Abstract
We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.
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