Spontaneous symmetry breaking of dual-layer solitons in spin–orbit-coupled Bose–Einstein condensates

It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by interplay cubic attractive nonlinearity spin–orbit coupling (SOC) in binary Bose–Einstein condensates. We introduce a double-layer system, which two condensates, stabilized SOC, linearly coupled tunneling. By means numerical methods, it found symmetric two-layer undergo spontaneous-symmetry-breaking (SSB) bifurcation subcritical type. The produces families asymmetric solitons, exist up to value total norm equal Townes above collapse occurs. This situation terminates at critical inter-layer coupling, beyond SSB absent, as sets earlier. Symmetric destabilized demonstrate dynamical symmetry breaking, combination with intrinsic oscillations or transition collapse, if soliton’s sufficiently large. Asymmetric MMs produced instability start spontaneous drift, addition vibrations. Consideration moving nontrivial problem because SOC breaks Galilean invariance. system supports velocity, they delocalization.