Spectroscopy and critical quantum thermometry in the ultrastrong coupling regime

We present an exact analytical solution of the anisotropic Hopfield model, and we use it to investigate in detail spectral thermometric response two ultrastrongly coupled quantum systems. Interestingly, show that depending on initial state system, vacuum Rabi splitting manifests significant asymmetries may be considered signatures counterintuitive decoupling effect. Using system as a thermometer for thermodynamics applications, obtain ultimate bounds estimation temperature remain valid ultrastrong coupling regime. Remarkably, if performs phase transition, Fisher information exhibits periodic divergences, suggesting one can have several points arbitrarily high precision such critical sensor.