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:1010.1778 · Physical Review A

Suppression of Faraday waves in a Bose-Einstein condensate in the presence of an optical lattice

P. Capuzzi, M. Gattobigio, Patrizia Vignolo

Published Jan 10, 2011• 18 citations
arXivHTMLPDF

Abstract

We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.

DOI
10.1103/physreva.83.013603

Related papers

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, 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

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

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

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

Propagation of sound in a Bose-Einstein condensate in an optical lattice

C. Menotti, Meret Krämer, Augusto Smerzi +2 more

We study the propagation of sound waves in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the velocity of the propagation of sound wave packets decreases with increasing optical lattice depth, as predicted by the Bogoliubov theory. The strong interplay between nonlinearities and the periodicity of the external potential generates phenomena that are not present in the uniform case. Shock waves, for instance, can propagate slower than sound waves, due to the negative curvature of the dispersion relation. Moreover, nonlinear corrections to the Bogoliubov theory appear to be important even with very small density perturbations, inducing a saturation of the amplitude of the sound signal.

arXiv:cond-mat/0404272•Physical Review A•Aug 26, 2004•30 citations
We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.
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.
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.
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 propagation of sound waves in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the velocity of the propagation of sound wave packets decreases with increasing optical lattice depth, as predicted by the Bogoliubov theory. The strong interplay between nonlinearities and the periodicity of the external potential generates phenomena that are not present in the uniform case. Shock waves, for instance, can propagate slower than sound waves, due to the negative curvature of the dispersion relation. Moreover, nonlinear corrections to the Bogoliubov theory appear to be important even with very small density perturbations, inducing a saturation of the amplitude of the sound signal.