Critical quantum metrology in a stabilized two-photon Rabi model

Abstract: We investigate a generalized quantum Rabi model (QRM) with two- and four-photon terms with respect to applications for non-linear critical quantum metrology. In the introduced model, the spectral collapse occurring in the standard two-photon QRM is stabilized by the presence of the quartic potential. The collapse is then transformed into a quantum phase transition, which occurs in the low-frequency limit of the light mode, whose remnant at finite ratio between qubit and mode frequencies can be applied to critically enhanced quantum metrology. We find that the four-photon term entails a much higher measurement precision compared to the standard two-photon QRM. The mechanism behind the higher precision can be traced to the different behavior of the ground state wave function as the system is tuned through the transition. As the standard two-photon QRM, despite the absence of the spectral collapse, our model allows for a finite preparation time for the probe state (PTPS).