Enhanced quantum thermometry near a dissipative phase transition in a driven Kerr cavity

Precise temperature estimation in quantum systems often requires operating near critical regimes where physical observables are highly sensitive to small parameter changes. This paper investigates whether the finite-size precursor of a dissipative phase transition in a driven-dissipative Kerr cavity can be harnessed for enhanced quantum thermometry. The researchers model a single-mode nonlinear cavity coupled to a thermal reservoir, governed by a Lindblad master equation in the presence of a coherent drive. By tuning the drive amplitude and analyzing the steady-state properties, the Liouvillian gap, and the quantum Fisher information (QFI), the authors evaluate the ultimate precision bounds for temperature estimation.

In the thermodynamic limit, a driven-dissipative Kerr cavity exhibits a first-order dissipative phase transition characterized by a discontinuous jump in the steady-state photon density. For finite systems, this transition is smoothed into a crossover region accompanied by a pronounced minimum in the real part of the first nonzero Liouvillian eigenvalue (the Liouvillian gap). This minimum signifies critical slowing down and the emergence of slow relaxation dynamics. Rather than requiring an exactly closed gap—which would cause impractically long relaxation times—the finite-size precursor allows the system to retain a small, finite gap that provides high susceptibility while remaining dynamically accessible.

Computing the quantum Fisher information reveals a sharp peak in temperature sensitivity located precisely near the finite-size transition precursor. This peak aligns closely with the region of rapid steady-state restructuring, where the average photon number exhibits a steep crossover from a low-occupation to a high-occupation branch. By employing an effective two-branch description, the authors demonstrate that the QFI enhancement originates from a temperature-induced redistribution of statistical weight between these low- and high-photon-number branches. Because this mechanism relies on steady-state population restructuring rather than standard thermalization, the enhanced thermometric response persists over an extended low-temperature, low-thermal-occupation regime and remains accessible in circuit-QED-compatible parameter configurations.