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arXiv:1812.06671 · Physical Review A

Rabi-coupling-driven motion of a soliton in a Bose-Einstein condensate

Sh. Mardonov, Michele Modugno, Eugene Ya. Sherman, Boris A. Malomed

Published Jan 15, 2019• 16 citations
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Abstract

We study the motion of a self-attractive Bose-Einstein condensate with pseudospin $\frac{1}{2}$ driven by a synthetic Rabi (Zeeman-like) field. This field triggers the pseudospin dynamics resulting in a density redistribution between its components and, as a consequence, in changes of the overall density distribution. In the presence of an additional external potential, the latter produces a net force acting on the condensate and activates its displacement. As an example, here we consider the case of a one-dimensional condensate in a random potential.

DOI
10.1103/physreva.99.013611

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We study the motion of a self-attractive Bose-Einstein condensate with pseudospin 12\frac{1}{2}21​ driven by a synthetic Rabi (Zeeman-like) field. This field triggers the pseudospin dynamics resulting in a density redistribution between its components and, as a consequence, in changes of the overall density distribution. In the presence of an additional external potential, the latter produces a net force acting on the condensate and activates its displacement. As an example, here we consider the case of a one-dimensional condensate in a random potential.
We investigate theoretically the dynamics of a spin-orbit-coupled soliton formed by a self-interacting Bose-Einstein condensate immersed in a random potential, in the presence of an artificial magnetic field. We find that, due to the anomalous spin-dependent velocity, the synthetic Zeeman coupling can play a critical role in the soliton dynamics by causing its localization or delocalization, depending on the coupling strength and on the parameters of the random potential. The observed effects of the Zeeman coupling qualitatively depend on the type of self-interaction in the condensate, since the spin state and the self-interaction energy of the condensate are mutually related if the invariance of the latter with respect to the spin rotation is lifted.
The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur.
Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO ``defect'' can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.
Solitons in general are configurations of extended fields which move like isolated particles. Vector bright solitons can occur in a two-component self-attractive Bose-Einstein condensate. If the components of the condensate have different chemical potentials, the total spin of the soliton can serve as an internal energy depot that makes the soliton into an active particle, able to move against an external force using energy carried within the particle---if there is a dynamical mechanism for steadily transferring energy from soliton spin into soliton motion. Here we present such a dynamical mechanism, embed it in an experimentally feasible way within the larger system of a spinor condensate mean field, and show how the mechanism works to realize a solitonic active particle. In what can be considered a toy model for the project of going beyond toy models for active particles, we test the robustness of the activity mechanism by exploring a range of deformations to the simplest model for embedding the nonlinear mechanism in the condensate system.
We consider a binary Bose-Einstein condensate with linear and nonlinear interactions between its components, which emulate the spinor system with spin-orbit (SO) and Rabi couplings. For a relatively dense condensate, one-dimensional coupled equations with the nonpolynomial nonlinearity of both repulsive and attractive signs are derived from the three-dimensional Gross-Pitaevskii equations. Profiles of modes confined in an external potential under the action of the self-repulsion, and self-trapped solitons in the case of the self-attraction, are found in a numerical form and by means of analytical approximations. In the former case, the interplay of the SO and Rabi couplings with the repulsive nonlinearity strongly distorts shapes of the trapped modes, adding conspicuous sidelobes to them. In the case of the attractive nonlinearity, the most essential result is reduction of the collapse threshold under the action of the SO and Rabi couplings.