Quantum coherence in modern hybrid many-body systems out of equilibrium

The prospect of bringing genuine quantum effects to technological application relies on our ability to reliably create and control quantum states. One of the biggest challenges is the interaction between the quantum states and their environment. On the one hand such an interaction is required because the states need to be created and manipulated. On the other hand, however, the same interaction causes decoherence, which is an uncontrolled decay of well defined quantum states making them useless for any application. But this interaction offers also the chance for new physics. For instance, by tracking how exactly decoherence builds up it is possible to gain information about the environment and devise protocols to change the state of the environment [1]; or one can induce a quantum coherent coupling between different quantum systems that are mediated through many-body excitations in the otherwise incoherent environment [2]. Understanding this type of physics requires a concise modelling of many-body excitations in the hybrid systems consisting of the quantum system and the (quantum) environment under driven or non-equilibrium conditions. Most interesting will be the study of modern topological or strongly correlated quantum materials, and this will be the main topic of this PhD. An example is the coupling of a topological insulator or superconductor to a system of localised quantum states such as magnetic impurities, quantum dots, or different types of qubits. Such systems have very unconventional quantum properties that in a hybrid setup have an impact on the coupled system. This opens the door to non-local quantum state diagnosis and manipulation. The work will have a strong focus on understanding and therefore will involve a large part of pencil-paper work, building on everything we can bring in from many-body theories and calculus. But such an approach has limitations and numerical methods will be used whenever this makes more sense. [1] S. Matern, D. Loss, J. Klinovaja and B. Braunecker, arXiv:1905.11422 (2019). [2] C. Jackson and B. Braunecker, in preparation (2019).