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Physical Review A

Emergence of isotropy in rotating turbulence of Bose-Einstein condensates

Yuto Sano, Makoto Tsubota

Published Mar 11, 2024• 0 citations
Publisher

Abstract

The authors numerically study the development of rotating turbulence in Bose-Einstein condensates. They quantitatively investigate the decay process of the anisotropy of the kinetic energy distribution and find the anisotropic power law of the incompressible kinetic energy component.
DOI
10.1103/physreva.109.l031301

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We present a study on the development of rotating turbulence in Bose-Einstein condensates with a dissipative Gross-Pitaevskii model. Turbulence is generated by driving the lattice of quantized vortices in a harmonic potential with a random forcing potential. As the turbulence progressed, the initial alignment of vortices underwent slight disruptions, thereby increasing the high-wavenumber components of the kinetic energy. In the turbulent state, the distribution of incompressible kinetic energy exhibits milder anisotropy than that in the initial lattice state and demonstrates a scaling behavior of kz−2.5k_z^{-2.5}kz−2.5​ in the direction parallel to the rotation axis. In contrast, the compressible kinetic energy exhibits an isotropic scaling behavior at high wavenumbers.
We investigate the dynamics of a decaying rotating turbulence using the dissipative Gross-Pitaevskii model.The turbulence is created by oscillating a Bose-Einstein condensate trapped in a cylindrical box potential.After the turbulence appears with the energy spectrum of a power law, we turn off the oscillation and rotate the condensate with an angular frequency Ω, thus realizing a decaying rotating turbulence.When Ω is low, the condensate shows a turbulent structure, and the power law behavior is modified by the rotation.For higher Ω, quantized vortices along the rotation axis are created.For much higher Ω, the stronger centrifugal force creates a 'giant vortex' that includes phase singularities in the central low-density hole, which yields an anisotropic energy spectrum.
Since the idea of quantum turbulence was first proposed by Feynman and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put on finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and also has been found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.
We investigate the scaling of the energy cascade in a harmonically trapped, turbulent, rotating Bose-Einstein condensate in two dimensions. We achieve turbulence by injecting a localized perturbation into the condensate and gradually increasing its rotation frequency from an initial value to a maximum. The main characteristics of the resulting turbulent state depend on the initial conditions, rotation frequency, and ramp-up time. We analyze the energy and the fluxes of kinetic energy by considering initial profiles without vortices and with vortex lattices. In the case without initial vortices, we find the presence of Kolmogorov-like scaling (k−5/3) of the incompressible kinetic energy in the inertial range. However, with initial vortex lattices, the energy spectrum follows Vinen scaling (k−1) at transient iterations. For cases with high rotating frequencies, Kolmogorov-like scaling emerges at longer durations. We observe positive kinetic energy fluxes with both initial states across all final frequencies, indicating a forward cascade of incompressible and compressible kinetic energy.