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:2511.07147 · Physical Review A

Pattern formation in ring condensates subjected to bichromatic driving

Premabrata Manna, S. I. Mistakidis, P. G. Kevrekidis, Pankaj Kumar Mishra

Published May 21, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is analytically derived through a suitable biharmonic variant of the Mathieu equation and computing the associated Floquet spectrum. It reveals the complex interplay between the driving parameters, i.e., amplitude, frequencies, and the so-called frequencies' mixing angle, which dictate the instability onset and the selective enhancement of higher-order resonance tongues, thus offering precise control over the excited modes. These results are in agreement with time-dependent mean-field simulations evidencing the emergence of density wave modulations of specific momenta, while enabling a deeper understanding of the nonlinear stage of the relevant instability. Further insights on the ensuing unstable nonlinear dynamics are provided through a reduced {five-mode} model which captures the instability onset, the oscillatory behavior of the mode populations and the phase-space dynamics, in agreement with the mean-field predictions. Our study highlights the versatility of bichromatic driving to generate and control complex nonlinear patterns that are within reach in present day ultracold atom experiments.

DOI
10.1103/9rjc-vcvv

Related papers

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

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

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

Parametric resonance of a Bose-Einstein condensate in a ring trap with periodically driven interactions

Chen-Xi Zhu, Wei Yi, Guang‐Can Guo +1 more

We study the instability of a ring Bose-Einstein condensate under a periodic modulation of interatomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by Bogoliubov quasiparticle excitations in the Floquet basis. As the ring geometry significantly limits the number of excitable Bogoliubov modes, we are able to capture the nonlinear dynamics of the condensate using a three-mode model. We further demonstrate the robustness of the temporal and spatial patterns against disorder, which is attributed to the mode-locking mechanism under the ring geometry. Our results can be observed in cold atomic systems and are also relevant to physical systems described by the nonlinear Schr\"odinger equation.

arXiv:1804.10755•Physical Review A•Feb 13, 2019•13 citations

Density Modulations Associated with the Dynamical Instability in the Bose–Hubbard Model

Rui Asaoka, Hiroki Tsuchiura, Makoto Yamashita +1 more

A superfluid flow beyond a critical momentum in an optical lattice decays drastically by the interplay between nonlinearity due to the interparticle interactions in Bose-Einstein condensate and periodicity of the lattice; this instability is called dynamical instability. The complex density modulational profiles after the condensate becomes unstable observed experimentally is not completely understood, while the dynamical instability has been studied theoretically and experimentally. In this paper, we analyze the density modulation of condensates as a precursor of the dynamical instability in the two-dimensional Bose-Hubbard model. Our analysis has clarified the unexplored properties of the density modulations associated with the dynamical instability at low filling and in a wide range of interactions, while the previous works have analyzed the density modulation on the basis of Gross-Pitaevskii equation under the specific condition that one-dimensional optical lattice is very shallow and the filling is very large. The numerical simulations based on the dynamical Gutzwiller approximation elucidate that the principal mode of density modulation highly depends on interaction strength U and the momentum acceleration rate. We briefly discuss these features with the stability phase diagram calculated on the basis of the Bogoliubov theory.

arXiv:1410.7869•Journal of the Physical Society of Japan•Nov 12, 2014•6 citations

Floquet-engineered moire quasicrystal patterns of ultracold Bose gases in twisted bilayer optical lattices

Fan, Zhenze, Juan Wang, Yan Li

We investigate the formation of moire quasicrystal patterns in Bose gasses confined in twisted bilayer optical lattices via Floquet-engineered intralayer atomic interactions. Dynamical evolutions of the total density wave amplitude exhibit the stage for the emergence of moire quasicrystal patterns, where the pattern formation is closely associated with the momenta of collective modes excited by the weak periodic drive. Through analyzing the radial and angular density wave amplitude, we find that these new collective modes are only coupled radially and cannot be decoupled eventually. The symmetry of quasicrystal patterns can be easily manipulated by the modulation frequencies and amplitudes. Reducing the frequencies and increasing the amplitudes can both facilitate lattice symmetry breaking and the subsequent emergence of rotational symmetry. Notably, a twelve-fold quasicrystal pattern emerges under specific parameters, closely resembling the moire quasicrystal in twisted bilayer graphene. The momentum-space distributions also exhibit high rotational symmetry, which is consistent with the real-space patterns at specific evolution times. Our findings establish a new quantum platform for exploring quasicrystals and their symmetry properties in ultracold bosonic systems.

arXiv:2508.21093•Aug 27, 2025•0 citations
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is analytically derived through a suitable biharmonic variant of the Mathieu equation and computing the associated Floquet spectrum. It reveals the complex interplay between the driving parameters, i.e., amplitude, frequencies, and the so-called frequencies' mixing angle, which dictate the instability onset and the selective enhancement of higher-order resonance tongues, thus offering precise control over the excited modes. These results are in agreement with time-dependent mean-field simulations evidencing the emergence of density wave modulations of specific momenta, while enabling a deeper understanding of the nonlinear stage of the relevant instability. Further insights on the ensuing unstable nonlinear dynamics are provided through a reduced {five-mode} model which captures the instability onset, the oscillatory behavior of the mode populations and the phase-space dynamics, in agreement with the mean-field predictions. Our study highlights the versatility of bichromatic driving to generate and control complex nonlinear patterns that are within reach in present day ultracold atom experiments.
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.
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 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.
We study the instability of a ring Bose-Einstein condensate under a periodic modulation of interatomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by Bogoliubov quasiparticle excitations in the Floquet basis. As the ring geometry significantly limits the number of excitable Bogoliubov modes, we are able to capture the nonlinear dynamics of the condensate using a three-mode model. We further demonstrate the robustness of the temporal and spatial patterns against disorder, which is attributed to the mode-locking mechanism under the ring geometry. Our results can be observed in cold atomic systems and are also relevant to physical systems described by the nonlinear Schr\"odinger equation.
A superfluid flow beyond a critical momentum in an optical lattice decays drastically by the interplay between nonlinearity due to the interparticle interactions in Bose-Einstein condensate and periodicity of the lattice; this instability is called dynamical instability. The complex density modulational profiles after the condensate becomes unstable observed experimentally is not completely understood, while the dynamical instability has been studied theoretically and experimentally. In this paper, we analyze the density modulation of condensates as a precursor of the dynamical instability in the two-dimensional Bose-Hubbard model. Our analysis has clarified the unexplored properties of the density modulations associated with the dynamical instability at low filling and in a wide range of interactions, while the previous works have analyzed the density modulation on the basis of Gross-Pitaevskii equation under the specific condition that one-dimensional optical lattice is very shallow and the filling is very large. The numerical simulations based on the dynamical Gutzwiller approximation elucidate that the principal mode of density modulation highly depends on interaction strength U and the momentum acceleration rate. We briefly discuss these features with the stability phase diagram calculated on the basis of the Bogoliubov theory.
We investigate the formation of moire quasicrystal patterns in Bose gasses confined in twisted bilayer optical lattices via Floquet-engineered intralayer atomic interactions. Dynamical evolutions of the total density wave amplitude exhibit the stage for the emergence of moire quasicrystal patterns, where the pattern formation is closely associated with the momenta of collective modes excited by the weak periodic drive. Through analyzing the radial and angular density wave amplitude, we find that these new collective modes are only coupled radially and cannot be decoupled eventually. The symmetry of quasicrystal patterns can be easily manipulated by the modulation frequencies and amplitudes. Reducing the frequencies and increasing the amplitudes can both facilitate lattice symmetry breaking and the subsequent emergence of rotational symmetry. Notably, a twelve-fold quasicrystal pattern emerges under specific parameters, closely resembling the moire quasicrystal in twisted bilayer graphene. The momentum-space distributions also exhibit high rotational symmetry, which is consistent with the real-space patterns at specific evolution times. Our findings establish a new quantum platform for exploring quasicrystals and their symmetry properties in ultracold bosonic systems.