Engineering quantum Fisher information and non-Markovian dynamics via classical driving in cavity QED

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We investigate the simultaneous control of quantum parameter-estimation precision and non-Markovian memory effects in a driven two-qubit system that is collectively coupled to a leaky cavity. Using a dressed-state formalism, we derive analytical solutions for identical and non-identical qubits and analyze how classical driving and detuning affect metrological performance. Classical driving enhances the quantum Fisher information (QFI) by sustaining coherence and shifting effective transitions away from cavity resonance, thereby suppressing decoherence in both weak- and strong-coupling regimes. The steady-state QFI is further improved by positive classical-field detuning, which reduces spectral overlap with the lossy reservoir. To characterize memory effects, we examine the QFI-flow and the Breuer–Laine–Piilo (BLP) trace-distance measure. Our results reveal a nontrivial control trade-off: increasing the Rabi frequency suppresses non-Markovian information backflow, whereas increasing qubit detuning enhances memory effects by promoting system–environment correlations. Despite their different definitions, the QFI-flow and BLP measures yield consistent qualitative behavior in this system. These findings demonstrate that classical-field parameter tuning empowers researchers to optimize estimation precision and non-Markovianity in dissipative cavity-QED, with direct applicability to superconducting circuit platforms.

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