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arXiv:2503.13767 · Physical Review A

Rayleigh-Taylor, Kelvin-Helmholtz, and immiscible-to-miscible quenching instabilities in binary Bose-Einstein condensates

R. Kishor Kumar, Subramaniyan Sabari, A. Gammal, Lauro Tomio

Published Aug 5, 2025• 2 citations
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Abstract

We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ 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 $k$. 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.

DOI
10.1103/y226-17w9

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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{k}^{\ensuremath{-}5/3}k\ensuremath−5/3 and k\ensuremath−3{k}^{\ensuremath{-}3}k\ensuremath−3, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals.
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.
Abstract Immiscible to miscible quenching transitions (IMQT) in homogeneous Bose-Einstein condensate are investigated, considering rubidium isotopes 85^{85}85Rb and 87^{87}87Rbconfined 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.
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.
Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.
Binary Bose-Einstein condensates of two distinct atomic species are studied, with interesting effects being verified due to the imbalance of atomic masses. We study the formation of vortices and associated turbulence flows created by stirring two mass-imbalanced coupled Bose-Einstein condensates in the miscible regime. We consider the mixture in the laboratory frame, confined in a pancake-like harmonic trap slightly perturbed elliptically by a time-dependent periodic potential, which introduces turbulent dynamics with final stable patterns of vortices, induced by the periodicity of the perturbation. Derived rotational frequencies are shown to be associated with the observed vortex patterns in the asymptotic regime, with a correspondence between the stirring procedure and a direct time-independent approach being indicated. It was also confirmed that a larger pattern of vortices is supported by the higher mass condensed species at the same frequency. For the experimentally accessible mixtures $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$, we numerically solve the equations of motion and analyze the system dynamics using a range of measures including energy spectra. In the transient turbulent regime, spectral analysis shows evidence for the characteristic ${k}^{\ensuremath{-}5/3}$ Kolmogorov classical law associated with turbulence, modified by the universal ${k}^{\ensuremath{-}3}$ vortex core scaling in the ultraviolet regime.
We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose–Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin–Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system’s boundary is found to dominate.