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arXiv:1402.2560 · Physical Review A

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

Antun Balaž, Remus Paun, Alexandru I. Nicolin, Sudharsan Balasubramanian, Ramaswamy Radha

Published Feb 11, 2014• 39 citations
arXivHTMLPDF

Abstract

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.

DOI
10.1103/physreva.89.023609

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We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.
Abstract We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose–Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive numerical simulations that, as the system exhibits stronger spatially-localised binary collisions (whose scattering length is taken for convenience to be of Gaussian form), the system becomes effectively a linear one. In other words, as the scattering length approaches a delta-function, we observe that the two nonlinear configurations typical for binary cigar-shaped condensates, namely the segregated and the symbiotic one, turn into two overlapping Gaussian wave functions typical for linear systems, and that the instability onset times of the Faraday and resonant waves become longer. Moreover, our numerical simulations show that the spatial period of the excited waves (either resonant or Faraday ones) decreases as the inhomogeneity becomes stronger. Our results also demonstrate that the topology of the ground state impacts the dynamics of the ensuing density waves, and that the instability onset times of Faraday and resonant waves, for a given level of inhomogeneity in the two-body interactions, depend on whether the initial configuration is segregated or symbiotic.
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.
In this study we introduce a variational model for the dynamics of Faraday waves in longitudinally-inhomogeneous Bose-Einstein condensates subject to anisotropic transverse confinement and periodic modulations of the scattering length. We derive a set of variational equations under the assumption that the period of the Faraday wave is smaller than the longitudinal width of the condensate and determine analytically the dispersion relation for large condensates through a Mathieu-type ana- lysis of the variational equations. Finally, we show the emergence of Faraday waves in a realistic anisotropic 87 Rb Bose-Einstein condensate and discuss possible extensions of the variational treatment to binary condensates.
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.