Nonequilibrium quantum thermometry with noncommutative system-bath couplings

TL;DR

Problem: precise temperature estimation in quantum and cryogenic regimes is challenging due to nonequilibrium and memory effects. Approach: analyze a single-qubit thermometer in a spin-boson setting with a tunable noncommuting coupling σ_α, deriving an exact non-Markovian master equation and evaluating QFI and coherence vs population observables. Findings: noncommutative couplings generate strong interference between dephasing and dissipative channels, causing coherence trapping and a quadratic low-T scaling of QFI; intermediate α optimizes nonequilibrium thermometric sensitivity, and coherence-based measurements are most informative early on. Significance: demonstrates a practical resource for high-precision quantum thermometry in realistic open systems and suggests experimental routes in superconducting and spin-photon platforms.

Abstract

Accurate temperature estimation in the quantum and cryogenic regimes remains a fundamental challenge. Here, we investigate nonequilibrium quantum thermometry using a single-qubit probe coupled to a bosonic bath through noncommuting interaction operators, which unify pure dephasing and dissipative dynamics within a spin-boson model. We show that the interference between these two coupling channels induces strong non-Markovian feedback between populations and coherences, leading to coherence trapping and enhanced thermal sensitivity. Remarkably, by tuning the coupling structure, the probe's temperature sensitivity exhibits a quadratic low-temperature scaling, even under weak coupling. Moreover, while coherence-based measurements are formally suboptimal, they become the most informative in the early nonequilibrium regime, where memory effects dominate. Our findings identify noncommutative system-bath couplings as a practical and tunable resource for achieving high-precision quantum thermometry in realistic open-system architectures.

Figures (3)

• Figure 1: Top panel: Qubit coherence dynamics visualized as a path on the Bloch sphere equator, where the left (right) panel stands for $\alpha=1/2$ ($\alpha=0$ and $\alpha=1$). Bottom panel: plots of Non-Markovianity (Blue line) and the absolute value of $\Delta_x (t\to\infty)$ (red-dashed line) versus $\alpha$. Moreover, we set $T=0.2~\omega_c$, $\varepsilon=0.5~\omega_c$, and $\eta=0.05$.
• Figure 2: Top panel: QFI as a function of the mixing parameter $\alpha$ for fixed short and intermediate times. Bottom panel: QFI at large times. All other parameters are the same as in Fig. (\ref{['fig: 1']}).
• Figure 3: Top panel: QFI as a function of temperature for different probing times. The black solid line shows the $T^2$ scaling. The dotted line indicates the Fisher information obtained from the steady state of a secular Born–Markov master equation, which exhibits exponential scaling at low temperatures. Bottom panel: Fisher information obtained from coherence-based measurements (solid lines) and population-based measurements (dashed lines). Moreover, we set $\alpha = 1/2$, $\varepsilon = 0.5\omega_c$, and $\eta = 0.05$.