Nonadiabatic dynamics of superfluid spin-orbit-coupled degenerate Fermi gas

We study a problem of nonadiabatic superfluid dynamics of spin-orbit-coupled neutral fermions in two spatial dimensions. We focus on the two cases when the out-of-equilibrium conditions are initiated by either a sudden change of the pairing strength or the population imbalance. For the case of a zero-population imbalance and within the mean-field approximation, the nonadiabatic evolution of the pairing amplitude in a collisionless regime can be found exactly by employing the method of Lax vector construction. Our main finding is that the presence of the spin-orbit coupling significantly reduces the region in the parameter space where a steady state with periodically oscillating pairing amplitude is realized. For the collisionless dynamics initiated by a sudden disappearance of the population imbalance, we obtain an exact expression for the steady-state pairing amplitude. In the general case of quenches to a state with finite population imbalance, we show that there is a region in the steady-state phase diagram where at long times the pairing amplitude dynamics is governed by the reduced number of the equations of motion in full analogy with the exactly integrable case.