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