Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

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.

Automated summary

We analytically and numerically study the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates in a harmonic potential. The ground state is determined by minimizing the Lagrange density, and the equations of motions for the center-of-mass coordinate and width are derived. We obtain two low energy excitation modes, breathing dynamics and dipole dynamics, analytically, and reveal the mechanism of exciting anharmonic collective dynamics. The coupling among spin-orbit coupling, Raman coupling, and spin-dependent interaction leads to multiple external collective modes and coupling between dipolar and breathing dynamics, with distinct behaviors in different phases.