Metastable dynamics of Rydberg electromagnetically induced transparency

Open quantum systems, which are coupled to an external bath, are a critical research field of quantum physics. The steady state, which is a state that any initial state converges after a long time, usually attracts the most interest. In contrast, there are relatively few studies on the nonequilibrium dynamical processes of quantum many-body systems. This is mainly due to the fact that quantum many-body systems generally have interactions, and the Hilbert space required for a complete description of their dynamical processes will grow exponentially with the number of particles and the computational diffculty will increase dramatically as well. Hence the complete description of their dynamical processes has been a diffcult problem. With the advancing quantum technologies, there is increasing interest in the nonequilibrium dynamics of open quantum many-body systems. A common phenomenon is that of metastability, where the system initially relaxes into long-lived states, with subsequent converging to the final stationarity at much longer times. In this paper, we establish a low dimensional approximation to describe the metastability dynamics in Markovian open quantum systems, based on the spectra of the Liouvillian super-operator. The separation of time scales implies a splitting in the spectrum, and this spectral division allows us to eliminate the fast decay modes by perturbation method, and then we establish the effective description in the low-lying eigenmodes subspace. Furthermore, we study the dynamics process for the Rydberg atomic systems under electromagnetically induced transparency (EIT) conditions and find that the system can process metastable dynamics if the interactions between the atoms are considered. We compare the effective dynamics in the subspace and the actual dynamics in the full space, and the results show that the effective dynamics works well under the condition that the perturbation approximation holds. Our work provides a feasible idea and method to establish an effective and simplified description of the dynamical process of open quantum many-body systems.