Tradeoffs in quantum thermometry: Consistent quantum thermodynamic frameworks

测温学似乎微不足道；它在19世纪被表述为热力学的第零定律。在经典的宏观测温中，探针与样品接触。通过测量一定数量的探针，可以推断样品的温度。然而，一旦量子原理发挥作用，这种直观的协议就会失效，这就是纳米级探针和低温下的情况。这是因为对于小型和量子系统，热化不一定会发生，或者在很长的时间尺度上发生。此外，温度不是量子可观测的，人们需要思考如何在量子进化下以及在进行量子测量时推断它。量子效应可以通过协调来提高测温的精度和灵敏度，例如通过同时操作和关联多个量子探针。这项提议的目标是建立在量子力学原理的基础上，设计出精确、在广泛的温度范围内敏感、快速、低成本的纳米级温度计。首先，由于量子探针很小，它们与样品的相互作用会改变它们，例如，通过改变它们的能量，从而阻碍温度估计。我们将评估探针-样品相互作用在测温中的作用，并对其进行校正。其次，样品可以在温度计中产生时间量子相干。我们将利用这些可以长期存在的相干来设计不依赖于热力学零定律的增强测温方案。最后，我们将通过推导精度、灵敏度、成本和持续时间之间的权衡关系，针对不同的测量方法优化量子温度计。这项工作将有助于小型化温度传感器和精确热导测量的发展。应用领域包括生物系统和其他动态环境的原位成像和传感、电子和热电器件散热的开发和表征、量子计算硬件的进步以及量子热机、发动机和冰箱的设计。

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.