Dynamical properties of a driven dissipative dimerized <i>S = 1/2 </i>chain

We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. We deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the non-equilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of non-trivial properties. We characterize these NESS by their frequency and wave-vector content, explore the timescales for transient and relaxation behavior, and discuss the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modelling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials.