Fermionic Quantum Many-Body Systems with Cold Atoms

I propose a research project to investigate theoretical questions on strongly correlated fermionic quantum many-body systems in relation to current experiments with cold fermionic quantum gases. Strongly correlated fermionic quantum many-body systems have fascinated and challenged physicists for decades. The interplay of interactions and the Pauli principle leads to complicated quantum correlations and quantum phases with no classical counterpart. These phases require a description via complex many-body wave functions, making the theoretical understanding of interacting fermionic quantum systems and their quantum mechanical correlations a daunting task for Condensed Matter Physics and Quantum Information Theory. During the last years, experiments with cold fermionic atoms and molecules have gained the attention of these communities. Such experiments allow a control of the interaction strength and a manipulation at the single atom level, and can be probed with quantum optical tools, like time-of flight imaging and spectroscopy. Based on these achievements, I propose theoretical research related to these experiments with the goal to address questions in Condensed Matter Physics and Quantum Information Theory. This proposal is divided into three parts. In the first part, possibilities to use current experiments with cold fermionic quantum gases for Quantum State Engineering and Quantum Simulation are explored. The problem to engineer topological order in interacting Hamiltonian systems or via dissipative dynamics governed by two-body processes is investigated. Further, finite temperature quantum simulation of SU(N) ground state physics is proposed. In the second part, cold fermionic quantum systems are investigated as a platform for applications. On the one hand, questions related to Topological Quantum Computation are explored. This includes the proposal of protocols to realize braiding of atomic Majorana Fermions and proof-of-principle demonstrations of Topological Quantum Computation. These proposals are based on the single-site addressing available in optical lattice experiments. On the other hand, optical lattice clocks with fermionic Alkaline Earth Atoms are explored with the goal to improve their precision. In the last part, the quantum correlations emerging in interacting fermionic many-body systems are investigated from a Quantum Information perspective. First, possibilities to apply concepts and methods from Quantum Information Theory to topologically ordered systems that emerge from interactions are explored. The goal of this approach is to classify topological order that emerges due to interaction and further to detect and quantify it as a resource for Applications. Second, the physical properties that can be captured by the recently introduced de Finetti states are explored, and their power as variational wave functions is explored. In case that de Finetti states capture exotic quantum phases, possibilities to engineer these states in cold atom systems are investigated.