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In this work we numerically investigate the fate of theBardeen-Cooper-Schrieffer (BCS) pairing in the presence of quenched phase underPeierls substitution using time-dependent real space and momentum spaceBogoliubov-de Gennes equation methods and Anderson pseudospin representationmethod. This kind of phase imprint can be realized by modulating electric fieldin ultracold atoms and illumining of THz optical pump pulse in solids withconventional and unconventional superconductors. In the case of weak phaseimprint, the BCS pairing is stable; while in the strong phase imprint,instability towards finite-momentum pairing is allowed, in which the real spaceand momentum space methods yield different results. In the pulsed gaugepotential, we find that this instability will not happen even with muchstronger vector potential. We also show that the uniform and staggered gaugepotentials yield different behaviors. While the staggered potential inducestransition from the BCS pairing to over-damped phase, the uniform gauge mayenhance the pairing and will not induce to the over-damped phase. These resultmay shade light on the realization of finite momentum pairing, such asFulde-Ferrell-Larkin-Ovchinnikov phase with dynamical modulation.

Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phases