An optimal local quantum thermometer is a quantum many-body system that saturates the fundamental lower bound for the thermal state temperature estimation accuracy [L. Correa et al., Phys. Rev. Lett. 114, 220405 (2015)]. Such a thermometer has a particular energy-level structure with a single ground state and highly degenerated excited-state manifold, with an energy gap proportional to the estimated temperature. In this paper, we show that the optimal local quantum thermometer can be realized in an experimentally feasible system of spinless fermions confined in a one-dimensional optical lattice described by the Rice-Mele model. We characterize the system's sensitivity to temperature changes in terms of quantum Fisher information and the classical Fisher information obtained from experimentally available site occupation measurements.
We provide a detailed description of the quantum interferometric thermometer, which is a device that estimates the temperature of a sample from the measurements of the optical phase. We rigorously analyze the operation of such a device by studying the interaction of the optical probe system prepared in a single-mode Gaussian state with a heated sample modeled as a dissipative thermal reservoir. We find that this approach to thermometry is capable of measuring the temperature of a sample in the nanokelvin regime. Furthermore, we compare the fundamental precision of quantum interferometric thermometers with the theoretical precision offered by the classical idealized pyrometers, which infer the temperature from a measurement of the total thermal radiation emitted by the sample. We find that the interferometric thermometer provides a superior performance in temperature sensing even when compared with this idealized pyrometer. We predict that interferometric thermometers will prove useful for ultraprecise temperature sensing and stabilization of quantum optical experiments based on the nonlinear crystals and atomic vapors.
We study quantum-impurity models as a platform for quantum thermometry. A single quantum spin-
21 impurity is coupled to an explicit, structured, fermionic thermal sample system, which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.
We investigate the sensitivity of an ion sensor in determining the temperature of an atomic Fermi gas. Our study extends to charged impurities the proposal by M. T. Mitchison et al. [Phys. Rev. Lett. 125, 080402 (2020)], where atomic neutral impurities were used as an in situ thermometer of the quantum gas. We find that the long-range character of the atom-ion interaction enhances the thermometer's sensitivity for certain system parameters. In addition, we investigate the impact of the ion quantum motional state on the sensitivity by assuming that it is confined in a harmonic trap. We observe that the temperature sensitivity of the ion is noticeably influenced by its spatial extension, making the latter a versatile tool to be manipulated for improving the thermometer performance. We finally discuss our findings in the context of current experimental atom-ion mixtures.
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.
Precise low-temperature thermometry is a key requirement for virtually any quantum technological application. Unfortunately, as the temperature
T decreases, the errors in its estimation diverge very quickly. In this paper, we determine exactly how quickly this may be. We rigorously prove that the ``conventional wisdom'' of low-
T thermometry being exponentially inefficient is limited to local thermometry on translationally invariant systems with short-range interactions, featuring a nonzero gap above the ground state. This result applies very generally to spin and harmonic lattices. On the other hand, we show that a power-law-like scaling is the hallmark of local thermometry on gapless systems. Focusing on thermometry on one node of a harmonic lattice, we obtain valuable physical insight into the switching between the two types of scaling. In particular, we map the problem to an equivalent setup, consisting of a Brownian thermometer coupled to an equilibrium reservoir. This mapping allows us to prove that, surprisingly, the relative error of local thermometry on gapless harmonic lattices does not diverge as $T\ensuremath{\rightarrow}0$; rather, it saturates to a constant. As a useful by-product, we prove that the low-
T sensitivity of a harmonic probe arbitrarily strongly coupled to a bosonic reservoir by means of a generic Ohmic interaction, always scales as
T2 for $T\ensuremath{\rightarrow}0$. Our results thus identify the energy gap between the ground and first excited states of the global system as the key parameter in local thermometry, and ultimately provide clues to devising practical thermometric strategies deep in the ultracold regime.