Role of Statistics as a Thermodynamic Resource in Quantum Engines

Abstract

Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyUltracold atomic gases serve as ideal platforms for studying complex quantum effects, offering precise control over many degrees of freedom. They are therefore an excellent testbed for exploring fundamental ideas and concepts in quantum thermodynamics, where the principles of quantum mechanics and thermodynamics are linked from first principles. One of the most prominent areas of interest in this field is the study of quantum heat engines—systems in which a quantum working medium undergoes cyclic interactions with hot and cold reservoirs to convert heat into work. In this thesis I explore heat engines that utilize quantum many-body systems as their working medium. At ultracold temperatures, quantum statistical effects play a crucial role, with the fermionic or bosonic nature of the quantum gas directly influencing its energetic behavior. It is therefore an interesting question to ask what an engine that operates based on a quantum statistical energy difference would look like? To address this, I investigate two experimentally realizable settings where quantum statistics can be manipulated: the BEC-BCS crossover in three-dimensional quantum gases and the Lieb-Liniger model in one dimension. In the first part of this thesis, I introduce the concept of the Pauli engine, a purely quantum engine that operates within the BEC-BCS crossover region. Here, the change in particle statistics effectively replaces conventional heat reservoirs, offering a novel mechanism for work production. I compare the performance of the Pauli engine to both a statistics-based thermal engine and a solely interaction-driven engine. The findings demonstrate that the Pauli engine outperforms both alternatives, establishing quantum statistics as a valuable thermodynamic resource for work extraction. Additionally, I compare my theoretical predictions to experimental data from the realization of the Pauli engine conducted by the group at Kaiserslautern University. The second part of the thesis focuses on implementing a quantum heat engine using a one-dimensional repulsively interacting Bose gas as the working medium. This system is described by the Lieb-Liniger model, an integrable framework that can be exactly solved using the Bethe ansatz. Within this model, the many-body interactions can be continuously tuned from the non-interacting limit to the strongly interacting Tonks-Girardeau regime, where bosonic atoms exhibit fermionic statistical behavior. Leveraging this statistical transition, I introduce and theoretically analyze two statistically enhanced engine cycles: the A-cycle and the T-cycle. For both cycles, I examine their efficiency at maximum work by optimizing the performance with respect to system length. The results demonstrate that tailoring quantum statistics can significantly enhance engine performance, reinforcing the potential of statistical effects as a thermodynamic resource.doctoral thesi