Patterning by dynamically unstable spin–orbit-coupled Bose–Einstein condensates

In a two-dimensional atomic Bose-Einstein condensate, we demonstrate Rashba spin-orbit coupling can always introduce dynamical instability into specific zero-quasimomentum states in all parameter regimes. During the evolution of states, such spin-orbit-coupling-induced fragment and lead to dynamically patterning process. The features formed patterns are identified from symmetries Bogoliubov-de Gennes Hamiltonian. We show that spin-orbit-coupled condensates provide an interesting platform for investigation pattern formations.