PhD Defense of Mohsen Yarmohammadi

Due to the rise in experimental progress in several photonic facilities, theoretical addressing the non-equilibrium behavior in driven-dissipative quantum systems has triggered considerable interest in recent times. This thesis is devoted to the analysis of dynamics of a dimerized spin chain model which is driven out-of-equilibrium by the presence of a classical steady laser field. A particular study is given on the spin-phonon coupling effect treated as weak-to-strong perturbations, that the infrared-active phonon is driven by the laser. All systems in nature are interacting with their surroundings and the effects of the environment have to be approximated. To begin with, we employ the quantum Markovian master equation, which follows the construction of the dissipation path to a phononic bath for both phonon and spin sectors in the driven coupled spin-lattice system. We approach this thesis by exploring how the non-equilibrium steady states are created, controlled, and preserved by the internal and external interactions. This includes a detailed study of non-equilibrium dynamics of driven-dissipative quantum magnetic materials. First, we prepare the tools, protocols, and approximations needed to model a dimerized spin-1/2 chain as a chain of non-interacting triplons. The spin-phonon coupling is treated by the theoretical framework of the mean-field formalism. Second, we approximate the phononic bath with constant damping for each sector to easily derive the master equations of motion for the physical observables in the entire system. Third, we discuss the validity of such approximative master equations by considering many physical degrees of freedom. These settings produce a large variety of interesting phenomena and physical insights.