Symmetries and conserved quantities in open quantum systems

Recent developments in quantum engineering and quantum information highlight the need to better understand the steady-state behavior of open systems whose steady state is dependent on initial conditions. This work analyzes the structure and response to perturbations of the steady-state subspace of time-independent Lindblad master equations. We discuss the role of symmetries and conserved quantities in Lindblad systems and show that the effect of the environment in the infinite-time limit can be tracked exactly for arbitrary initial state and without knowledge of dynamics at intermediate time [1]. Applying this approach, we analytically determine the steady state for driven single-mode two-photon absorption and calculate that dephasing is exponentially suppressed to first order in such a system [2]. \newline [1] V.V. Albert and Liang Jiang, arXiv:1310.1523 \newline [2] M. Mirrahimi {\it et al.} (in preparation)