Quantum thermodynamics and metrology with mechanical degrees of freedom

Quantum metrology and quantum thermodynamics are two relatively young fields that, in the spirit of the second quantum revolution, apply quantum theory to address fundamental questions and to develop technological applications. While the research in these fields is predominantly conducted with discrete, finite-dimensional quantum systems in mind, this thesis makes the case for continuous variable mechanical degrees of freedom.
In the first of three projects, we present two realizations of the Otto cycle with a planar rotor as the working medium. As a mechanical system, the planar rotor has a well-defined classical analogue that allows the identification of genuine quantum effects by comparing classical and quantum machine. Here, we mainly focus on the parameter regimes, where the machine admits a certain operation mode, i.e. an engine, a refrigerator, or a heater.
In the first realization, we find a systematic disadvantage of the quantum machine. The opposite is true for the second realization: It can be shown that the classical machine can, in general, not be run in a useful operation mode. The quantum machine, on the other hand, admits an engine operation mode for sufficiently cold temperatures of the cold bath.
The second project is devoted to the dynamics of a quantum system subjected to a thermal gas. In contrast to repeated interaction models, we consider any gas particle as a motional degree of freedom. We Employ quantum mechanical scattering theory to derive a low-density limit master equation, including gases with internal structure. Then, the thermodynamic consistency of the master equation is shown. A comparison with repeated interaction models makes evident that the inclusion of motional degrees of freedom of the gas plays a curial role for the consistency. Finally, we consider a nonequilibrium scenario, where the internal and motional degrees of freedom of the gas are thermal with respect to different temperatures. We show that, under the influence of this gas, the ergotropy of the system can increase.
In the last project, we apply quantum metrology on the measurement of magnetic moments in an electron microscope. We consider two types of sample, one that is static and does not change under the influence of the electron and another one that is described by a quantum system and experiences quantum backaction. For both samples, we derive the scattering operator from first principles. Then, two metrological tasks are considered: First, the sensing of the strength of the magnetic moment. We derive the Fisher information in several bases and find that momentum measurements are already optimal in the case without backaction. With backaction included, a measurement of angular momentum is optimal. The second task, we consider, is the optimal discrimination of the scattered and unscattered motional electron state. We derive the trace distance and find the experimentally achievable basis with the highest classical trace distance, which is still significantly worse than the theoretical optimum.