the kinetic-energy spectrum of the BEC. In the transition period, a Kolmogorov $k^{-5/3}$ spectrum appears in the infrared regime with the wave number $k$, $kζ^{-1}$, the spectrum behaves as $k^{-3}$. On the other hand in the steady states, another scaling low appears. We find a relationship between the above mentioned kinetic-energy spectra and the velocity of vortices. By an inverse cascade, the large velocity of a few created vortices develops the Kolmogorov $k^{-5/3}$ spectrum.

DOI
10.48550/arxiv.1703.02750

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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 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 introduce a mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that the energy spectrum obeys Kolmogorov 5/3 law in the turbulent region. As the stirring is turned off, the flow decays to an agitated nonequilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled three-dimensional Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
We observed a new mechanism for vortex nucleation in Bose–Einstein condensates (BECs) subject to synthetic magnetic fields. We made use of a strong synthetic magnetic field initially localized between a pair of merging BECs to rapidly create vortices in the bulk of the merged condensate. Unlike previous implementations and in agreement with our Gross–Pitaevskii equation simulations, our dynamical process rapidly injects vortices into our system's bulk, and with initial number in excess of the system's equilibrium vortex number.
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.