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arXiv:2610.23314

Interfacial Faraday instability driven by interspecies-interaction modulation in a phase-separated binary Bose-Einstein condensate

Yating Huang, Yan Li

Published Oct 16, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate interfacial Faraday instabilities in a quasi-two-dimensional, phase-separated binary Bose-Einstein condensate driven by periodic modulation of the interspecies scattering length. In the strongly immiscible regime, the interspecies interaction energy is concentrated near the internal interface, linking the modulation to interfacial tension and the capillary restoring force. We quantify the first-order tension response through its logarithmic sensitivity and account for nonlinear tension variations at finite modulation amplitudes. A sharp-interface capillary model and Floquet analysis yield discrete azimuthal-mode frequencies and primary instability tongues that shift toward higher driving frequencies with increasing mode order. Gross-Pitaevskii simulations reveal star-shaped interface patterns with threefold to eightfold rotational symmetry. The eightfold mode exhibits subharmonic oscillations and approximately exponential growth of its period-averaged amplitude over a small-deformation interval. These results provide a route to frequency-selective excitation of interfacial capillary modes through interspecies-interaction control.

DOI
10.48550/arxiv.2610.23314

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We investigate interfacial Faraday instabilities in a quasi-two-dimensional, phase-separated binary Bose-Einstein condensate driven by periodic modulation of the interspecies scattering length. In the strongly immiscible regime, the interspecies interaction energy is concentrated near the internal interface, linking the modulation to interfacial tension and the capillary restoring force. We quantify the first-order tension response through its logarithmic sensitivity and account for nonlinear tension variations at finite modulation amplitudes. A sharp-interface capillary model and Floquet analysis yield discrete azimuthal-mode frequencies and primary instability tongues that shift toward higher driving frequencies with increasing mode order. Gross-Pitaevskii simulations reveal star-shaped interface patterns with threefold to eightfold rotational symmetry. The eightfold mode exhibits subharmonic oscillations and approximately exponential growth of its period-averaged amplitude over a small-deformation interval. These results provide a route to frequency-selective excitation of interfacial capillary modes through interspecies-interaction control.
A Faraday-wave-like parametric instability is investigated via mean-field and Floquet analysis in immiscible binary Bose-Einstein condensates. The condensates form a so-called ball-shell structure in a two-dimensional harmonic trap. To trigger the dynamics, the scattering length of the core condensate is periodically modulated in time. We reveal that in the dynamics the interface becomes unstable towards the formation of oscillating patterns. The interface oscillates subharmonically, exhibiting an mmm-fold rotational symmetry that can be controlled by maneuvering the amplitude and the frequency of the modulation. Using Floquet analysis we are able to predict the generated interfacial tension of the mixture and derive a dispersion relation for the natural frequencies of the emergent patterns. A heteronuclear system composed of $^{87}\mathrm{Rb}\ensuremath{-}^{85}\mathrm{Rb}$ atoms can be used for the experimental realization of the phenomenon, yet our results are independent of the specifics of the employed atomic species and of the parameters such as scattering lengths and trap strengths at which the driving is applied.
The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength KKK (>1>1>1) of the phase segregation. The dispersion relation $\ensuremath{\omega}(k)\ensuremath{\propto}{k}^{3/2}$ is derived directly from the Bogoliubov--de Gennes equations in the limit that the wavelength $2\ensuremath{\pi}/k$ is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $\ensuremath{\omega}(k)$ of order k5/2{k}^{5/2}k5/2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov--de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity $\ensuremath{\omega}/k$ to the sound velocity ccc. For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.
We investigate both analytically and numerically the dynamics of Rydberg-dressed Bose-Einstein condensates subjected to periodic modulation of the nonlocal repulsive interactions in time through temporally modulated control laser field. We show that, by utilizing such a control laser field, the nonlocal nonlinear interactions may be tuned actively, and hence a plane-wave state of matter wave can undergo a roton instability (RI) and Faraday instability (FI) simultaneously or separately, depending on the choice of the system parameters. Specifically, based on Floquet stability analysis, we find the evolution of small perturbations of the background allows the instability growth, thereby identifying instability regions with respect to density waves. Furthermore, we find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. From the direct numerical simulations of nonlocal Gross-Pitaevskii equation (GPE) and the Fourier analysis on profile of the density waves, we further show the frequency of temporal oscillations of density waves coincides with half of the driving frequency, which, therefore, is the evidence of the parametric resonance and is characteristic of Faraday waves. In addition, an interesting possibility would be to generate a steady stand-wave in the condensate which can persist after the creation even though canceling the modulation, and finally the two-dimensional Faraday waves are excited through manipulating local or nonlocal nonlinear coefficients in the system.
We investigate parametric excitation and pattern formation in a harmonically trapped two-component Bose-Einstein condensate. We assume the condensate to be in the miscible phase, but near the miscible-immiscible phase transition, where total-density and spin-density excitations are decoupled. By periodically modulating the atomic scattering lengths, Faraday patterns can be generated in both density and spin channels. In an elongated condensate, the pattern in the spin channel corresponds to a one-dimensional standing wave with the two components exhibiting an out-of-phase density oscillation, where the modulation frequency and the oscillation period are related to the velocity of the spin sound. After the spin pattern is fully developed, the system quickly enters a nonlinear destabilization regime. For a pancake-shaped condensate, a two-dimensional Faraday pattern is generated with an interesting lll-fold rotational symmetry. The number of nodes along the radial and angular directions increases with larger modulation frequencies. We also compare the growth rates of spin Faraday patterns generated with different modulation protocols, which are accessible to current experiments.
Interfacial hydrodynamic instabilities in multicomponent superfluids provide a versatile platform to explore nonequilibrium quantum dynamics beyond classical fluid analogues. We study dynamical interfacial instabilities in a quasi-two-dimensional three-component Bose-Einstein condensate confined in a harmonic trap, where rotation is applied selectively to the intermediate component to generate controlled relative motion at two interfaces. This selective rotation protocol enables the independent tuning of shear and counterflow across the inner and outer boundaries, allowing direct control over the nature and strength of the resulting instability mechanisms. Three regimes are examined: Kelvin-Helmholtz instability in the strongly immiscible limit, counter-superflow instability in the partially miscible regime, and a parameter window where both unstable mechanisms are present. The onset condition for the Kelvin-Helmholtz instability is derived using a hydrodynamic pressure-balance approach, and the subsequent nonlinear evolution is obtained from time-dependent Gross-Pitaevskii simulations. A Bogoliubov-de Gennes analysis is performed to identify the dominant unstable modes excited during the dynamical evolution of the system. The conniving features of the collective excitations and their spatial structures have been consistent with the density modulations observed during the dynamics. The results demonstrate that the presence of two interfaces and tunable intercomponent interactions in a three-component condensate modifies the instability mechanisms relative to binary mixtures and provides a controlled parameter regime to study multicomponent quantum hydrodynamics.
We study the parametric resonance of capillary waves on the interface between two immiscible Bose-Einstein condensates pushed towards each other by an oscillating force. Guided by analytical models, we solve numerically the coupled Gross-Pitaevskii equations for a two-component Bose-Einstein condensate at zero temperature. We show that, at moderate amplitudes of the driving force, the instability is stabilized due to nonlinear modifications of the oscillation frequency. When the amplitude of the driving force is large enough, we observe a detachment of droplets from the Bose-Einstein condensates, resulting in the generation of quantum vortices (skyrmions). We analytically investigate the vortex dynamics, and conditions of quantized vortex generation.