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We study the coherent dynamic interaction of a time-dependent spin-splittingfield with the homogeneous superconducting order parameter $\Delta(t)$ mediatedby spin-orbit coupling using the time-dependent Bogoliubov-de Gennes theory. Inthe first part of the work we show that linear response of the superconductoris strongly affected by the Zeeman field and spin-flip processes, giving riseto multiple resonant frequencies of the superconducting Higgs modes. Thesemodes can be excited either by a quench, or by an additional non-stationarycomponent of the spin-splitting field, which couples linearly to the Higgsmodes. In the second part, we analyze the nonadiabatic dynamics ofquasiparticle states arising from the intersection of spectral branches fromdifferent spin subbands, which can be provoked by a linearly growing Zeemanfield. We provide insights into the dependence of the order parameter$\Delta(t)$ on this field and interference effects caused by tunneling ofstates at the avoided crossing points. We also show that since the nonadiabatictunneling is related to spin-flip processes, the quasiparticle gas experiencesa dynamic magnetization that contributes to its spin susceptibility.

Collisionless dynamics of superconducting gap excited by spin-splitting field