Engineered quantum systems play a central role in quantum information processing. Typically, these systems are strongly coupled to their environments, which presents challenges and opportunities to harness controllable quantum effects in such systems. One of the outstanding challenges is to characterize the quantum correlations that develop in such out-of-equilibrium quantum systems. Here we present a method that utilizes low-dimensional projections of eigenvectors to distinguish different types of correlations in an N-mode open system. The proposed method presents a nontrivial extension of eigenvalue-based analysis employed for such systems; specifically, it not only diagnoses crossovers between weak and strong coupling regimes (also known as “exceptional points”) but also can identify the physical systems of interest spanning the correlated subspaces in different regions of the multimode strong-coupling regime. As a demonstration of this feature, we apply our method to study hybridization physics in a three-mode optomechanical system and determine the parameter regime for efficient sideband cooling of the system in the presence of reservoir correlations.
