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.
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.
We investigate a nonequilibrium quantum thermometry protocol in which an ensemble of qubits, acting as temperature probes, is weakly coupled to a macroscopic thermal bath. The temperature of the bath, the parameter of interest, is encoded in the dissipator of a Markovian thermalization process. For some relevant initial states, we observe a peak in the Quantum Fisher Information (QFI) during the transient of the thermalization, indicating enhanced sensitivity in early-time dynamics. This effect becomes more pronounced at higher bath temperatures and is further enhanced when the initial reduced state of the qubits has a large ground-state population and/or it is highly coherent. We also focus on the role of initial quantum correlations in the thermometric performance, which emerge as a central feature of this work. We find strong numerical evidence that, given same single-qubit reduced states, the inclusion of quantum correlations among the qubits of the ensemble always yields an enhanced QFI. Moreover, even if none of the considered states outperform the (pure, separable) ground state, maximally entangled states display QFIs values remarkably close to the standard quantum limit when probing extremely hot thermal baths. Finally, although the Markovian dynamics does not permit superlinear scaling of the QFI with the number of probes, we identify the most effective initial states for designing high-precision quantum thermometers within this setting. We also provide concrete guidelines for experimental implementations.
Abstract We characterise the measurement sensitivity, quantified by the quantum Fisher information (QFI), of a single-fermionic thermometric probe strongly coupled to the sample of interest, a fermionic bath, at temperature T. For nonequilibrium protocols, in which the probe is measured before reaching equilibrium with the sample, we find new behaviour of the measurement sensitivity arising due to non-Markovian dynamics. First, we show that the QFI displays a highly non-monotonic behaviour in time, in contrast to the Markovian case where it grows monotonically until equilibrium, so that non-Markovian revivals can be exploited to reach a higher QFI. Second, the QFI rate is maximised at a finite interrogation time t ∗ , which we characterize, in contrast to the solution t ∗ → 0 known in the Markovian limit (Pavel Sekatski and Martí Perarnau-Llobet 2022 Quantum 6 869). Finally, we consider probes make up of few fermions and discuss different collective enhancements in the measurement precision.
We study low-temperature non-equilibrium quantum thermometry with a bosonic probe: a quantum harmonic oscillator strongly coupled to a bosonic bath at temperature T through a Drude--Ohmic spectral density. We treat the probe--bath dynamics both exactly, using the quadratic solution of Boyanovsky and Jasnow, and within a renormalized Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) master equation. From the time-dependent covariance matrix we extract the quantum Fisher information (QFI) for general single-mode Gaussian probe states, including squeezed ones. In the strong-coupling, non-Markovian regime the QFI is non-monotonic in time, displaying bath-memory revivals that make a finite interrogation time t∗>0 strictly optimal. By contrast, we prove that the Markovian QFI rises monotonically to its stationary value and develops no interior optimum, so that its optimum is always pinned to the boundary t∗→∞; this complements existing Markovian precision-rate bounds, which concern (F(t)/t) rather than the single-shot QFI (F(t)). Squeezed initial states yield a large transient advantage that thermalisation eventually erases, establishing squeezing and interrogation time as complementary thermometric resources. At equilibrium, strong coupling replaces the exponential Boltzmann suppression of the low-temperature relative error by a far milder polynomial divergence. As the model maps directly onto circuit quantum electrodynamics, these protocols appear within current experimental reach.
The precise measurement of low temperatures is significant for both the fundamental understanding of physical processes and technological applications. In this work, we present a method for low-temperature measurement that improves thermal range and sensitivity by generating quantum coherence in a thermometer probe. Typically, in temperature measurements, the probes thermalize with the sample being measured. However, we use a two-level quantum system, or qubit, as our probe and prevent direct probe access to the sample by introducing a set of ancilla qubits as an interface. We describe the open system dynamics of the probe using a global master equation and demonstrate that while the ancilla-probe system thermalizes with the sample, the probe per se evolves into a nonthermal steady state due to nonlocal dissipation channels. The populations and coherences of this steady state depend on the sample temperature, allowing for precise and wide-range low-temperature estimation. We characterize the thermometric performance of the method using quantum Fisher information and show that the quantum Fisher information can exhibit multiple and higher peaks at different low temperatures with increasing quantum coherence and the number of ancilla qubits. Our analysis reveals that the proposed approach, using a nonthermal qubit thermometer probe with temperature-dependent quantum coherence generated by a multiple qubit interface between a thermal sample and the probe qubit, can enhance the sensitivity of temperature estimation and broaden the measurable low-temperature range.
Superconducting transmon systems are promising platforms for nanoscale thermometry due to their high sensitivity to environmental fluctuations. Their intrinsic anharmonicity, which is essential for qubit operations, gives rise to a non-equidistant energy spectrum that significantly affects the thermal populations and, consequently, the thermometric sensitivity. In this work, we investigate the ultimate quantum limits of temperature estimation with a transmon beyond the two-level approximation. We compare the thermometric performance of three complementary models: the qubit, a harmonic oscillator and a weakly anharmonic Duffing oscillator, evaluating their corresponding quantum Fisher information (QFI) as a function of the temperature. We show that the multilevel anharmonic structure of the transmon affects its thermometric precision. Indeed, including higher excited states enhances the maximum amount of information that can be extracted about the system temperature, compared to a qubit probe. Furthermore, we address a fundamental limitation of the standard quartic truncation, which yields a potential that is unbounded from below and supports only spurious metastable states. By introducing bounded anharmonic models, namely a confined quartic potential and a sextic correction term, we assess the robustness of the thermometric precision beyond the Duffing regime. Our results provide practical guidelines for transmon-based nanoscale thermometry and clarify the role of the anharmonic multilevel spectrum in quantum temperature estimation.
The precision of a quantum thermometer is fundamentally constrained by the spectral structure of the probe itself, and a systematic mapping between the configurations of energy levels and thermometric performance provides relevant information to design optimized devices. In this work, we establish such a mapping by analyzing a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum models. We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes: finite-spectrum probes exhibit a T−4 decay, while unbounded or continuous spectra yield a slower T−2 decay. At low temperatures, we show that sensitivity, though universally exponentially suppressed, can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology. By contrast, specific quantum walk topologies provide a distinct enhancement mechanism based on gap engineering, whereby an optimal network size yields an optimized T−2 low-temperature scaling. Furthermore, power-law spectra enable tunable scaling of thermometric performance with system size, offering a design principle for optimal probes in specific temperature windows. Our results contribute to transform spectral information into a resource for quantum thermometry, providing both fundamental bounds and practical guidelines to tailored temperature sensing.