The unknown temperature of a sample can be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read-out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact, and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.

Thermodynamics is a branch of science blessed by an unparalleled combination of generality of scope and formal simplicity. Based on few natural assumptions together with the four laws, it sets the boundaries between possible and impossible in macroscopic aggregates of matter. This triggered groundbreaking achievements in physics, chemistry and engineering over the last two centuries. Close analogues of those fundamental laws are now being established at the level of individual quantum systems, thus placing limits on the operation of quantum-mechanical devices. Here we study quantum absorption refrigerators, which are driven by heat rather than external work. We establish thermodynamic performance bounds for these machines and investigate their quantum origin. We also show how those bounds may be pushed beyond what is classically achievable, by suitably tailoring the environmental fluctuations via quantum reservoir engineering techniques. Such superefficient quantum-enhanced cooling realises a promising step towards the technological exploitation of autonomous quantum refrigerators.

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.

An implementation of quantum absorption chillers with three qubits has been recently proposed that is ideally able to reach the Carnot performance regime. Here we study the working efficiency of such self-contained refrigerators, adopting a consistent treatment of dissipation effects. We demonstrate that the coefficient of performance at maximum cooling power is upper bounded by $3/4$ of the Carnot performance. The result is independent of the details of the system and the equilibrium temperatures of the external baths. We provide design prescriptions that saturate the bound in the limit of a large difference between the operating temperatures. Our study suggests that delocalized dissipation, which must be taken into account for a proper modeling of the machine-baths interaction, is a fundamental source of irreversibility which prevents the refrigerator from approaching the Carnot performance arbitrarily closely in practice. The potential role of quantum correlations in the operation of these machines is also investigated.

We consider the problem of estimating the temperature $T$ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low $T$ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures—a regime which is particularly relevant to quantum technologies.