Immiscible to miscible quenching instabilities in two-dimensional binary Bose-Einstein condensates

TL;DR

This study investigates the transition from immiscible to miscible states in 2D binary Bose-Einstein condensates, revealing vortex and sound wave dynamics and their spectral properties during the transition.

Contribution

It provides a detailed numerical analysis of IMQT instabilities in 2D BECs, highlighting the role of vortices, sound waves, and spectral scaling behaviors.

Findings

Instability driven by vortex production and sound waves.

Spectral analysis shows Kolmogorov-like scaling during instability onset.

Vorticity and sound production stabilize in the long-term miscible regime.

Abstract

Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes $^{85}$Rb and $^{87}$Rb 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 $a_{12}$, 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 $k$, are confronted with the classical Kolmogorov scaling, $k^{-5/3}$ 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.