Temperature estimation, known as thermometry, is a critical sensing task for physical systems operating in the quantum regime. Indeed, thermal fluctuations can significantly degrade quantum coherence. Therefore, accurately determining the system's operating temperature is a crucial first step toward distinguishing thermal noise from other sources of decoherence. In this work, we estimate the unknown temperature of a collection of identical and independent two-level atoms dispersively probed by a single-mode quantized electromagnetic field. In contrast to previous works, we present an analytical sensing analysis demonstrating that the joint atom-field evolution -- without any assumptions or approximations -- can achieve, at best, the standard quantum limit of precision concerning the number of field excitations. To investigate our analysis further, we propose and implement a quantum thermometer based on a nonlinear Mach-Zehnder interferometer, which we realize through quantum digital simulation. Our simulation is highly flexible regarding atomic state preparation, allowing the initialization of atomic ensembles with positive and effective negative temperatures. This makes our platform a promising and versatile testbed for benchmarking thermometric capabilities in current quantum simulators.
Temperature estimation, known as thermometry, is a critical sensing task for physical systems operating in the quantum regime. Indeed, thermal fluctuations can significantly degrade quantum coherence. Therefore, accurately determining the system's operating temperature is a crucial first step toward distinguishing thermal noise from other sources of decoherence. In this work, we estimate the unknown temperature of a collection of identical and independent two-level atoms dispersively probed by a single-mode quantized electromagnetic field. In contrast to previous works, we present an analytical sensing analysis demonstrating that the joint atom-field evolution -- without any assumptions or approximations -- can achieve, at best, the standard quantum limit of precision concerning the number of field excitations. To investigate our analysis further, we propose and implement a quantum thermometer based on a nonlinear Mach-Zehnder interferometer, which we realize through quantum digital simulation. Our simulation is highly flexible regarding atomic state preparation, allowing the initialization of atomic ensembles with positive and effective negative temperatures. This makes our platform a promising and versatile testbed for benchmarking thermometric capabilities in current quantum simulators.
Abstract Temperature estimation, known as thermometry, is a critical sensing task for physical systems operating in the quantum regime. Indeed, thermal fluctuations can significantly degrade quantum coherence. Therefore, accurately determining the system’s operating temperature is a crucial first step toward distinguishing thermal noise from other sources of decoherence. In this work, we estimate the unknown temperature of a collection of identical and independent two-level atoms dispersively probed by a single-mode quantized electromagnetic field. In contrast to previous works, we present an analytical sensing analysis demonstrating that the joint atom-field evolution—without any assumptions or approximations—can achieve, at best, the standard quantum limit of precision concerning the number of field excitations. To investigate our analysis further, we propose and implement our thermometry scheme on a nonlinear Mach–Zehnder interferometer, which we realize through quantum digital simulation. Our proposal is highly flexible regarding atomic state preparation, allowing the initialization of atomic ensembles with positive and effective negative temperatures. This makes our proposal a promising and versatile testbed for benchmarking thermometric capabilities in current quantum simulators.
Quantum thermometry has long promised sensitivities beyond classical limits, with recent paradigms highlighting quantum coherence as a primary driver of precision. While most studies focus on single-point temperature estimation, we extend this framework to the spatial domain. We consider a probe two-level system (TLS) coupled asymmetrically to an auxiliary TLS that equilibrates with a sample of profile T(x). The reduced probe state carries coherence in its local basis that remains temperature-sensitive after the probe transition has frozen out, yielding a Fisher information exponentially larger at low temperature than that of a population-only readout. An exact reparametrization converts the thermometric precision into a local spatial distinguishability bound; its validity requires only a sufficiently small relative temperature uncertainty and yields an explicit measurement budget. Adding auxiliary TLSs shifts the array's optimal working temperature upward and broadens the useful sensing window, with the achievable gain ultimately limited by the total available coupling rather than by an indefinite scaling law. Finally, we propose a microwave Mach-Zehnder interferometer that maps the temperature-dependent probe coherence onto an experimentally accessible quadrature observable.
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.
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.
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.
We consider the question: Is it possible to measure two temperatures simultaneously using a single thermometer? Under common circumstances, where the thermometer can interact with only one bath at a time and the interaction leads to complete thermalization, this is clearly impossible because the final state of the thermometer would be independent of the temperature of the first bath. In this work, we show that this task can indeed be accomplished with the assistance of quantum control. In particular, we consider a composite particle with multiple quantum degrees of freedom (DoF) as a temperature sensor, where one of the DoF -- termed as internal DoF -- is susceptible to the local temperature, thereby functioning as a thermometer, whereas another DoF -- termed external DoF -- is quantum-controlled. We leverage the entanglement between the aforementioned DoF in a composite particle for two-temperature thermometry by preparing the external DoF in a quantum superposition, exposing the internal DoF to two local temperatures. We show that such a particle used in a Mach-Zehnder type interferometer, or a quantum switch -- which allows quantum control over the order of application of quantum channels -- can be used to estimate two temperatures simultaneously, thus affirming our main proposition. For each of these setups, we obtain the variance in the estimated temperatures through the multi-parameter Cramér-Rao bound, and compare their performances based on the range of total variance of the two temperatures estimated. On benchmarking all the setups based on the total variance of the estimated temperatures, we find that a quantum switch with a qudit probe outperforms other setups. On restricting our probe to be a qubit, we find that quantum switch performs equally well as a Mach-Zehnder type interferometer.