Anomaly to Resource: The Mpemba Effect in Quantum Thermometry

TL;DR

The paper demonstrates that the quantum Mpemba effect can be harnessed as a resource for finite-time quantum thermometry. By proving that Mpemba inversions guarantee a finite-time boost of the temperature QFI, it shows that hotter nonequilibrium preparations can transiently outperform both colder and equilibrium strategies, illustrated with two-level and $\Lambda$-level probes in bosonic baths. A concrete sensing workflow is developed, combining equilibrium calibration, dynamical Mpemba detection, and an empirical Fisher-information map to identify optimal finite-time measurement windows for unknown-bath temperature estimation. This work reframes anomalous relaxation as a general design principle for ultrafast, nanoscale quantum sensing, potentially enabling robust nonequilibrium thermometry in fast, noisy, or nonstationary settings. $F_T$-based metrological gains are demonstrated conceptually and provide a clear path toward experimental realization on current platforms like superconducting circuits, trapped ions, and NV centers.

Abstract

Quantum thermometry provides a key capability for nanoscale devices and quantum technologies, but most existing strategies rely on probes initialized near equilibrium. This equilibrium paradigm imposes intrinsic limitations: sensitivity is tied to long-time thermalization and often cannot be improved in fast, noisy, or nonstationary settings. In contrast, the \textit{Mpemba effect}, the counterintuitive phenomenon where hotter states relax faster than colder ones, has mostly been viewed as a thermodynamic anomaly. Here, we bridge this gap by proving that Mpemba-type inversions generically yield a finite-time enhancement of the quantum Fisher information (QFI) for temperature estimation, thereby converting an anomalous relaxation effect into a concrete metrological resource. Through explicit analyses of two-level and $Λ$-level probes coupled to bosonic baths, we show that nonequilibrium initializations can transiently outperform both equilibrium strategies and colder states, realizing a \emph{metrological Mpemba effect}. Our results establish anomalous relaxation as a general design principle for nonequilibrium quantum thermometry, enabling ultrafast and nanoscale sensing protocols that exploit, rather than avoid, transient dynamics.

Figures (5)

• Figure 1: Schematic of the metrological Mpemba effect.
• Figure 2: Relaxation of the excited state population with mpemba crossover of the hotter state over the close to equilibrium state. The Hamiltonian parameter: atomic frequency $\omega_0 = 1.0$, spontaneous emission rate $\gamma = 1.0$, and the bath temperature $T = 0.5$ (in units of $\omega_0$).
• Figure 3: QFI with the variation of time $t$ where the hotter state is denoted by red and the near equilibrium state is denoted by blue for (a) two-level probe, and (b) $\Lambda-$level probe. The Hamiltonian parameters are the same as fig. \ref{['fig1']}.
• Figure 4: (a) Mpemba-enhanced QFI Gain in log scale with time for the two-level probe. (b) Density plot of QFI over the initial state and time for the two-level probe. It shows a clear gain of the Mpemba effect. The Hamiltonian parameters are the same as Fig. \ref{['fig1']}.
• Figure 5: Same as Fig. 4b (of main text), clearly showing the influence of the Mpemba effect.

Theorems & Definitions (1)

• Theorem 1