Abstract
We investigate dynamics of two-dimensional chiral solitons of semi-vortex (SV) and mixed-mode (MM) types in spin-orbit-coupled Bose-Einstein condensates with the Manakov nonlinearity, loaded in a dual-core (double-layer) trap. The system supports two novel manifestations of Josephson phenomenology: one in the form of persistent oscillations between SVs or MMs with opposite chiralities in the two cores, and another one demonstrating robust periodic switching (identity oscillations) between SV in one core and MM in the other, provided that the strength of the inter-core coupling exceeds a threshold value. Below the threshold, the system creates composite states, which are asymmetric with respect to the two cores, or suffer the collapse. Robustness of the chirality and identity oscillations against deviations from the Manakov nonlinearity is investigated too. These dynamical regimes are possible only in the nonlinear system. In the linear one, exact stationary and dynamical solutions for SVs and MMs of the Bessel type are found. They sustain Josephson self-oscillations in different modes, with no interconversion between them.
Highlights
Josephson oscillations, induced by tunneling of wave functions between weakly coupled cores, is a ubiquitous effect in macroscopic quantum systems [1]
We investigate dynamics of 2D chiral solitons of semivortex (SV) and mixed-mode (MM) types in spinorbit-coupled Bose-Einstein condensates with the Manakov nonlinearity, loaded in a dual-core trap
Note that the Josephson oscillations do not change the chemical potential in Eq (35), which is borrowed from the respective single-layered solutions, that contain the factor of exp (−iμt )
Summary
Josephson oscillations, induced by tunneling of wave functions between weakly coupled cores, is a ubiquitous effect in macroscopic quantum systems [1]. In the experimental realization of SOC in binary BEC, two components are represented by different hyperfine states of the same atom, with nearly equal strengths of the SPM and XPM interactions, suggesting one to consider the Manakov nonlinearity [61], with equal SPM and XPM coefficients In such a case, the system is invariant with respect to rotation of the pseudo-spinor wave function in the plane of its two components. In the full nonlinear system, solutions for self-trapped states are obtained in a numerical form They readily demonstrate robust periodic oscillations between components of the 2D solitons with opposite chiralities in the two layers. IV, where we give estimates of the predicted effects in physical units, and discuss directions for the further work; one of them may be the use of beyond-mean-field effects [51] for the stabilization of the
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