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

Physical Review A

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

Zeyun Shi, Lu Qin, Fazal Badshah, Yuan Zhou, Haibo Huang

Published Dec 27, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.108.063317

Related papers

Generation of density waves in dipolar quantum gases by time-periodic modulation of atomic interactions

B Kh Turmanov, Bakhtiyor B. Baizakov, F. Kh. Abdullaev

We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. 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. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.

arXiv:1911.10870•Physical Review A•May 11, 2020•10 citations

Optically controlled Faraday-roton patterns in Rydberg-dressed Bose–Einstein condensates

Yao Ou, Zeyun Shi, Lu Qin +1 more

We theoretically investigate optically controlled pattern formation in a Rydberg-dressed Bose-Einstein condensate by employing two-frequency modulation of the control laser field. This approach enables direct and periodic tuning of the long-range nonlocal interactions in time, thereby intrinsically modulating the system's nonlinearity. A Floquet analysis reveals parametric resonances that simultaneously excite roton and Faraday instabilities (RI and FI), identifying distinct regimes of pure RI, pure FI, and a joint RI-FI phase. Direct numerical simulations confirm the emergence of novel Faraday patterns, which are selected by the relative amplitude and frequency ratio of the modulation. Our results establish a theoretical framework for studying nonlinear dynamics in driven nonlocal quantum fluids, providing a phase diagram that may serve as a benchmark for future experiments in Rydberg-dressed systems.

Optics Letters•Jul 10, 2026•0 citations

Pattern formation in driven condensates

Ivana Vasić, D. Vudragović, Mihaela Carina Raportaru +1 more

The onset of pattern formation in a spatially homogeneous system subjected to external driving is an important topic in various scientific fields. A celebrated classical example is the Faraday instability, where a vertically oscillated fluid surface undergoes a parametric resonance, giving rise to standing waves that self-organize into regular spatial patterns. Bose-Einstein condensates (BECs) provide an ideal quantum-mechanical platform for studying pattern-forming mechanisms due to their exceptional degree of experimental control. As a compressible state of quantum matter, a condensate responds sensitively to external perturbations, including time-periodic modulation of interactions, trapping potentials, or external fields. These features make BECs particularly well suited for exploring driven nonequilibrium phases and pattern formation. In this chapter, we review the remarkable progress achieved in this field over the past two decades. We begin with the first theoretical proposal predicting parametric instabilities and emergent Faraday waves in driven condensates. We then discuss key experimental and theoretical breakthroughs that confirmed these predictions and refined the understanding of the underlying mechanisms. This line of research has culminated in the recent observation of a stabilized square lattice pattern in a periodically driven BEC confined in a two-dimensional geometry. This driven superfluid state with superposed density modulation was shown to exhibit some features of a supersolid state.

arXiv:2603.11870•Mar 12, 2026•0 citations

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

Dilip Kumar Maity, K. Mukherjee, S. I. Mistakidis +4 more

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.

arXiv:2005.00296•Physical Review A•Sep 14, 2020•46 citations

Faraday waves in binary nonmiscible Bose-Einstein condensates

Antun Balaž, Alexandru I. Nicolin

We show by extensive numerical simulations and analytical variational calculations that elongated binary nonmiscible Bose-Einstein condensates subject to periodic modulations of the radial confinement exhibit a Faraday instability similar to that seen in one-component condensates. Considering the hyperfine states of ${}^{87}$Rb condensates, we show that there are two experimentally relevant stationary-state configurations: one in which the components form a dark-bright symbiotic pair (the ground state of the system) and one in which the components are segregated (first excited state). For each of these two configurations, we show numerically that far from resonances the Faraday waves excited in the two components are of similar periods, emerge simultaneously, and do not impact the dynamics of the bulk of the condensate. We derive analytically the period of the Faraday waves using a variational treatment of the coupled Gross-Pitaevskii equations combined with a Mathieu-type analysis for the selection mechanism of the excited waves. Finally, we show that for a modulation frequency close to twice that of the radial trapping, the emergent surface waves fade out in favor of a forceful collective mode that turns the two condensate components miscible.

arXiv:1202.2059•Physical Review A•Feb 9, 2012•70 citations

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
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 study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. 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. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.
We theoretically investigate optically controlled pattern formation in a Rydberg-dressed Bose-Einstein condensate by employing two-frequency modulation of the control laser field. This approach enables direct and periodic tuning of the long-range nonlocal interactions in time, thereby intrinsically modulating the system's nonlinearity. A Floquet analysis reveals parametric resonances that simultaneously excite roton and Faraday instabilities (RI and FI), identifying distinct regimes of pure RI, pure FI, and a joint RI-FI phase. Direct numerical simulations confirm the emergence of novel Faraday patterns, which are selected by the relative amplitude and frequency ratio of the modulation. Our results establish a theoretical framework for studying nonlinear dynamics in driven nonlocal quantum fluids, providing a phase diagram that may serve as a benchmark for future experiments in Rydberg-dressed systems.
The onset of pattern formation in a spatially homogeneous system subjected to external driving is an important topic in various scientific fields. A celebrated classical example is the Faraday instability, where a vertically oscillated fluid surface undergoes a parametric resonance, giving rise to standing waves that self-organize into regular spatial patterns. Bose-Einstein condensates (BECs) provide an ideal quantum-mechanical platform for studying pattern-forming mechanisms due to their exceptional degree of experimental control. As a compressible state of quantum matter, a condensate responds sensitively to external perturbations, including time-periodic modulation of interactions, trapping potentials, or external fields. These features make BECs particularly well suited for exploring driven nonequilibrium phases and pattern formation. In this chapter, we review the remarkable progress achieved in this field over the past two decades. We begin with the first theoretical proposal predicting parametric instabilities and emergent Faraday waves in driven condensates. We then discuss key experimental and theoretical breakthroughs that confirmed these predictions and refined the understanding of the underlying mechanisms. This line of research has culminated in the recent observation of a stabilized square lattice pattern in a periodically driven BEC confined in a two-dimensional geometry. This driven superfluid state with superposed density modulation was shown to exhibit some features of a supersolid state.
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.
We show by extensive numerical simulations and analytical variational calculations that elongated binary nonmiscible Bose-Einstein condensates subject to periodic modulations of the radial confinement exhibit a Faraday instability similar to that seen in one-component condensates. Considering the hyperfine states of 87{}^{87}87Rb condensates, we show that there are two experimentally relevant stationary-state configurations: one in which the components form a dark-bright symbiotic pair (the ground state of the system) and one in which the components are segregated (first excited state). For each of these two configurations, we show numerically that far from resonances the Faraday waves excited in the two components are of similar periods, emerge simultaneously, and do not impact the dynamics of the bulk of the condensate. We derive analytically the period of the Faraday waves using a variational treatment of the coupled Gross-Pitaevskii equations combined with a Mathieu-type analysis for the selection mechanism of the excited waves. Finally, we show that for a modulation frequency close to twice that of the radial trapping, the emergent surface waves fade out in favor of a forceful collective mode that turns the two condensate components miscible.
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.