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arXiv:2412.04878 · Physical Review Applied

Enhancing low-temperature quantum thermometry via sequential measurements

Ning Zhang, Chong Chen, Ping Wang

Published Sep 11, 2025• 2 citations
arXivHTMLPDF

Abstract

We propose a sequential measurement protocol for accurate low-temperature estimation based on Ramsey interferometry. The resulting correlated outputs significantly enhance the low-temperature precision compared to that of the independent measurement scheme. This enhancement manifests a Heisenberg scaling of the signal-to-noise ratio for small measurement numbers $N$. Detailed analysis reveals that the final precision is determined by the pair correlation of the sequential outputs induced by the low-frequency noise of the thermal sample, which produces a dependence ${N}^{2}$ on the signal-to-noise ratio. Remarkably, we find that quantum thermometry within the sequential protocol functions as a high-resolution quantum spectroscopy of the thermal noise, underscoring the pivotal role of the sequential measurements in enhancing the spectral resolution and the temperature-estimation precision. Our methodology signifies the role of the temporal correlation induced by the thermal sample in low-temperature quantum thermometry, which represents an advancement in low-temperature measurement.

DOI
10.1103/sr7z-kxwp

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We propose a sequential measurement protocol for accurate low-temperature estimation based on Ramsey interferometry. The resulting correlated outputs significantly enhance the low-temperature precision compared to that of the independent measurement scheme. This enhancement manifests a Heisenberg scaling of the signal-to-noise ratio for small measurement numbers NNN. Detailed analysis reveals that the final precision is determined by the pair correlation of the sequential outputs induced by the low-frequency noise of the thermal sample, which produces a dependence N2{N}^{2}N2 on the signal-to-noise ratio. Remarkably, we find that quantum thermometry within the sequential protocol functions as a high-resolution quantum spectroscopy of the thermal noise, underscoring the pivotal role of the sequential measurements in enhancing the spectral resolution and the temperature-estimation precision. Our methodology signifies the role of the temporal correlation induced by the thermal sample in low-temperature quantum thermometry, which represents an advancement in low-temperature measurement.
We investigate correlation-enhanced low temperature quantum thermometry. Recent studies have revealed that bath-induced correlations can enhance the low-temperature estimation precision even starting from an uncorrelated state. However, a comprehensive understanding of this enhancement remains elusive. Using the Ramsey interferometry protocol, we illustrate that the estimation precision of NNN thermometers sparsely coupled to a common low-temperature bath can achieve the Heisenberg scaling in the low-temperature regime with only a π/2π/2π/2 rotation of the measurement axis, in contrast to the standard Ramsey scheme. This result is based on the assumption that interthermometer correlations are induced exclusively by low-frequency noise in the common bath, a condition achievable in practical experimental scenarios. The underlying physical mechanism is clarified, revealing that the Heisenberg scaling arises from the intrinsic nature of the temperature, which is associated solely with the fluctuation of thermal noise. In contrast to the paradigm of independent thermometers, our proposed scheme demonstrates a significant enhancement in precision for low-temperature measurement, making it suitable for precisely measuring the temperature of ultracold systems.
Equilibrium quantum thermometry seeks to enhance temperature estimation for reservoirs at thermal equilibrium using quantum resources, yet achieving the Heisenberg scaling in a physical protocol remains a significant challenge. Moreover, quantum measurements face an intrinsic limitation arising from an exponential suppression of thermometric sensitivity as the temperature approaches zero. This limitation severely hinders access to high precision in the low-temperature regime. Here, we demonstrate a simple but powerful quantum engineering protocol to overcome these limitations and reach high precision for temperature estimation. By engineering a small subset of central probes and their linear coupling to a larger array of adjacent probes, we show that the composite partition function can be tailored to yield Heisenberg-limited precision for temperature estimation. Critically, we show that this protocol can simultaneously saturate the Landau bound at low temperatures, an inverse quadratic scaling with the temperature, thereby fully exploiting the potential of equilibrium thermometry and circumventing the exponential suppression of thermometric sensitivity in the low-temperature regime. This scheme relies solely on linear interactions, avoiding complicated many-body couplings and ensuring scalability with the number of probes. Moreover, we find that the comparable precision can be achieved using only local measurements on the central probes, substantially reducing the implementation complexity compared to global measurement schemes and offering a promising approach toward high-precision equilibrium thermometry in physical systems.
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, therefore these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.
We study the role of bath-induced correlations in temperature estimation of cold bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a bosonic sample and reach a nonthermal steady state, which is measured to estimate the temperature of the sample. It is well known that in the steady state such noninteracting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold bosonic gases and show that, although being classical, bath-induced correlations can lead to significant enhancement of precision for thermometry. The improvement is especially important at low temperatures, where attaining high precision thermometry is particularly demanding. The proposed thermometry scheme does not require any precise dynamical control of the probes and tuning the parameters and is robust to noise in initial preparation, as it is built upon the steady state generated by the natural dissipative dynamics of the system. Therefore, our results put forward new possibilities in thermometry at low temperatures, of relevance, for instance, in cold gases and Bose-Einstein condensates.
We study the role of bath-induced correlations in temperature estimation of cold Bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a Bosonic sample and reach a non-equilibrium steady state, which is measured to estimate the temperature of the sample. It is well-known that in the steady state such non-interacting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold Bosonic gases and show that, although being classical, bath-induced correlations can indeed lead to sub-shot-noise precision for thermometry at low temperatures; e.g., for a probe of 303030 non-interacting impurities they can enhance the quantum Fisher information by two orders of magnitude. The proposed thermometry scheme here does not require precise dynamical control of the probes and tuning the parameters, as it is build upon the non-equilibrium steady state of a non-interacting system. Our results put forward new possibilities in thermometry at low temperatures, of relevance for instance in cold gases and Bose--Einstein condensates.
Abstract Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.