Equilibrium thermometry in the multilevel quantum Rabi model

TL;DR

This paper investigates how a multilevel quantum Rabi model can be used as a sensitive equilibrium thermometer, analyzing its thermal quantum Fisher information and identifying conditions for optimal temperature sensitivity across a broad range.

Contribution

It generalizes the quantum Rabi model to multilevel systems and derives an approximate expression for thermal QFI, revealing mechanisms for enhanced thermometric sensitivity.

Findings

Dark-state manifold enhances sensitivity via population transfer.

Maximum sensitivity occurs at an intermediate light-matter coupling.

Increasing the number of levels broadens the temperature range of sensitivity.

Abstract

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.