Collisionless dynamics of the superconducting gap excited by a spin-splitting field

We study the coherent dynamic interaction of a time-dependent spin-splitting field with the homogeneous superconducting order parameter A(t) mediated by spin-orbit coupling using the time-dependent Bogoliubov-de Gennes theory. In the first part of the work we show that the linear response of the superconductor is strongly affected by the Zeeman field and spin-flip processes, giving rise to multiple resonant frequencies of the superconducting Higgs modes, which can be coupled linearly to the fluctuating part of the Zeeman field. In the second part, we analyze the nonadiabatic dynamics of quasiparticle states arising from the intersection of spectral branches from different spin subbands provoked by a monotonically changing Zeeman field. Nonadiabatic spin-flip tunneling in the spectrum leads to drastic change in the order parameter A(t) above the Pauli limit and results in a nonequilibrium magnetization of the quasiparticle gas.