We propose a mechanism to realize nontrivial spin dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate by abruptly shaking the harmonic trap. Continuously varying the shaking strength, it is found that the Bose-Einstein condensate may exhibit exotic nonequilibrium spin dynamics. Specifically, at some special values of the shaking strength, the time-averaged spin polarization shows sharp resonant peaks, whereas it tends to be zero at any other positions. Furthermore, the spacings between any two nearest peaks depend only on the system parameters and are thus identical to each other. By simplifying this time-dependent system to an exactly solvable ``quantum quench'' model, we show that the essential physics behind the exotic spin dynamics comes from periodic suppressing and enhancing of the out-of-phase interference. It is further shown that the presented physical picture persists under weak atomic interactions. This work may shed light on the ongoing research of spin-based quantum control and quantum information.
We propose a mechanism to realize nontrivial spin dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate by abruptly shaking the harmonic trap. Continuously varying the shaking strength, it is found that the Bose-Einstein condensate may exhibit exotic nonequilibrium spin dynamics. Specifically, at some special values of the shaking strength, the time-averaged spin polarization shows sharp resonant peaks, whereas it tends to be zero at any other positions. Furthermore, the spacings between any two nearest peaks depend only on the system parameters and are thus identical to each other. By simplifying this time-dependent system to an exactly solvable ``quantum quench'' model, we show that the essential physics behind the exotic spin dynamics comes from periodic suppressing and enhancing of the out-of-phase interference. It is further shown that the presented physical picture persists under weak atomic interactions. This work may shed light on the ongoing research of spin-based quantum control and quantum information.
We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
Dynamical characteristics of internal and external states of a Bose-Einstein condensate are generally different and independent, thus requiring different experimental manipulation techniques. The spin-orbit coupling recently achieved in Bose-Einstein condensates essentially connects spin and motion degree of freedom, endowing spin states with the ability to respond to orbital manipulation, and vice versa. In this work, a dynamical response effect, induced by simultaneously manipulating the internal and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulating the internal and external states” means that the driving field combines the Zeeman field applied to the internal state of the atom and the orbital potential affecting the external states of the atom. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e. neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relationship connecting spin frequency spectrum and the parameters of the driving fields is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in good agreement with the results from the analytical relationship. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. Due to the fact that a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here provides a candidate method for determining and calibrating various system parameters by measuring the spin frequency spectrum.
We study the collective excitation spectrum of a Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap while varying either the Raman coupling or quadratic Zeeman field strength by using the Bogoliubov approach. A few low-lying modes, which can be used to delineate the phase boundaries, are identified by exciting them with suitable perturbations. We also investigate the coarsening dynamics of a homogeneous quasi-two-dimensional spin-orbit-coupled spin-1 condensate by quenching from the zero momentum into the plane wave phase through a sudden change in Raman coupling or quadratic Zeeman field strength. We demonstrate that the correlation function of the order parameter displays dynamic scaling during the late-time dynamics, allowing us to determine the dynamic critical exponent.
We investigate the ground-state phases and spin-scissors dynamics of binary Bose-Einstein condensates confined in a twisted two-dimensional harmonic trap. The ground state hosts three distinct phases-phase-separated, polarized, and phase-mixed-determined by the Rabi coupling, interaction ratio G (between inter-component and intra-component interactions), and spin-twisting which induces edge-localized polarization through position-dependent detuning. In the phase-mixed regime, the ground state is characterized by a finite spin-scissors susceptibility and can be accurately described using local density approximation. In the dynamics, the system exhibits stable periodic beating in the phase-mixed state for G<1. For G>1, its evolution progresses from beat damping (phase-separated state) to polarized relaxation (polarized state), finally reaching stable periodic beating (phase-mixed state) after a finite waiting time. The dependence of the waiting time contrasts sharply with the monotonic behavior of one-dimensional spin-dipole dynamics, revealing qualitatively distinct mechanisms governed by geometry and interactions. In summary, these results establish a unified link between ground-state properties and nonequilibrium responses in twisted spinor condensates, offering a versatile platform for exploring spin-related quantum many-body phenomena.
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.