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arXiv:2605.04441 · Journal of Physics B Atomic Molecular and Optical Physics

Stability and dynamics of dark–bright solitons in spin–orbit and Rabi-coupled binary Bose–Einstein condensates

K. Rajaswathi, Rajamanickam Ravisankar, R. Radha, P. K. Mishra, Paulsamy Muruganandam

Published Aug 14, 2026• 0 citations
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Abstract

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.

DOI
10.1088/1361-6455/ae9a1f

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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.
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.
We study the dynamics of non-autonomous bright-dark matter-wave solitons in two- and three- component Bose-Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross-Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross-Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy-sharing collision), that can be profitably used to control Rabi switching or vice-versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting.
We numerically investigate the ground state, the Raman-driving dynamics, and the nonlinear excitations of a realized spin-orbit-coupled Bose–Einstein condensate in a 1D harmonic trap. Depending on the Raman coupling and the interatomic interactions, three ground-state phases are identified: stripe, plane wave, and zero-momentum phases. A narrow parameter regime with coexistence of stripe and zero-momentum or plane wave phases in real space is found. Several sweeps progress across different phases by driving the Raman coupling linearly in time are simulated and the nonequilibrium dynamics of the system in these sweeps are studied. We find several kinds of nonlinear excitations, with the particular dark solitons excited in the sweep from the stripe phase to the plane wave or zero-momentum phase within the trap. Moreover, the number and the stability of the dark solitons can be controlled in the driving, which provides a direct and easy way to generate dark solitons and study their dynamics and interaction properties.
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the existence of robust DB-soliton molecules, in the form of stationary two- and three-DB-soliton states. Also the equilibrium distance of the constituent solitons and the corresponding oscillation frequencies are found semianalytically, where the latter corresponds to the characteristic anomalous modes' eigenfrequencies that we numerically computed via a so called Bogoliubov-de Gennes (BdG) linearization analysis. Those studies are discussed in Chapter 2. Then, we extend our studies to the dynamics of dark-bright (DB) solitons in binary BECs at finite temperature using a system of two-coupled dissipative GPs. We show that the effect of the bright soliton is to partially stabilize dark solitons against temperature-induced dissipation, thus providing longer lifetimes in Chapter 3. Furthermore, the dark-dark (DD) solitons as a prototypical coherent structure that emerges in two-component BECs are studied and are connected to dark-bright (DB) solitons via SO(2) rotation. We obtained their beating frequency and their frequency of oscillation inside a parabolic trap. They are identified as exact periodic orbits in the Manakov limit of equal inter- and intra- species nonlinearity strengths with and without the trap and we showcase the persistence of such states upon weak deviations from this limit. Also we investigated in detail the effect of the deviation from the Manakov case by considering different from unity scattering length ratios in Chapter 4. Next, we revisited Hamiltonian eigenvalue problems that typically arise in the linearization around a stationary state of a Hamiltonian nonlinear PDE. Also we presented a overview of the known facts for the eigenvalue counts of the corresponding unstable spectra. In particular, we focused on a straightforward plan to implement finite-dimensional techniques for locating this spectrum via the singular points of the meromorphic Krein Matrix and illustrated the value of the approach by considering realistic problems for recently observed experimentally multivortex and multisoliton solutions in atomic Bose-Einstein condensates in Chapter 5. In the two dimensional scenario, we also examine the stability and dynamics of vortices under the effect of dissipation used as a simplified model for the inclusion of the effect of finite temperatures in atomic BECs, which enables an analytical prediction that can be compared directly to numerical results in Chapter 6. In all the above studies, our analytical prediction from the equation of motion are in good agreement with the numerical results from the BdG analysis.
The dynamics of non-autonomous bright matter-wave solitons in Rabi coupled binary Bose–Einstein condensates is explored. By performing a unitary and similarity/lens-type transformation, we reduce the non-autonomous Gross–Pitaevskii (GP) equation into the celebrated Manakov model. Then, we construct the exact bright solitons of the non-autonomous GP system in the presence of time dependent nonlinearities for two specific forms, namely hyperbolic nonlinearities, which are of physical interest. The experimental possibilities of realizing the forms of temporally modulated potentials corresponding to these time dependent nonlinearities and supporting such localized structures are explored. Our study on the propagation of one soliton shows that the amplitude, velocity and shape of the bright soliton are altered by the time-dependent scattering length. We also analyze the non-trivial energy sharing collision of Manakov solitons in the presence of Rabi coupling and aforementioned nonlinearities. We find that breathers arise in two-soliton collisions and the nature of energy sharing collisions is altered from that of Manakov system due to Rabi coupling only. Further in the presence of time-dependent nonlinearities the collision scenario is again altered significantly. Finally, the stability of these localized structures is examined using a recently developed powerful analytic method by Quintero et al (2015 Phys. Rev. E 91 , 012905) and it is shown that the non-autonomous bright solitons are indeed stable. The evolution of position and velocity is also studied.