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Atomic Dark-Bright Solitons: Theory and Experiments

D. J. Frantzeskakis, P. G. Kevrekidis, Dong Yan, R. Carretero-González, Mark A. Hoefer, Peter Engels, JiaJia Chang, Chris Hamner, Peter Schmelcher, Stephan Middelkamp, Jan Stockhofe, Jesús Cuevas–Maraver, María Azucena Álvarez Chillida, Vassos Achilleos, Vassilis M. Rothos

Published Jan 1, 2012• 0 citations
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Abstract We develop a direct perturbation theory for dark-bright solitons and derive evolution equations for the soliton parameters. In particular, first the linearization equation around the solitons is solved by expanding its solution into a set of complete eigenfunctions of the linearization operator. Then, suppression of secular growth in the linearized solution leads to the evolution equations of soliton parameters. The results are applied to a number of case examples motivated by the physics of atomic Bose-Einstein condensates, where dark-bright solitons have recently been studied both in theory and in experiments. We thus consider perturbations corresponding to (a) finite temperature-induced thermal losses, and (b) the presence of localized ( δ -function) impurities. In these cases, relevant equations of motion for the dark-bright soliton center are in agreement with ones previously obtained via alternative methods, including energy-based methods, as well as numerical linear stability analysis and direct simulations.
We analyze the dynamics of two-component vector solitons, namely, dark-bright solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to multicomponent Bose-Einstein condensates. The variational approximation is based on a hyperbolic tangent (hyperbolic secant) for the dark (bright) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright solitons. Analytical calculations are performed for same-width components in the vector soliton, and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it to be proportional to the intercomponent coupling interaction and numerically demonstrate the breakup or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely, the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the number of atoms in the bright component is required to be less than the number of atoms displaced by the dark soliton in the other component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright solitons in 87Rb^{87}\mathrm{Rb}87Rb we find that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments.