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Advances in intelligent and soft computing

Faraday Waves and Collective Modes in Bose-Einstein Condensates

Alexandru I. Nicolin, Ivana Vidanović, Antun Balaž

Published Jan 1, 2012• 1 citation
Publisher
DOI
10.1007/978-3-642-28664-3_23

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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.

arXiv:1402.2560•Physical Review A•Feb 11, 2014•39 citations
We numerically study the dynamics of Faraday waves in a pancake-shaped Bose--Einstein condensate (BEC) subject to periodic modulation of the interaction. After the modulation starts, Faraday waves appear and, thereafter, the BEC enters the "nonlinear regime", in which several collective modes are excited. By maintaining the modulation without dissipation, the kinetic energy that contributes to the density gradient causes quasiperiodic motion and increases monotonically. In the nonlinear regime, the dips in the density similar to dark solitons move around in the BEC, intersecting with each other and maintaining their shapes. On the other hand, even by turning off the modulation, Faraday waves and the nonlinear regime appear. The kinetic energy converges to the statistical steady state. The calculation of the modulation with the dissipation illustrates the collapse and revival of Faraday waves. When the dissipation is small, the appearance and collapse of the Faraday waves and the nonlinear regime occur again.
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 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.