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:2507.15263

Spin Faraday pattern formation in a circular spin-orbit coupled Bose-Einstein condensate with stripe phase

Shixiang Chen, Hongguang Liang, Juan Wang, Yan Li

Published Jul 21, 2025• 0 citations
arXivHTMLPDF

Abstract

We investigate the spin Faraday pattern formation in a periodically driven, pancake-shaped spin-orbit-coupled (SOC) Bose-Einstein condensate (BEC) prepared with stripe phase. By modulating atomic interactions using in-phase and out-of-phase protocols, we observe collective excitation modes with distinct rotational symmetries (L-fold). Crucially, at the critical modulation frequency, out-of-phase modulation destabilizes the L = 6 pattern, whereas in-phase modulation not only preserves high symmetry but also excites higher-order modes. Unlike conventional binary BECs, Faraday patterns emerge here without initial noise due to SOC-induced symmetry breaking, with all patterns exhibiting supersolid characteristics. Furthermore, we demonstrate control over pattern symmetry, radial nodes, and pattern radius by tuning the modulation frequency, providing a new approach for manipulating quantum fluid dynamics. This work establishes a platform for exploring supersolidity and nonlinear excitations in SOC systems with stripe phase.

DOI
10.48550/arxiv.2507.15263

Related papers

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

Faraday patterns in spin-orbit-coupled Bose-Einstein condensates

Huan Zhang, Sheng Liu, Yong-Sheng Zhang

We study the Faraday patterns generated by spin-orbit-coupling induced parametric resonance in a spinor Bose-Einstein condensate with repulsive interaction. The collective elementary excitations of the Bose-Einstein condensate, including density waves and spin waves, are coupled as the result of the Raman-induced spin-orbit coupling and a quench of the relative phase of two Raman lasers without the modulation of any of the system's parameters. We observed several higher parametric resonance tongues at integer multiples of the driving frequency and investigated the interplay between Faraday instabilities and modulation instabilities when we quench the spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to plane-wave phase. If the detuning is equal to zero, the wave number of combination resonance barely changes as the strength of spin-orbit coupling increases. If the detuning is not equal to zero after a quench, a single combination resonance tongue will split into two parts.

arXiv:2206.10222•Physical Review A•Jun 17, 2022•17 citations

Dynamics of Stripe Patterns in Supersolid Spin-Orbit-Coupled Bose Gases

Kevin T. Geier, Giovanni Italo Martone, Philipp Hauke +2 more

Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid's density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.

arXiv:2210.10064•Physical Review Letters•Apr 12, 2023•32 citations

Interacting spin-orbit-coupled spin-1 Bose-Einstein condensates

Kuei Sun, Chunlei Qu, Yong Xu +2 more

The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.

arXiv:1510.03787•Physical Review A•Feb 10, 2016•74 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

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
We investigate the spin Faraday pattern formation in a periodically driven, pancake-shaped spin-orbit-coupled (SOC) Bose-Einstein condensate (BEC) prepared with stripe phase. By modulating atomic interactions using in-phase and out-of-phase protocols, we observe collective excitation modes with distinct rotational symmetries (L-fold). Crucially, at the critical modulation frequency, out-of-phase modulation destabilizes the L = 6 pattern, whereas in-phase modulation not only preserves high symmetry but also excites higher-order modes. Unlike conventional binary BECs, Faraday patterns emerge here without initial noise due to SOC-induced symmetry breaking, with all patterns exhibiting supersolid characteristics. Furthermore, we demonstrate control over pattern symmetry, radial nodes, and pattern radius by tuning the modulation frequency, providing a new approach for manipulating quantum fluid dynamics. This work establishes a platform for exploring supersolidity and nonlinear excitations in SOC systems with stripe phase.
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 study the Faraday patterns generated by spin-orbit-coupling induced parametric resonance in a spinor Bose-Einstein condensate with repulsive interaction. The collective elementary excitations of the Bose-Einstein condensate, including density waves and spin waves, are coupled as the result of the Raman-induced spin-orbit coupling and a quench of the relative phase of two Raman lasers without the modulation of any of the system's parameters. We observed several higher parametric resonance tongues at integer multiples of the driving frequency and investigated the interplay between Faraday instabilities and modulation instabilities when we quench the spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to plane-wave phase. If the detuning is equal to zero, the wave number of combination resonance barely changes as the strength of spin-orbit coupling increases. If the detuning is not equal to zero after a quench, a single combination resonance tongue will split into two parts.
Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid's density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
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 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.