Non-autonomous bright-dark solitons and Rabi oscillations in multi-component Bose-Einstein condensates

Abstract

We study the dynamics of non-autonomous bright-dark matter-wave solitons in two- and three- component Bose-Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross-Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross-Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy-sharing collision), that can be profitably used to control Rabi switching or vice-versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting.

30 pages, 20 figures

References in corpus (8)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
• Double species condensate with tunable interspecies interactions
• Generation of dark-bright soliton trains in superfluid-superfluid counterflow
• Observation of coherent many-body Rabi oscillations
• Fully three dimensional breather solitons can be created using Feshbach resonance
• Rabi switch of condensate wavefunctions in a multicomponent Bose gas
• Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions

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• Bright Matter-Wave Bound Soliton Molecules in Spin-1 Bose-Einstein Condensates with Non-autonomous Nonlinearities
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