Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates

TL;DR

This paper explores different regimes of two-dimensional turbulence in trapped Bose-Einstein condensates, identifying quantum and classical turbulence behaviors through spectral analysis under various stirring conditions.

Contribution

It systematically characterizes three turbulence regimes in BECs and links vortex injection patterns to classical and quantum turbulence spectra, providing experimental relevance.

Findings

Regime B shows Kolmogorov $k^{-5/3}$ spectrum intermittently.

Regime C exhibits $k^{-3/2}$ and $k^{-7/2}$ power laws.

Distinct forcing regimes generate quantum or classical turbulence.

Abstract

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 $k^{-5/3}$ power law over almost a decade of length or wavenumber ($k$) scales. The kinetic energy spectrum of regime (C) exhibits a clear $k^{-3/2}$ power law associated with an inertial range for weak-wave turbulence, and a $k^{-7/2}$ power law for high wavenumbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.