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arXiv:2007.06171 · Journal of Physics B Atomic Molecular and Optical Physics

Quenching dynamics of the bright solitons and other localized states in spin–orbit coupled Bose–Einstein condensates

Rajamanickam Ravisankar, Thangarasu Sriraman, Luca Salasnich, Paulsamy Muruganandam

Published Jul 15, 2020• 17 citations
arXivHTMLPDF

Abstract

Abstract We study the dynamics of binary Bose–Einstein condensates made of ultracold and dilute alkali-metal atoms in a quasi-one-dimensional setting. Numerically solving the two coupled Gross–Pitaevskii equations which accurately describe the system dynamics, we demonstrate that the spin transport can be controlled by suitably quenching spin–orbit and Rabi coupling strengths. Moreover, we predict a variety of dynamical features induced by quenching: broken oscillations, breathers-like oscillating patterns, spin-mixing–demixing, miscible–immiscible transition, emerging dark–bright states, dark solitons, and spin-trapping dynamics. We also outline the experimental relevance of the present study in manipulating the spin states in 39 K condensates.

DOI
10.1088/1361-6455/aba661

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Abstract We study the dynamics of binary Bose–Einstein condensates made of ultracold and dilute alkali-metal atoms in a quasi-one-dimensional setting. Numerically solving the two coupled Gross–Pitaevskii equations which accurately describe the system dynamics, we demonstrate that the spin transport can be controlled by suitably quenching spin–orbit and Rabi coupling strengths. Moreover, we predict a variety of dynamical features induced by quenching: broken oscillations, breathers-like oscillating patterns, spin-mixing–demixing, miscible–immiscible transition, emerging dark–bright states, dark solitons, and spin-trapping dynamics. We also outline the experimental relevance of the present study in manipulating the spin states in 39 K condensates.
Abstract We investigate the stability and nonlinear dynamics of dark–bright (DB) solitons in a one-dimensional binary Bose–Einstein condensate subjected to synthetic spin–orbit(SO) and Rabi couplings. In the absence of SO coupling, we map the coupled Gross–Pitaevskii equations onto the integrable Manakov model to obtain exact DB soliton solutions, providing a rigorous theoretical benchmark. We demonstrate that finite SO coupling breaks integrability by inducing spin-dependent phase gradients that drive component-wise spatial separation and intrinsic density oscillations. By contrast, coherent Rabi driving enforces phase locking between spin components and supports robust breather-like excitations. Furthermore, we derive analytical continuity relations for mass and spin current densities, mapping the internal spin dynamics onto an internal Josephson-junction framework in which the gauge field acts as a continuous spatial momentum bias. Using imaginary-time propagation together with Bogoliubov–de Gennes analysis, we systematically characterise ground-state phases and excitation spectra for both symmetric and asymmetric interaction regimes in homogeneous and harmonically trapped systems. Real-time simulations further demonstrate that synthetic gauge fields and interaction quenches drive the system far from equilibrium, triggering modulational-instability-induced multi-soliton fragmentation, breathing stripe patterns, and non-equilibrium transport. Our results highlight the interplay of synthetic gauge fields, external confinement, and interaction engineering as powerful tools for controlling the stability and internal dynamics of multicomponent quantum fluids.
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.
We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=1)(F=1)(F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the ${m}_{F}=+1,\ensuremath{-}1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasielastic collisions. It is also shown that in the presence of a parabolic trap the bright component(s) is (are) guided by the dark one(s) and, as a result, the small-amplitude vector soliton as a whole performs quasiharmonic oscillations. The oscillation frequency is found as a function of the spin-dependent interaction strength for both small-amplitude and large-amplitude solitons.
We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton’s spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton’s spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.
In chapter 7, the focus shifts to the dynamics of spin–orbit and Rabi-coupled Bose–Einstein condensates (BECs) for spin-F = 1/2. Employing Darboux transformation, nonlinear excitations like bright solitons, rogue waves, breathers, mixed (dark–bright) bound state solutions are explicitly derived assuming a suitable correlation between trapping frequency and temporal scattering length. For a general choice of trapping potentials and interatomic interactions, numerical techniques like split-step Fourier transform method and Newton conjugate gradient method are employed to numerically solve the dynamics of spin–orbit and Rabi-coupled BECs and the stability of the nonlinear excitations is studied.
We study the formation of stable bright solitons in quasi-one-dimensional (quasi-1D) spin-orbit- (SO-) and Rabi-coupled two pseudospinor dipolar Bose-Einstein condensates (BECs) of 164Dy^{164}\mathrm{Dy}164Dy atoms in the presence of repulsive contact interactions. As a result of the combined attraction-repulsion effect of both interactions and the addition of SO and Rabi couplings, two kinds of ground states in the form of self-trapped bright solitons can be formed, a plane-wave soliton (PWS) and a stripe soliton (SS). These quasi-1D solitons cannot exist in a condensate with purely repulsive contact interactions and SO and Rabi couplings (no dipole). Neglecting the repulsive contact interactions, our findings also show the possibility of creating PWSs and SSs. When the strengths of the two interactions are close to each other, the SS develops an oscillatory instability indicating a possibility of a breather solution, eventually leading to its destruction. We also obtain a phase diagram showing regions where the solution is a PWS or SS.