Spin-orbit coupling effects on localization and correlated tunneling for two interacting bosons in a double-well potential

We theoretically study the tunneling dynamics of two interacting spin-orbit-coupled (SOC) atoms trapped in a periodically perturbed double-well potential. We find that the phenomenon of coherent destruction of tunneling (CDT) can exist only for certain values of SOC, and two different mechanisms for the appearance of CDT are identified in this system. One is the conventional CDT resulting from quasi-energy degeneracy, while the other CDT originates from the dark Floquet state with zero quasi-energy for all values of the driving parameters. We discover that under double modulation combining the double-well potential shaking and a time-periodic Zeeman field, it is possible to realize spin-flipping single-atom Rabi tunneling and the CDT induced by the dark Floquet state at any value of SOC strength, which is not accessible with a single-drive field. Furthermore, we show that the detuning of Zeeman field with respect to the multiphoton energy is particularly significant in the case of the correlated two-particle tunneling mediated by SOC. We expect that these results will stimulate further exploration of the many-body dynamics in the interacting systems and expand the possibilities for manipulating the spin dynamics.