Collective excitations and universal coarsening dynamics of a spin-orbit-coupled spin-1 Bose-Einstein condensate

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.