Thesis 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-ofequilibrium
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 (NESS) are created, controlled, and preserved by the internal and external interactions. This includes a detailed study of non-equilibrium dynamics of drivendissipative 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. We firstly endeavor to thoroughly show that laser-driven infrared-active phonon and triplons reach a coherent steady-state. We present the numerical results by implementing resonant and off-resonant levels for the driven phonon in the triplon-band limit as well as in the weak-to-strong coupling regime. Adopting useful arguments, we derive the analytic expressions for the average of observable dynamics to compare them with the numerical data in the NESS; we find some quantitative agreement. We look at different regimes of the driving frequency and consider what properties they possess; while higher driving frequencies satisfy the description of some aspects, very low ones can create unphysical states. The advantage of the different regimes is that one can better understand the model. To control and preserve the NESS, the region of applicability of all parameters with various regimes is considered. Moreover, a preliminary detailed analysis suggests that the energy flows in different parts of the system can secure a better understanding of the driving, coupling, and damping effect. We employ the same model and equations of motion to study the dynamics in the strong coupling regime by investigating the spin system responses in and around the triplon band to the driven phonon. We find that the stationary state in the strong coupling regime leads to a giant resonant self-blocking effect between the phonon and triplons. We introduce hybrid states representing the frequency renormalization of both lattice and spin sectors over the strong couplings. Understanding how the spin-phonon coupling to both leading and the next-nearestneighbor magnetic interactions with the same degrees of freedom responds to the laser field is an intriguing problem. This problem will be approached in detail for the sake of completeness. To characterize the dimerization of the spin system in all spin-phonon coupling scenarios, we measure the modulation of superexchange integral in the spin sector by the vibration. Furthermore, we analyze the predictions of spin-band renormalization and verify them by comparison with the pump-probe protocols. These protocols also cover another phenomenon – the self-hybrid effect (static effect) – in the presence of very weak probe driving fields. In the final part, the applicability of results in possible materials in the experiment as well as the possible extensions of the implementation are presented.

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