Apart from quantum squeezing and entanglement, criticality is considered as a valuable resource for quantum sensing. They have a close relationship since squeezing and entanglement can be generated when a quantum system approaches the critical point of phase transition. To understand and improve critical metrology, it is necessary to study the strategy with squeezing prepared in the initial state. Here, we study quantum-sensing strategies in the quantum Rabi model with the system initially prepared in a squeezed thermal state, and the coupling of the system to a squeezed thermal reservoir is also taken into account. We characterize the metrological capability with the quantum Fisher information (QFI). It is found that the QFI can be grouped into two terms relating to variations in amplitudes and phase of system second-order operator moments, respectively. The classifications of the QFI provide privileges for delineating weights of variations coming from different physical origins, and thereby have implications on optimal measurement strategies design. Both the noiseless case and that with dissipation are studied. The role of initial state and reservoir quantum properties, criticality, and their interplay in quantum metrology are investigated in detail. We also identify time scaling of the QFI and propose feasible measurement schemes achieving the sensitivity bound of parameter estimation set by the QFI. Our analysis can be generalized to a diversity of quantum-sensing tasks.

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• Quantum Fisher information
• Quantum phase transitions