Bose-Einstein Condensate System Research Articles

Dissipation-Driven Superradiant Phase Transition of a Two-Dimensional Bose–Einstein Condensate in a Double Cavity

Abstract We study superradiant phase transitions in a hybrid system of a two-dimensional Bose-Einstein condensate of atoms and two cavities arranged with a tilt angle. By adjusting the loss rate of cavities, we map out the phase diagram of steady states within a mean field framework. We find that when the loss rates of the two cavities are different, superradiant transitions may not occur at the same time in the two cavities. A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance. In the case of both cavities are superradiant, a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate. The photon current shows a non-monotonic dependence on the loss rate difference, owing to the competition of photon number difference and cavity field phase difference. Our findings can be realized and detected in experiments.

Magnon Bose–Einstein condensates: From time crystals and quantum chromodynamics to vortex sensing and cosmology

Under suitable experimental conditions, collective spin-wave excitations, magnons, form a Bose–Einstein condensate (BEC), where the spins precess with a globally coherent phase. Bose–Einstein condensation of magnons has been reported in a few systems, including superfluid phases of 3He, solid state systems, such as yttrium-iron-garnet films, and cold atomic gases. The superfluid phases of 3He provide a nearly ideal test bench for coherent magnon physics owing to experimentally proven spin superfluidity, the long lifetime of the magnon condensate, and the versatility of the accessible phenomena. We first briefly recap the properties of the different magnon BEC systems, with focus on superfluid 3He. The main body of this review summarizes recent advances in the application of magnon BEC as a laboratory to study basic physical phenomena connecting to diverse areas from particle physics and cosmology to vortex dynamics and new phases of condensed matter. This line of research complements the ongoing efforts to utilize magnon BECs as probes and components for potentially room-temperature quantum devices. In conclusion, we provide a roadmap for future directions in the field of applications of magnon BEC to fundamental research.

Chaotic control problem of BEC system based on Hartree–Fock mean field theory

Abstract Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.

Quantum Dynamics of Cavity–Bose–Einstein Condensates in a Gravitational Field

We theoretically studied the quantum dynamics of a cavity–Bose–Einstein condensate (BEC) system in a gravitational field, which is composed of a Fabry–Pérot cavity and a BEC. We also show how to deterministically generate the transient macroscopic quantum superposition states (MQSSs) of the cavity by the use of optomechanical coupling between the cavity field and the BEC. The quantum dynamics of the cavity–BEC system specifically include phase space trajectory dynamics, system excitation number dynamics, quantum entanglement dynamics, and quantum coherence dynamics. We found that the system performs increasingly complex trajectories for larger values of the Newtonian gravity parameter. Moreover, the number of phonon excitations of the system can be increased by coupling the cavity–BEC system to Newtonian gravity, which is analogous to an external direct current drive. The scattering of atoms inside the BEC affects the periodicity of the quantum dynamics of the system. We demonstrate a curious complementarity relation between the quantum entanglement and quantum coherence of cavity–BEC systems and found that the complementarity property can be sustained to some extent, despite being in the presence of the cavity decay. This phenomenon also goes some way to show that quantum entanglement and quantum coherence can be referred to together as quantum resources.

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Parity-time () symmetry has drawn great research interest in non-Hermitian physics. Recently, there is an emerging model of -symmetric spin–orbit coupling (SOC) which could be realized with spin-1/2 atomic Bose–Einstein condensates (BECs) when the two spin components are respectively subjected to momentum-dependent gain and loss (Qin et al 2022 New J. Phys. 24 063025). In this model, inter-atom interaction has no influence on the -symmetric plane waves. Thus, collective excitation playing the role of fingerprint of inter-atom interaction is investigated in this paper. For the phonon excitation, it is shown that the repulsive interaction between atoms in different spin states, which tends to drive the atoms to populate in only one spin component, can break the -symmetry, and leads to a phonon instability. Whereas, for the case of the phonon-maxon-roton collective excitation spectrum, the repulsive interaction between atoms in different spin states can lead to a maxon instability, which does not occur in Hermitian BEC systems (dipolar BECs or BECs with Raman induced SOC). Simulation of the time evolution of the plane wave solution against small noise shows that the maxon instability can result in the formation of a supersolid-like stripe pattern at the initial stage, but the non-Hermitian nature of the system finally destroys the pattern. The phase diagram of stability shows that the Rabi coupling and repulsive interaction between the atoms in the same spin state can stabilize the system.

Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation

Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation

Giant nonlocal Kerr nonlinearity and polaritonic solitons in a Rydberg-dressed Bose-Einstein condensate.

We present a scheme to generate nonlocal optical Kerr nonlinearity and polaritonic solitons via matter-wave superradiance in a Rydberg-dressed Bose-Einstein condensate (BEC). We show that the polariton spectrum of the scattered field generated by the superradiance is changed significantly due to the existence of the long-range Rydberg-Rydberg interaction between atoms, i.e. it has a roton-maxon form; moreover, the BEC structure factor displays a strong dependence on the Rydberg-dressing, which can be tuned in a controllable way. We also show that such a Rydberg-dressed BEC system can support a giant nonlocal optical Kerr nonlinearity, and hence allow the formation and stable propagation of polaritonic solitons, which have ultraslow propagation velocity and ultralow generation power. The results reported here are useful to understand the unique properties of Rydberg-dressing in BECs and have potential applications in optical information processing and transmission.

Synchronization Analysis of a Master-Slave BEC System via Active Control

This paper will focus on theoretical treatment of the dynamic of the Bose-Einstein Condensate (BEC) systems contained different external trapping potentials. We construct the phase space diagrams and Lyapunov Characteristic Exponents (LCEs) for master and slave systems depended on the system parameters and propose a nonlinear control for the synchronization of systems in their chaotic states. The synchronization is obtained in master-slave scheme for different initial values. Numerical results are also given to show the efficiency of the used control technique.

Stability control in a helicoidal spin–orbit-coupled open Bose–Bose mixture

Abstract In this article, the modulation instability (MI) of open Bose–Bose mixtures with helicoidal spin–orbit coupling (SOC) was studied. Unlike previous spin–orbit (SO)-coupled Bose–Einstein condensate system with helicoidal gauge potential, the purpose of this article to study the input of the helicoidal SOC in the emergence of MI in open Bose–Bose mixtures by taking into account the Lee–Huang–Yang corrections to the coupled Gross–Pitaevskii equations. We present the detailed analyses of system parameters on the characteristics of MI and analytically conclude the parameter conditions for MI occurrence. Our results provide a potential way to manipulate the MI in the helicoidal SO-coupled open Bose–Bose mixtures.

Mode dynamics of Bose–Einstein condensates in a single-well potential

We investigate dynamics of Bose–Einstein condensates (BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.

The Casimir effect in a dilute Bose gas at zero-temperature taking into account the contribution of self-energy within CJT theory

The Casimir effect in a weakly interacting Bose-Einstein condensate (BEC) gas is investigated at zero temperature within the Cornwall-Jackiw-Tomboulis (CJT) effective action approach under elastic and twisted boundary conditions (BCs) of the wave vector. After discussing the rationales for applying the CJT theory to a confinement BEC system, we establish the analytical formulae and then evaluate the numerical values of the Casimir force, which are essential for the observation experiment of the theoretical results.

Chimera patterns in conservative Hamiltonian systems and Bose–Einstein condensates of ultracold atoms

Experimental realizations of chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been achieved for non-conservative systems with dissipation and exclusively in classical settings. The possibility of observing chimera patterns in quantum systems has rarely been studied and it remains an open question if chimera patterns can exist in closed, or conservative quantum systems. Here, we tackle these challenges by first proposing a conservative Hamiltonian system with nonlocal hopping, where the energy is well-defined and conserved. We show explicitly that such a system can exhibit chimera patterns. Then we propose a physical mechanism for the nonlocal hopping by using an additional mediating channel. This leads us to propose a possible experimentally realizable quantum system based on a two-component Bose–Einstein condensate (BEC) with a spin-dependent optical lattice, where an untrapped component serves as the matter-wave mediating field. In this BEC system, nonlocal spatial hopping over tens of lattice sites can be achieved and simulations suggest that chimera patterns should be observable in certain parameter regimes.

Rydberg-dressed solitons in Bose-Einstein condensates with parity-time symmetry

Generating stable bright solitons in free space has been a long-standing goal in the study of matter waves in Bose-Einstein condensates (BECs). Rydberg-induced matter wave demonstrates an excellent effect in balancing the repulsive and attractive interactions between remote atoms. Parity-time (PT) symmetric lattices have been widely studied in controlling the flow of matter waves. In this study, we theoretically investigated the localization of nonlinear matter waves in the PT-symmetric Rydberg atomic BECs system. The numerical simulation method was used to obtain the stationary solutions of the wave function by solving the Gross-Pitaevskii equation (GPE) of the Rydberg-dressed BECs system. Fundamental, higher-order solitons and vortical ones were uncovered, and their stabilities were evaluated through linear-stability analysis and direct simulation with perturbation. Furthermore, the collision of solitons exhibited a quasi-elastic feature.

Chirped nonlinear waves in the cubic-quintic distributed nonlinear Schrödinger equation with external trap, self-steepening and self-frequency shift

A cubic-quintic inhomogeneous nonautonomous nonlinear Schrödinger (NLS) equation with an external trap, self-steepening, and self-frequency shift that models the transmission of nonlinear waves in nonautonomous inhomogeneous systems is considered. The integrability conditions under which the equation is converted into the standard NLS equation are obtained and a variety of nonlinear wave solutions with nonlinear chirping such as one-soliton solution, two-soliton solution, Akhmediev breather (AB) solution, Ma breather (MB) solution, as well as first- and second-order rogue wave (RW) solution are reported. We show how various parameters of either the model equation or the solutions may affect the nature of nonlinear waves with their frequency chirps propagating in nonautonomous inhomogeneous systems modeled by the NLS equation under consideration. The density profiles of nonlinear waves obtained from all these solutions are analyzed. These solutions are used for investigating analytically the dynamics of nonlinear waves in Bose-Einstein condensates (BECs) with both two- and three-body interatomic interactions when the gain/loss of atoms is taken into consideration. Considering BEC systems with time-independent trap frequency, we show that under a constant gain/loss parameter, the trap parameter can be used to convert triplet second-order RWs into either doublet second-order RWs or a composite of one bright solitary wave and a doublet second-order RWs. Also, our results reveal that for BECs with constant trap frequency under kink-like gain/loss parameter, the trap parameter can be used to convert (i) triplet second-order RWs into single second-order RWs, and (ii) two-soliton into doublet rogue wave. The family of chirped nonlinear wave solutions presented in this work may prove significance for designing the manipulation and transmission of nonlinear waves. Also, the found here results may provide possibilities to manipulate experimentally some nonlinear waves such as rogue waves or two-soliton in BEC systems.

Chaos in coupled atom–molecular Bose–Einstein condensates

We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.

Spatial structure of a Bose–Einstein condensate in a combined trap* *Projects supported by the Natural Science Foundation of Hunan Province (2016JJ6020), the Scientific Research Fund of Hunan Provincial Education Department (18A436), and the Scientific Research Fund of Hunan First normal University (XYS13N16).

We study the spatial structure of a Bose–Einstein condensate (BEC) with a space-dependent s-wave scattering length in a combined trap. There exists a space-dependent nonlinear atomic current in the system. The atomic current has an important influence on the spatial structure of the BEC. Research findings reveal that a large chemical potential can effectively suppress the chaotic spatial structure in the BEC system. Due to the large chemical potential, a strong atomic current is necessary to make the system lose its periodic spatial structure and lead the system into a chaotic spatial structure. But when the atomic current intensity exceeds a critical value, the chaotic spatial structure of the BEC will be completely eliminated and the system will always be kept in a series of single-periodic states as the atomic current becomes stronger. For a very weak atomic current, the spatial structure of the BEC is very sensitive to the intensity of the atomic current and a very small change of the intensity can dramatically change the spatial structure of the BEC. The effects of the combined trap parameters on the spatial structure of BECs are also discussed.

Multi-solitons in the spin-orbit-coupled spin-1 Bose-Einstein condensates

We find a restrictive integrable reduction for the one-dimensional spin-orbit-coupled spin-1 Bose-Einstein condensate system, which allows us to reduce the three-component Gross-Pitaevskii system into the two-component Manakov system or the single cubic Schrödinger equation. Based on the reduction, we obtain the multi-breathers, higher-order rouge waves and multi-dark soliton solutions for ferromagnetic and anti-ferromagnetic system, respectively. Furthermore, the impacts of the spin-orbit coupling to the multi-soliton dynamics, and the stability of these soliton solutions have also been discussed.

Antibunching Effects in the Hybrid Cavity–Bose–Einstein Condensates System

We theoretically study the model of a hybrid cavity–Bose–Einstein condensates (BEC) system that consists of a two-level impurity atom coupled to a cavity–BEC system with radiation pressure coupling, where the system is weakly driven by a monochromatic laser field. The steady-states behavior of the entire system is researched in the framework of the impurity–cavity coupling dispersive limit. We find that the multiple types of photon steady-state antibunching effects can be obtained when only the dissipation of the cavity is included. Moreover, the strength and frequency range of conventional steady-state antibunching effects of the cavity can be significantly modified by the impurity atom and intrinsic non-linearity of BEC. This result shows that our study can provide a method to tune the antibunching effects of the cavity field. In addition, the non-standard photon blockade or superbunching effect with the suppression of two-photon correlation and enhancement of three-photon correlation can be realized. The frequency range of the superbunching effect also can be changed by the impurity atom and intrinsic non-linearity of BEC. Therefore, our study shows many quantum statistical characteristics in a hybrid cavity–BEC quantum system and its manipulation.

Von Kármán vortex street in dipole BEC induced by a circular moving potential

The dynamical behaviors of a dipole Bose-Einstein condensate (BEC), which is stirred by a circular moving Gaussian potential, are numerically investigated by using the mean-field theory. In this work, the atom is assumed to polarize along the<i> z</i>-axis. Firstly, the stationary state of the system is obtained by solving the quasi-two-dimensional Gross-Pitaevskki equation numerically under periodic boundary conditions. And then, taking the obtained ground state as the initial condition, the dynamic evolution of the dipole BEC system is studied by the time-splitting Fourier spectrum method. Four types of emissions, namely, the stable laminar flow, vortex dipole, Bénard–von Kármán (BvK) vortex street and irregular turbulence, are observed in the wake when the velocity and size of the Gaussian potential change gradually. When the velocity of the Gaussian potential reaches the critical velocity of vortex excitation, vortex pairs with opposite circulations alternately fall off from the surface of the Gaussian potential. Owing to the interaction between the vortex dipoles, the dipoles rotate around their own centers. Finally, a ring structure will be formed and exist in the wake stably for a long time. With the increase of the velocity of Gaussian potential, the period of dipoles shedding is also shortened. For the appropriate velocity and size of the Gaussian potential, the vortex pairs with the same circulations will periodically fall off from the Gaussian potential and stably distributed on the inner and outer rings, forming BvK vortex street. Our caculation reveals that the conditions for forming BvK vortex street when the dipole BEC is stirred with a circular moving potential are very restricted. When the velocity or size of the Gaussian potential continues to increase, the phenomenon of the periodic vortex pairs shedding in the wake of the Gaussian potential will disappear, and the shedding pattern of the dipole BEC becomes irregular. Using experimental parameters, the parameter ranges of different dipole interactions are obtained through numerical calculation. The influences of dipole interactions, velocity and size of the Gaussian potential on different emission are discussed. In the end, the physical mechanisms of different emissions are analyzed by calculating the drag force acting on Gaussian potential.

Soliton solutions of the spin-orbit coupled binary Bose-Einstein condensate system

In a quantum system with spin, spin-orbit coupling is manifested by linking the spin angular momentum of a particle with its orbital angular momentum, which leads to many exotic phenomena. The experimental realization of synthetic spin-orbit coupling effects in ultra-cold atomic systems provides an entirely new platform for exploring quantum simulations. In a spinor Bose-Einstein condensate, the spin-orbit coupling can change the properties of the system significantly, which offers an excellent opportunity to investigate the influence of spin-orbit coupling on the quantum state at the macroscopic level. As typical states of macroscopic quantum effects, solitons in spin-orbit coupled Bose-Einstein condensates can be manipulated by spin-orbit coupling directly, which makes the study on spin-orbit coupled Bose-Einstein condensates become one of the hottest topics in the research of ultracold atomic physics in recent years. This paper investigates exact vector soliton solutions of the Gross-Pitaevskii equation for the one-dimensional spin-orbit coupled binary Bose-Einstein condensates, which has four parameters <inline-formula><tex-math id="M1">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M1.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M2.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$\beta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M4.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M5">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M5.png"/></alternatives></inline-formula> denotes the strength of the spin-orbit coupling, <inline-formula><tex-math id="M6">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M6.png"/></alternatives></inline-formula> is the detuning parameter, <inline-formula><tex-math id="M7">\begin{document}$\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M7.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$\beta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M8.png"/></alternatives></inline-formula> are the parameters of the self- and cross-interaction, respectively. For the case <inline-formula><tex-math id="M9">\begin{document}$\beta=\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M9.png"/></alternatives></inline-formula>, by a direct ansatz, two kinds of stripe solitons, namely, the oscillating dark-dark solitons are obtained; meanwhile, a transformation is presented such that from the solutions of the integrable Manakov system, one can get soliton solutions for the spin-orbit coupled Gross-Pitaevskii equation. For the case <inline-formula><tex-math id="M10">\begin{document}$\beta=3\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M10.png"/></alternatives></inline-formula>, a bright-W type soliton for <inline-formula><tex-math id="M11">\begin{document}$\alpha>0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M11.png"/></alternatives></inline-formula> and a kink-antikink type soliton for <inline-formula><tex-math id="M12">\begin{document}$\alpha<0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M12.png"/></alternatives></inline-formula> are presented. It is found that the relation between <inline-formula><tex-math id="M13">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M13.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M14.png"/></alternatives></inline-formula> can affect the states of the solitons. Based on these solutions, the corresponding dynamics and the impact of the spin-orbit coupling effects on the quantum magnetization and spin-polarized domains are discussed. Our results show that spin-orbit coupling can result in rich kinds of soliton states in the two-component Bose gases, including the stripe solitons as well as the classical non-stripe solitons, and various kinds of multi-solitons. Furthermore, spin-orbit coupling has a remarkable influence on the behaviors of quantum magnetization. In the experiments of Bose-Einstein condensates, there have been many different methods to observe the soliton states of the population distribution, the magnetic solitons, and the spin domains, so our results provide some possible options for the related experiments.