Quantum metrology in the ultra-strong coupling limit

The recent theoretical and experimental advancements in controlling light-matter interactions place us on the verge of exploring and harnessing the physics of ultra-strong coupling, where the light-matter coupling strength is comparable to (but not greater than) the transition frequencies of the system. This regime leads to many counter-intuitive and intriguing physical effects. Most importantly, the system ground states are predicted to be strongly entangled which opens a possibility to harness them in quantum technologies. Interestingly, this entanglement exists only on the virtual level and thus cannot be destroyed and detected in a conventional manner, for example, by measuring correlations between atoms and photons. This rises questions whether such ground state entanglement can be useful for quantum technologies at all. Although virtual, the ground state entanglement manifests itself in properties of physical particles (or excitations) that are being measured in experiments. For example, virtual squeezing can manifest itself as non-linear frequency shifts of polaritons, which depend on the parameters of the system. If these modifications of physical excitations caused by virtual excitations are highly controlled, one might potentially use them for certain quantum technologies. In the talk, I will present how driving an ultra-strongly coupled light-matter system with a (non-classical) light can be used to harness the virtual entanglement in precision measurements. To this end, we consider an ensemble of atoms ultra-strongly coupled to a single mode cavity described by the paradigmatic Dicke model.