arXiv:2408.02200 · Physical Review A

Shear-induced decaying turbulence in Bose-Einstein condensates

Simeon Simjanovski, G. Gauthier, Halina H. Rubinsztein-Dunlop, Matthew T. Reeves, Tyler W. Neely

Published Feb 12, 2025• 4 citations

Abstract

The authors experimentally study the decaying of two-dimensional quantum turbulence in a Bose-Einstein condensate. The authors show that the quantum turbulence exhibits a characteristic power-law decay of vortex cluster number, in analogy with classical two-dimensional turbulence.

DOI: 10.1103/physreva.111.023314

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arXiv:2408.02200 · Physical Review A

Shear-induced decaying turbulence in Bose-Einstein condensates

Simeon Simjanovski, G. Gauthier, Halina H. Rubinsztein-Dunlop, Matthew T. Reeves, Tyler W. Neely

Published Feb 12, 2025• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.111.023314

Related papers

Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

Thudiyangal Mithun, Kenichi Kasamatsu, Bishwajyoti Dey +1 more

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 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.

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We numerically model turbulence in a trapped atomic Bose-Einstein condensate by solving the Gross-Pitaevskii nonlinear Schroedinger equation. We find that, after an initial growth, the vortex length decays approximately as t(-1) where t is time, consistent with experiments in turbulent superfluid helium, and that the velocity components obey power-law statistics, again in agreement with observations in turbulent superfluid helium. We find the same statistics, which contrasts to the Gaussian statistics observed in ordinary classical turbulence, in a variety of quantum fluids in two and three dimensions (trapped condensates, homogeneous condensates, vortex points, vortex filaments). We argue that the non-Gaussianity arises from the singular nature of quantised vorticity.We numerically model turbulence in a trapped atomic Bose-Einstein condensate by solving the Gross-Pitaevskii nonlinear Schroedinger equation. We find that, after an initial growth, the vortex length decays approximately as t(-1) where t is time, consistent with experiments in turbulent superfluid helium, and that the velocity components obey power-law statistics, again in agreement with observations in turbulent superfluid helium. We find the same statistics, which contrasts to the Gaussian statistics observed in ordinary classical turbulence, in a variety of quantum fluids in two and three dimensions (trapped condensates, homogeneous condensates, vortex points, vortex filaments). We argue that the non-Gaussianity arises from the singular nature of quantised vorticity.

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{N}_{\mathrm{v}}

, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law ${N}_{\mathrm{v}}\ensuremath{\sim}{t}^{\ensuremath{-}1/3}$ where

t

is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.

k^{-5/3}

law, while for large momenta it reassures the universal behavior of the core-size

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.

k

) 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.