The temperature sensitivity of a probe in equilibrium can be gauged by its thermal quantum Fisher information (QFI). It is known that probes exhibiting degeneracy in their energy-level structure can achieve larger sensitivities, while probes with a more uniform spectrum may remain sensitive over a broader temperature range. Here, we study the thermometric performance of a multilevel quantum Rabi model in which two well-separated atomic manifolds of near-degenerate levels couple to a single cavity mode. We generalise the standard quantum Rabi treatment in the adiabatic regime to find an approximate closed-form expression for the thermal QFI. We then characterise two complementary limits. On the one hand, a large dark-state manifold (dark-manifold saturation) produces a robust peak in thermal sensitivity due to bright--dark population transfer. Such increase in sensitivity is further maximised at an intermediate light--matter coupling strength. Maximising instead the number of bright states (bright-manifold saturation) generates a broadband thermal response that becomes increasingly stable under random light--matter couplings as the number of levels is increased. The rich spectral structure of our cavity-QED model thus makes it a versatile and sensitive equilibrium thermometer over a broad range of temperatures.
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术国际理论中心）；Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano（米兰大学阿尔多·蓬特莫利物理系）
Collective Chirped STIRAP in a Pair of Three-Level Atoms: Dressed-Manifold Dynamics and Compensation of the Rydberg-Rydberg Interaction-Induced Detuning
