Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2005.00296 · Physical Review A

Parametrically excited star-shaped patterns at the interface of binary Bose-Einstein condensates

Dilip Kumar Maity, K. Mukherjee, S. I. Mistakidis, Subrata Das, P. G. Kevrekidis, Sonjoy Majumder, Peter Schmelcher

Published Sep 14, 2020• 46 citations
arXivHTMLPDF

Abstract

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 $m$-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.

DOI
10.1103/physreva.102.033320

Related papers

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

Yating Huang, Yan Li

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.

arXiv:2610.23314•Oct 16, 2026•0 citations

Parametric excitations in a harmonically trapped binary Bose-Einstein condensate

Meiling Wang, Juan Wang, Yan Li +2 more

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 $l$-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.

arXiv:2505.17409•Physical Review A•Nov 11, 2025•5 citations

Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate

Kiryang Kwon, K. Mukherjee, SeungJung Huh +7 more

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with l-fold symmetry, ranging from quadrupole (l=2) to heptagon modes (l=7), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the l=6 mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.

arXiv:2105.09794•Physical Review Letters•Sep 10, 2021•44 citations

Faraday pattern formations in temporally driven Rydberg-dressed Bose-Einstein condensates

Zeyun Shi, Lu Qin, Fazal Badshah +2 more

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.

Physical Review A•Dec 27, 2023•5 citations

Faraday waves on a bubble-trapped Bose-Einstein-condensed binary mixture

Leonardo Brito da Silva, Lauro Tomio, A. Gammal

By studying the dynamic stability of Bose-Einstein-condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s\text{\ensuremath{-}}wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov--de Gennes and Floquet methods, with predictions being analyzed by full numerical solutions applied to the corresponding time-dependent coupled formalism.

arXiv:2309.14878•Physical Review A•Nov 16, 2023•9 citations

Parametric resonance of an interface in coherently coupled Bose–Einstein condensates and possible implications for pilot-wave theories

Vicky Howse, Raymond J. Spiteri

Abstract Faraday or parametric instability has been observed in various contexts in Bose–Einstein condensates. In Rabi-coupled condensates, the instability can arise without explicit modulation of external parameters. We study the dynamics of an interface in a two-component immiscible condensate near the miscible-immiscible threshold, with Rabi coupling between components. We show that a small initial perturbation leads to oscillations that grow in amplitude with increasing Rabi frequency until the interface produces droplet-like structures. We find that the interface oscillations are driven by parametric resonance with density oscillations in the bulk. This parametric instability of the interface provides a link to the walking droplet pilot wave system, which is governed by the Faraday instability. Because walking droplets simulate fundamentally quantum behaviors, and ‘vortex molecules,’ which are hosted by a Rabi-coupled condensate, simulate quark confinement, this observation suggests a mechanism-level connection between these systems and provides a possible bridge between distinct analog models of fundamental particles.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 4, 2026•0 citations
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 87Rb\ensuremath−85Rb^{87}\mathrm{Rb}\ensuremath{-}^{85}\mathrm{Rb}87Rb\ensuremath−85Rb 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.
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.
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.
We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with l-fold symmetry, ranging from quadrupole (l=2) to heptagon modes (l=7), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the l=6 mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.
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.
By studying the dynamic stability of Bose-Einstein-condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s\text{\ensuremath{-}}wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov--de Gennes and Floquet methods, with predictions being analyzed by full numerical solutions applied to the corresponding time-dependent coupled formalism.
Abstract Faraday or parametric instability has been observed in various contexts in Bose–Einstein condensates. In Rabi-coupled condensates, the instability can arise without explicit modulation of external parameters. We study the dynamics of an interface in a two-component immiscible condensate near the miscible-immiscible threshold, with Rabi coupling between components. We show that a small initial perturbation leads to oscillations that grow in amplitude with increasing Rabi frequency until the interface produces droplet-like structures. We find that the interface oscillations are driven by parametric resonance with density oscillations in the bulk. This parametric instability of the interface provides a link to the walking droplet pilot wave system, which is governed by the Faraday instability. Because walking droplets simulate fundamentally quantum behaviors, and ‘vortex molecules,’ which are hosted by a Rabi-coupled condensate, simulate quark confinement, this observation suggests a mechanism-level connection between these systems and provides a possible bridge between distinct analog models of fundamental particles.