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arXiv:2307.10977 · Physical Review A

Chiral currents in Bose-Einstein condensates subject to current-density interactions

María Arazo, M. Guilleumas, R. Mayol, V. Delgado, Antonio Muñoz Mateo

Published Nov 1, 2023• 5 citations
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Abstract

The authors study a quasi-one-dimensional Bose-Einstein condensate in a rotating ring geometry subject to a current nonlinearity. The stability of stationary states is examined both by linear excitation analysis and time evolution of the Gross-Pitaevskii equation with current-density interactions.
DOI
10.1103/physreva.108.053302

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Recently achieved chiral condensates open intriguing avenues for the study of the chiral properties induced by current-density interactions. An attempt to include these features in a spinor system is presented, which gives rise to a nonlinear, effective spin-orbit coupling that emerges from the differential orbital currents, along with constraints in the conserved quantities due to the linear coupling between spin components. Chirality pervades the resulting spectrum of stationary states and their dynamical stability, which are explored in plane waves, dark and bright solitons, and Josephson vortices. Our analytical and numerical results reveal the destabilizing role of polarization and Josephson currents and support the existence of stable nonlinear states built of linear superpositions of plane waves.
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We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.