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:cond-mat/0309578 · Physical Review A

Faraday patterns in low-dimensional Bose-Einstein condensates

Kęstutis Staliūnas, Stefano Longhi, Germán J. de Valcárcel

Published Jul 12, 2004• 68 citations
arXivHTMLPDF

Abstract

Excitation of Faraday patterns in the weak confinement space of low-dimensional Bose-Einstein condensates (BEC) by a periodic modulation of the trap frequency, ${\ensuremath{\Omega}}_{\text{tight}}$, in the tight confinement space is shown. For slow modulation the low-dimensional dynamics of the BEC in the weak confinement space is described by a Gross-Pitaevskii equation with time modulated nonlinearity coefficient. For increasing modulation frequencies a noticeable reduction of the pattern formation threshold is observed near $2{\ensuremath{\Omega}}_{\text{tight}}$, which is related to the parametric excitation of the internal breathing mode in the tight confinement space. These predictions could be relevant for the experimental excitation of Faraday patterns in BEC.

DOI
10.1103/physreva.70.011601

Related papers

Faraday Waves in Bose–Einstein Condensates

Nobuyuki Shukuno, Yuto Sano, Makoto Tsubota

We numerically studied Faraday waves in Bose-Einstein Condensates(BECs) trapped by anisotropic harmonic potentials using the three-dimensional Gross-Pitaevskii equation.The response of BECs was studied by modulating the interaction parameter twice the trap frequency in the tight confinement direction.In the case of elongated BECs, breathing modes were excited in the tight confinement direction, followed by Faraday waves in the weak confinement direction.First, we discuss the appearance of breathing modes and/or Faraday waves which depended strongly on the modulation frequencies.Second, we investigate the dependence of dynamics on the anisotropy of the potentials.Faraday waves appeared only for the elongated BECs.

International Conference on Low Temperature Physics (LT)•May 22, 2023•0 citations

Faraday patterns in Bose-Einstein condensates

Kęstutis Staliūnas, Stefano Longhi, Germán J. de Valcárcel

A mechanism leading to spontaneous breaking of the space symmetry, and to the appearance of spatial patterns in the most recently created state of matter, the Bose-Einstein condensate (BEC), is proposed. The pattern formation are due to a periodic modulation in time of the scattering length of the condensed atoms. Experimentally this can be achieved via the Feshbach resonance, or, for low dimensional (1D or 2D) condensates, also by modulation of the trapping potential along a spatial coordinate normal to the "working" space. The parametric excitation of patterns in condensates by considering the mean-field Gross-Pitaevskii equation, and its dissipative generalization are investigated.

European Quantum Electronics Conference (EQEC)•Jan 1, 2003•10 citations

Faraday Waves in Bose–Einstein Condensates —The Excitation by the Modulation of the Interaction and the Potential—

Nobuyuki Shukuno, Yuto Sano, Makoto Tsubota

We numerically study the dynamics of Faraday waves for Bose-Einstein condensates(BECs) trapped by anisotropic potentials using the three-dimensional Gross-Pitaevskii equation. In previous studies, Faraday waves were excited by periodic modulation of the interaction or potential; in contrast, this study systematically addresses the excitations of the two methods. When the interaction is modulated with a modulation frequency resonant with Faraday waves, the breathing mode along the tight confinement direction is excited, and the Faraday waves appear in the direction of weak confinement. A modulation frequency that is not resonant with Faraday waves does not excite Faraday waves. Thus, the dynamics depend on modulation frequencies. The behavior of the total energy and its decomposition characterize the dynamics. The excitation of Faraday waves depends on the anisotropy of the potentials as well; Faraday waves are excited only for elongated BECs. We compare the differences of the dynamics in modulation methods. There are no qualitative differences between the modulation of the interaction and potential. When the interaction and potential are simultaneously modulated, Faraday waves are excited but they do not necessarily work additively. To understand this phenomenon as a dynamical system, we choose a few dynamical variables and follow their trajectory in a phase space. The trajectory characteristics of Faraday waves and the breathing mode show that the methods of modulation are not very relevant; determining the target mode to excite is important.

arXiv:2305.14729•Journal of the Physical Society of Japan•May 22, 2023•6 citations

Observation of Faraday Waves in a Bose-Einstein Condensate

Peter Engels, Collin Atherton, Mark A. Hoefer

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

•Jan 1, 2007•0 citations

Observation of Faraday Waves in a Bose-Einstein Condensate

Peter Engels, C. R. Atherton, Mark A. Hoefer

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

Physical Review Letters•Feb 26, 2007•227 citations

Observation of Faraday Waves in a Bose-Einstein Condensate

Peter Engels, Collin Atherton, Mark A. Hoefer

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

arXiv:cond-mat/0701028•Jan 1, 2007•0 citations
Excitation of Faraday patterns in the weak confinement space of low-dimensional Bose-Einstein condensates (BEC) by a periodic modulation of the trap frequency, \ensuremathΩtight{\ensuremath{\Omega}}_{\text{tight}}\ensuremathΩtight​, in the tight confinement space is shown. For slow modulation the low-dimensional dynamics of the BEC in the weak confinement space is described by a Gross-Pitaevskii equation with time modulated nonlinearity coefficient. For increasing modulation frequencies a noticeable reduction of the pattern formation threshold is observed near 2\ensuremathΩtight2{\ensuremath{\Omega}}_{\text{tight}}2\ensuremathΩtight​, which is related to the parametric excitation of the internal breathing mode in the tight confinement space. These predictions could be relevant for the experimental excitation of Faraday patterns in BEC.
We numerically studied Faraday waves in Bose-Einstein Condensates(BECs) trapped by anisotropic harmonic potentials using the three-dimensional Gross-Pitaevskii equation.The response of BECs was studied by modulating the interaction parameter twice the trap frequency in the tight confinement direction.In the case of elongated BECs, breathing modes were excited in the tight confinement direction, followed by Faraday waves in the weak confinement direction.First, we discuss the appearance of breathing modes and/or Faraday waves which depended strongly on the modulation frequencies.Second, we investigate the dependence of dynamics on the anisotropy of the potentials.Faraday waves appeared only for the elongated BECs.
A mechanism leading to spontaneous breaking of the space symmetry, and to the appearance of spatial patterns in the most recently created state of matter, the Bose-Einstein condensate (BEC), is proposed. The pattern formation are due to a periodic modulation in time of the scattering length of the condensed atoms. Experimentally this can be achieved via the Feshbach resonance, or, for low dimensional (1D or 2D) condensates, also by modulation of the trapping potential along a spatial coordinate normal to the "working" space. The parametric excitation of patterns in condensates by considering the mean-field Gross-Pitaevskii equation, and its dissipative generalization are investigated.
We numerically study the dynamics of Faraday waves for Bose-Einstein condensates(BECs) trapped by anisotropic potentials using the three-dimensional Gross-Pitaevskii equation. In previous studies, Faraday waves were excited by periodic modulation of the interaction or potential; in contrast, this study systematically addresses the excitations of the two methods. When the interaction is modulated with a modulation frequency resonant with Faraday waves, the breathing mode along the tight confinement direction is excited, and the Faraday waves appear in the direction of weak confinement. A modulation frequency that is not resonant with Faraday waves does not excite Faraday waves. Thus, the dynamics depend on modulation frequencies. The behavior of the total energy and its decomposition characterize the dynamics. The excitation of Faraday waves depends on the anisotropy of the potentials as well; Faraday waves are excited only for elongated BECs. We compare the differences of the dynamics in modulation methods. There are no qualitative differences between the modulation of the interaction and potential. When the interaction and potential are simultaneously modulated, Faraday waves are excited but they do not necessarily work additively. To understand this phenomenon as a dynamical system, we choose a few dynamical variables and follow their trajectory in a phase space. The trajectory characteristics of Faraday waves and the breathing mode show that the methods of modulation are not very relevant; determining the target mode to excite is important.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.