Estimating the temperature of a cold quantum system is difficult. Usually one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes minimal knowledge of the state of a system and is potentially nondestructive. Our method uses a universal temperature dependence of the quench dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for nonequilibrium work distributions. We provide examples for a cold-atom system, in which our thermometry protocol may retain accuracy and precision at subnano-Kelvin temperatures.
Estimating the temperature of a cold quantum system is difficult. Usually one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes minimal knowledge of the state of a system and is potentially nondestructive. Our method uses a universal temperature dependence of the quench dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for nonequilibrium work distributions. We provide examples for a cold-atom system, in which our thermometry protocol may retain accuracy and precision at subnano-Kelvin temperatures.
Estimating the temperature of a cold quantum system is difficult. Usually, one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes no knowledge of the state of a system and is potentially non-destructive. Our method uses a universal temperature-dependence of the non-equilibrium dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for non-equilibrium work distributions. We provide examples, for a cold atom system, for which our thermometry protocol may retain accuracy and precision at subnanokelvin temperatures.
Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. However, temperature is not a quantum observable, and most theoretical studies have therefore concentrated on analyzing fundamental precision limits set by the quantum Fisher information through the quantum Cramer-Rao bound. In contrast, whether a direct temperature readout can be achieved in quantum thermometry remains largely unexplored, particularly under the nonequilibrium conditions prevalent in real-world applications. To address this, we develop a direct temperature readout scheme based on a thermodynamic inference strategy. The scheme integrates two conceptual developments: (i) By applying the maximum entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive semi-definite error functions that lower-bound the deviation of the reference temperature from the true temperature-in analogy to the quantum Cramer-Rao bound for the mean squared error-and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature readout under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout.
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.
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.
The precise measurement of low temperatures is a challenging, important, and fundamental task for quantum science. In particular, in situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here, we demonstrate that the temperature of a noninteracting Fermi gas can be accurately inferred from the nonequilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity.
Measuring the temperature of a quantum system is an essential task in almost all aspects of quantum technologies. Theoretically, an optimal strategy for thermometry often requires measuring energy, which demands full accessibility over the entire system as well as a complex entangled measurement basis. In this paper, we take a different approach and show that single-qubit sequential measurements in the computational basis not only allow for precise thermometry of a many-body system, but may also achieve precision beyond the thermometry capacity of the probe at equilibrium, given by the Cram\'er-Rao bound. Thus, using consecutive single-qubit measurements of the probe out of equilibrium is, in most cases, very beneficial, as it achieves lower-temperature uncertainties and avoids demanding energy measurements when compared with probes at thermal equilibrium. To obtain such precision, the time between the two subsequent measurements should be smaller than the thermalization time so that the probe never thermalizes. Therefore, the nonequilibrium dynamics of the system continuously imprint information about temperature in the state of the probe. To demonstrate the generality of our findings, we consider thermometry in both spin chains and the Jaynes-Cummings model.