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

TL;DR

This paper investigates the decay dynamics and energy spectra of two-dimensional quantum turbulence in binary Bose-Einstein condensates, revealing how asymmetries and interactions influence vortex structures and turbulence decay.

Contribution

It provides new insights into turbulence decay, vortex formation, and energy spectra in binary BECs under various trapping and interaction asymmetries, supported by numerical simulations.

Findings

Decay to interlaced vortex-antidark structures with asymmetric parameters.

Energy spectrum shows a $k^{-3}$ power-law and a flat region at different scales.

Inter-component interactions lead to decay of vortex clusters.

Abstract

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 intra-component coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasi-equilibrium 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 intra-component couplings or the trap frequencies are enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a $k^{-3}$ 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 intra-component interaction. We also study the impact of the inter-component interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the inter-component coupling gives rise to the decay of the clustered configuration.