Ground-state phase and superfluidity of tunable spin-orbit-coupled Bose-Einstein condensates.

We theoretically study the ground-state phases and superfluidity of tunable spin-orbit-coupled Bose-Einstein condensates (BECs) under the periodic driving of Raman coupling. An effective time-independent Floquet Hamiltonian is proposed by using a high-frequency approximation, and we find single-particle dispersion, spin-orbit-coupling, and asymmetrical nonlinear two-body interaction can be modulated effectively by the periodic driving. The critical Raman coupling characterizing the phase transition and relevant physical quantities in three different phases (the stripe phase, plane-wave phase, and zero momentum phase) are obtained analytically. Our results indicate that the boundary of ground-state phases can be controlled and the system will undergo three different phase transitions by adjusting the external driving. Interestingly, we find the contrast of the stripe density can be enhanced by the periodic driving in the stripe phase. We also study the superfluidity of tunable spin-orbit-coupled BECs and find the dynamical instability can be tuned by the periodic driving of Raman coupling. Furthermore, the sound velocity of the ground-state and superfluidity state can be controlled effectively by tuning the periodic driving strength. Our results indicate that the periodic driving of Raman coupling provides a powerful tool to manipulate the ground-state phase transition and dynamical instability of spin-orbit-coupled BECs.