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Physical review. E

Collective dynamics of a spin-orbit-coupled Bose-Einstein condensate

Fang-Qi Hu, Jianjun Wang, Zi-Fa Yu, Ai‐Xia Zhang, Ju-Kui Xue

Published Feb 18, 2016• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.93.022214

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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.
We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin–orbit coupled spin-1 Bose–Einstein condensates trapped in harmonic potential. The ground state of the system is determined by minimizing the Lagrange density, and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically, and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly. The coupling among spin–orbit coupling, Raman coupling and spin-dependent interaction results in multiple external collective modes, which leads to the anharmonic collective dynamics. The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics, which strongly depends on spin-dependent interaction and behaves distinct characters in different phases. Interestingly, in the absence of spin-dependent interaction, the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic. Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.
We investigate the dynamics of kicked pseudo-spin-1/2 Bose–Einstein condensates (BECs) with spin–orbit coupling (SOC) in a tightly confined toroidal trap. The system exhibits different dynamical behaviors depending on the competition among SOC, kick strength, kick period and interatomic interaction. For weak kick strength, with the increase of SOC the density profiles of two components evolve from overlapped symmetric distributions into staggered antisymmetric distributions, and the evolution of energy experiences a transition from quasiperiodic motion to modulated quantum beating. For large kick strength, when the SOC strength increases, the overlapped symmetric density distributions become staggered irregular patterns, and the energy evolution undergoes a transition from quasiperiodic motion to dynamical localization. Furthermore, in the case of weak SOC, the increase of kick period leads to a transition of the system from quantum beating to Rabi oscillation, while for the case of strong SOC the system demonstrates complex quasiperiodic motion.
We present the collective excitation spectrum analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a quasi-two-dimensional system. In particular, we investigate the role of SO and Rabi coupling strengths in determining the dynamical stability of the coupled BECs using Bogoliubov--de Gennes (BdG) theory. Using the eigenenergy of the BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and interspecies contact interactions. The depth of the minimum corresponding to the roton mode strongly depends on the coupling strength. We find that the increase of the SO coupling leads to instability, while the increase in the Rabi coupling stabilizes the system. Also, the eigenvectors of the BdG spectrum indicate the presence of a densitylike mode in the stable regime and spinlike modes in the unstable regimes. A phase diagram demonstrating the stability regime in the plane of SO and Rabi coupling strengths is obtained. Finally, we complement the observation of the excitation spectrum with the direct numerical simulation results of coupled Gross-Pitaevskii equations.
The collective excitations of a spin-orbit–coupled Bose-Einstein condensate are investigated by using a variational method and numerical simulation. The collective modes are depicted in zero-momentum and plane-wave phases, while the mechanism for inducing the anharmonic collective oscillations is revealed analytically. The coupling among spin-orbit coupling, Raman coupling, and atomic interaction results in multiple external collective modes, which can lead to the collective dynamics being the superposition of the multiple harmonic oscillations. When one of the external frequencies is close to the inherent frequency of the conventional condensate and the amplitudes of other external frequencies vanish, the collective oscillations are harmonic, otherwise the collective oscillations are anharmonic. Thus the collective dynamics can undergo a harmonicity-anharmonicity transition. This can provide a possible way for elaborating distinct collective oscillation modes. Moreover, the collective excitations exhibit distinct properties in different phases, while the softening of collective modes is detected at the phase transition point, which can be used to map out the phase boundaries in experiment.
This study explores the dynamics of Bose-Einstein condensates (BECs) with helicoidal spin-orbit coupling (SOC) and Rabi coupling, confined under a two-dimensional harmonic potential. The relationship between helicoidal SOC, non-linear interactions along with Rabi coupling and their impact on the stability and non linear trapped modes of the condensate is analyzed using a coupled Gross-Pitaevski (GP) framework. A linearized GP equation is used to investigate modulation instability (MI), demonstrating the impact of strong coupling effects and anisotropic confinement on the instability dynamics. It has been shown that the modulation instability in the condensate is predominantly governed by the competition between the attractive and repulsive mean-field interactions. Additionally, stability regimes are altered by the harmonic confinement, enhancing their susceptibility to SOC-induced asymmetry and intra- and intercomponent interactions. These results shed light on the possibility for unique quantum phases and emergent characteristics of helicoidal SOC-driven condensates.
In this paper, we study the spin dynamics of spin-orbit-coupled (SOC) spin-2 Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the nonlocal Gross–Pitaevskii equation. Our discussions are divided into two parts. In the absence of DDI, the spin dynamics presents periodic oscillation. Increasing the magnetization makes the amplitude increase, and increasing SOC strength accelerates the spin dynamics and thus changes the period. Nevertheless, in the presence of DDI, the periodicity oscillation of spin dynamics is broken. The thermalization time decreases with the increase of magnetization for fixed SOC strength. In addition, the thermalization time becomes zero with strong SOC strength when magnetization is fixed. We also show the formation of domain in density profile when DDI is considered. Moreover, the components m = 2 and m = −2 exchange their location with a little increase of SOC strength. This is a specific reflection of the competition between the SOC and DDI.