Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field

We provide a theoretical framework to describe the quantum many-body dynamics of Andreev states in Josephson junctions with spin-orbit coupling and a magnetic Zeeman field. In such cases, employing a doubled Nambu spinor description is technically advantageous but one then has to be careful to avoid double-counting problems. By deriving the Lindblad master equation in the so-called excitation picture, we show that a physically consistent many-body theory free from double-counting problems follows. We apply our formalism to a study of dynamical parity stabilization of the Andreev sector at intermediate times after an initial microwave pulse, in particular addressing the combined effects of spin-orbit coupling and Zeeman field.