Interaction imbalanced spin-orbit coupled quantum droplets

We explore the ground states and quench dynamics of spin-orbit coupled (SOC) one-dimensional two-component quantum droplets featuring intracomponent interaction imbalance. A plethora of miscible ground state stripe and standard flat-top or Gaussian droplets is found depending on the interplay between the SOC wavenumber and interactions. Deformations among these states are accompanied by controllable spin population transfer. Upon considering a trap we identify a transition from a bound to a trapped gas many-body state, captured through a sign change of the chemical potential, which occurs at lower (larger) atom numbers for tighter traps (stronger interactions). The droplets breathing frequency is found to increase for larger intracomponent interaction ratio or reaches a maximum at SOC wavenumbers where the transition from non-modulated flat-top to stripe droplets exists. Dynamical droplet fragmentation occurs for abrupt changes of the Rabi-coupling, while large amplitude quenches of the SOC wavenumber trigger spin-demixed counterpropagating untrapped droplets or in-trap out-of-phase oscillating ones. Our results offer insights into controlled spin-mixing processes in droplets and the potential excitation of magnetic bound states, opening avenues for further research in this field.