Detecting initial correlations via correlated spectroscopy in hybrid quantum systems.

Generic mesoscopic quantum systems that interact with their environment tend to display appreciable correlations with environment that often play an important role in the physical properties of the system. However, the experimental methods needed to characterize such systems either ignore the role of initial correlations or scale unfavourably with system dimensions. Here, we present a technique that is agnostic to system-environment correlations and can be potentially implemented experimentally. Under a specific set of constraints, we demonstrate the ability to detect and measure specific correlations. We apply the technique to two cases related to Nitrogen Vacancy Centers (NV). Firstly, we use the technique on an NV coupled to a P1 defect centre in the environment to demonstrate the ability to detect dark spins. Secondly, we implement the technique on a hybrid quantum system of NV coupled to an optical cavity with initial correlations. We extract the interaction strength and effective number of interacting NVs from the initial correlations using our technique.