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arXiv:1309.1786 · Physical Review A

Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities

D. Kobyakov, A. Bezett, Emil Lundh, M. Marklund, Vitaly Bychkov

Published Jan 31, 2014• 31 citations
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Abstract

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold ${}^{87}\text{Rb}$ atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.

DOI
10.1103/physreva.89.013631

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Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb{}^{87}\text{Rb}87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.
We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb confined in two-dimensional circular box. Rayleigh-Taylor and Kelvin-Helmholtz (KH) instability types are studied under strong perturbations. Without external perturbation, instabilities are also probed by immiscible-to-miscible quenching transition, under two different initial configurations. Our numerical simulations show that all such instability dynamics are dominated by large vortex production and sound-wave (phonon) propagation. For long-term propagation, vortex dynamics become dominant over sound waves in the KH instability, while sound-wave excitations predominate in the other cases. For all the dynamical simulations, the emergence of possible scaling laws are investigated for the compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number kkk. The corresponding results are compared with the classical Kolmogorov scalings, ${k}^{\ensuremath{-}5/3}$ and ${k}^{\ensuremath{-}3}$, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals.
The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a Bose-Einstein condensate superfluid described by the Gross-Pitaevskii equation on grids up to 5760(3). For the first time, an accurate power-law scaling for the quantum Kelvin wave cascade is determined: k(-3). The incompressible kinetic energy spectrum exhibits very distinct power-law spectra in 3 ranges of k space: a classical Kolmogorov k(-(5/3)) spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum k(-3) on scales smaller than the inner radius of the quantum vortex core. The k(-3) quantum Kelvin wave spectrum due to phonon radiation is robust, while the k(-(5/3)) classical Kolmogorov spectrum becomes robust on large grids.
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.
Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes 85^{85}85Rb and 87^{87}87Rb confined in a two-dimensional (2D) circular box, under two different initial configurations. These IMQT instabilities, triggered by sudden reductions in the two-body interspecies scattering length a12a_{12}a12​, are explored under two distinct initialconditions, highlighting the critical role of nonlinear dynamics in their evolution. The numerical simulations indicate that the instability dynamics are primarily driven by the production of large vortices and the propagation of sound waves (phonons), with sound wave excitations prevailing in the long-term evolution. The compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number kkk, are confronted with the classical Kolmogorov scaling, k−5/3k^{-5/3}k−5/3 for turbulence, which is observed in the onset of instabilities. Before reaching the ultraviolet dissipation region at small scales, the IMQT spectra exhibit a bottleneck effect, indicating a clear departure from classical scaling behavior. In the time asymptotic miscible regime, it is observed that the vorticity and sound-wave production remain practically stable. In this regime, for both cases investigated, a linear relation is also recognized between the miscibility parameter and the initial IMQT configuration.