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arXiv:1309.6218 · Physical Review A

Quantum turbulence by vortex stirring in a spinor Bose-Einstein condensate

Bruno Villasenor, Roberto Zamora-Zamora, Damián Bernal, Vı́ctor Romero-Rochı́n

Published Mar 10, 2014• 17 citations
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Abstract

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.

DOI
10.1103/physreva.89.033611

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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.
We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov ${k}^{\ensuremath{-}5/3}$ power law over almost a decade of length or wave-number (kkk) scales. The kinetic energy spectrum of regime (C) exhibits a clear ${k}^{\ensuremath{-}3/2}$ power law associated with an inertial range for weak-wave turbulence and a ${k}^{\ensuremath{-}7/2}$ power law for high wave numbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.
We investigate the dynamics of turbulent flow in a two-dimensional trapped Bose-Einstein condensate by solving the Gross-Pitaevskii equation numerically. The development of the quantum turbulence is activated by the disruption of an initially embedded vortex quadrupole. By calculating the incompressible kinetic-energy spectrum of the superflow, we conclude that this quantum turbulent state is characterized by the Kolmogorov-Saffman scaling law in the wave-number space. Our study predicts the coexistence of two subinertial ranges responsible for the energy cascade and enstrophy cascade in this prototype of two-dimensional quantum turbulence.
We show the generation of two-dimensional quantum turbulence through simulations of a giant vortex decay in a trapped Bose-Einstein condensate. While evaluating the incompressible kinetic energy spectra of the quantum fluid described by the Gross-Pitaevskii equation, a bilinear form in a log-log plot is verified. A characteristic scaling behavior for small momenta shows resemblance to the Kolmogorov k−5/3k^{-5/3}k−5/3 law, while for large momenta it reassures the universal behavior of the core-size k−3k^{-3}k−3 power-law. This indicates a mechanism of energy transportation consistent with an inverse cascade. The feasibility of the described physical system with the currently available experimental techniques to create giant vortices opens up a new route to explore quantum turbulence.
We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a ${k}^{\ensuremath{-}3}$ power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.
We report the experimental generation of two-dimensional quantum turbulence in dilute-gas Bose-Einstein condensates by stirring the condensate with a laser beam, and the decay of the turbulent state to a large-scale flow in the form of a persistent current in a toroidal trap geometry. From numerical simulations of the stirring process, we characterize the dynamics of the quantized vortices in the condensate, and analyze the kinetic energy spectrum. Our observations are consistent with basic features of two-dimensional turbulence in classical incompressible fluids.