Instability-driven dynamics of spin–orbit and Rabi-coupled Bose–Einstein condensates

We investigate the dynamics of quasi-one-dimensional Bose–Einstein condensates (BECs) with spin–orbit and Rabi couplings focusing on the role of nonlinear interactions in shaping the stability and dynamics of quantum phases like plane-wave and stripe-wave phases. Using the Bogoliubov–de-Gennes theory, we first analyze the stability of binary BECs with and without spin–orbit and Rabi couplings. Our results reveal distinct unstable and stable regimes in the nonlinear interaction parameter space, highlighting the emergence of soliton trains, beating effects, and stable breathers in both quantum phases under varying nonlinear interaction strengths and non-equilibrium conditions. Furthermore, we identify that specific combinations of interspecies and intraspecies interactions facilitate the emergence of the stable phonons and infinitesimal roton instabilities, which underpin the dynamically stable superfluid quantum droplet-like nature of the plane-wave and stripe-wave phases. In this context, stable phonons create quantum droplet-like structures in the absence of a trap. However, infinitesimal roton instabilities result in metastable states that can be stabilized with a relatively weak trap leading to stable stripe quantum droplets. These results which are validated through numerical simulations provide deeper insights into the nonlinear effects in spin–orbit and Rabi-coupled BECs.