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Physical review. E

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices

Ai-Xia Zhang, Xiao-Wen Hu, Yan-Fang Jiang, Jun-Cheng Liang, Ying Zhang, Wei Zhang, Ju-Kui Xue

Published Dec 28, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreve.104.064215

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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.
The Bose-Einstein condensates in a finite depth potential well provide an ideal platform to study the quantum escape dynamics. In this paper, the ground state, tunneling, and diffusion dynamics of the spin-orbit coupling (SOC) of Bose-Einstein condensates with two pseudospin components in a shallow trap are studied analytically and numerically. The phase transition between the plane-wave phase and zero-momentum phase of the ground state is obtained. Furthermore, the stability of the ground state is discussed, and the stability diagram in the parameter space is provided. The bound state (in which condensates are stably trapped in the potential well), the quasibound state (in which condensates tunnel through the well), and the unstable state (in which diffusion occurs) are revealed. We find that the finite depth potential well has an important effect on the phase transition of the ground state, and, interestingly, SOC can stabilize the system against the diffusion and manipulate the tunneling and diffusion dynamics. In particular, spatial anisotropic tunneling and diffusion dynamics of the two pseudospin components induced by SOC in quasibound and unstable states are observed. We provide an effective model and method to study and control the quantum tunneling and diffusion dynamics.
We study two types of bright solitons in an attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schrödinger equations with the variational method and the imaginary time evolution method, fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength. The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose–Einstein condensate.
We study the collective dynamics of the spin-orbit coupled two pseudospin components of a Bose-Einstein condensate trapped in a quasi-one-dimensional harmonic potential, by using variational and directly numerical approach of binary mean-field Gross-Pitaevskii equations. The results show that, because of strong coupling of spin-orbit coupling (SOC), Rabi coupling, and atomic interaction, the collective dynamics of the system behave as complex characters. When the Rabi coupling is absent, the density profiles of the system preserve the Gauss type and the wave packets do harmonic oscillations. The amplitude of the collective oscillations increases with SOC. Furthermore, when the SOC strength increases, the dipole oscillations of the two pseudospin components undergo a transition from in-phase to out-of-phase oscillations. When the Rabi coupling present, there will exist a critical value of SOC strength (which depends on the Rabi coupling and atomic interaction). If the SOC strength is less than this critical value, the density profiles of the system can preserve the Gauss type and the wave packets do anharmonic (the frequency of dipole oscillations depends on SOC) oscillations synchronously (i.e., in-phase oscillations). However, if the SOC strength is larger than this critical value, the wave packets are dynamically fragmented and the stable dipole oscillations of the system can not exist. The collective dynamics of the system can be controlled by adjusting the atomic interaction, SOC, and Rabi-coupling strength.
The existence and dynamics of solitons in quasi-one-dimensional Bose-Einstein condensates with spin-orbit coupling (SOC) and attractive two-body interactions are described for two coupled atomic pseudospin components with slowly and rapidly varying time-dependent Raman frequency. By varying the Raman frequency linearly in time, it was shown that ordinary nonlinear Schr\"odinger-type bright solitons can be converted to striped bright solitons, and vice versa. The internal Josephson oscillations between atom number of the coupled soliton components and the corresponding center-of-mass motion are studied for different parameter configurations. In this case, a mechanism to control the soliton parameters is proposed by considering parametric resonances, which can emerge when using time-varying Raman frequencies. Full-numerical simulations confirm variational analysis predictions when applied to the region where regular solitons are expected. In the limit of high frequencies, the system is described by a time-averaged Gross-Pitaevskii formalism with renormalized nonlinear and SOC parameters and modified phase-dependent nonlinearities. By comparing full-numerical simulations with averaged results, we have also studied the lower limits for the frequency of Raman oscillations in order to obtain stable soliton solutions.
The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC's) in deep DDD-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC's, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.
We study analytically and asymptotically, as well as numerically, ground states and dynamics of two-component spin-orbit-coupled Bose--Einstein condensates (BECs) modeled by the coupled Gross--Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynamical properties become very rich and complicated. For the ground states, we establish existence and nonexistence results under different parameter regimes and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either nonperiodic or with different frequency than the trapping frequency when the external trapping potential is taken as harmonic and/or the initial data is chosen as a stationary state (e.g., ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclassical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.