Quantum measurement and many-body dynamics for the Dicke model

The Dicke model (DM) is a well-suited system for exploring enhanced metrology and quantum information processing. An entangled spin-boson cat-state in the DM is obtained when the spin and boson degrees of freedom interact in the strong coupling limit. This entangled spin-boson cat-state is a metrological resource to the spin cat-state in terms of the spin degrees of freedom. However, it is difficult to experimentally explore features of coherence of the entangled spin-boson cat state, and it is hard to control and measure the boson and spin degrees of freedom simultaneously. Treating the spin subsystem as the main system of interest, we consider the bosonic degrees of freedom as an environment that can be controlled and probed to some extent. We investigate a measurement process on the bosonic system to extract partial information about the spin system. The degree to which the spin system is affected by such a measurement can be controlled by the coupling strength between the spin and boson systems. We also discuss the measurement context on the bosonic system to preserve or retrieve coherence of the spin subsystem.