Tradeoffs in quantum thermometry: Consistent quantum thermodynamic frameworks

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The science of thermometry seems trivial; it was formulated in the 19th century as the zeroth law of thermodynamics. In classical macroscopic thermometry, a probe is brought into contact with a sample. By measuring a certain quantity of the probe, the temperature of the sample can be inferred. However, this intuitive protocol breaks down once quantum principles play a role, which is the situation for nanoscale probes and at low temperatures. This is because for small and quantum systems, thermalization does not necessarily take place, or it is happening yet on very long timescales. Moreover, temperature is not a quantum observable, and one needs to ponder on how to infer it under quantum evolution and when performing quantum measurements. Quantum effects can be orchestrated to enhance the precision and sensitivity of thermometry, for example by simultaneously operating and correlating multiple quantum probes. The objective of this proposal is to build on principles of quantum mechanics and devise nanoscale thermometers that are accurate, sensitive over a broad range of temperatures, fast, and operative at low cost. First, since quantum probes are small, their interaction with the sample alter them, for example, by changing their energetic, thus obstructing temperature estimation. We will asses the role of probe-sample interactions in thermometry, and correct for it. Second, temporal quantum coherences can be generated in a thermometer by the sample. We will utilize these coherences, which can be long-lived, to devise enhanced thermometry protocols that do not rely on the zero law of thermodynamics. Finally, we will optimize quantum thermometers against different measures by deriving tradeoff relations between their accuracy, sensitivity, cost, and duration. The work will contribute to the development of miniaturized temperature sensors and precise thermal conductance measurements. Application are e.g., for in situ imaging and sensing of biological systems and other dynamic environments, development and characterization of heat dissipation in electronic and thermoelectric devices, advancement of quantum computing hardware, and design of quantum heat machines, engines and refrigerators.