Metrological power of single-qubit dynamical Casimir effect in circuit QED

We consider a nonstationary circuit QED system described by the quantum Rabi model, in which an artificial two-level atom with a tunable transition frequency is coupled to a single-mode resonator. We focus on regimes where the external modulation takes the form $\sin[η(t) t]$, with the modulation frequency $η(t)$ varying slowly and linearly in time near $2ν$ and $4ν$, $ν$ being the resonator frequency. Starting from the vacuum state, we numerically compute the Quantum Fisher Information for single-mode phase and displacement estimation, showing that it significantly exceeds the classical limits for the same average photon number, even in the presence of dissipation. Thus, appropriate parametric modulation of the qubit not only simulates the dynamical Casimir effect but also enables the generation of nonclassical states of light that offer a metrological advantage over classical states of equivalent energy.