Exchange fields and relaxation times in quantum dot

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The goal of the proposed project is to give a theoretical description of (A) time-dependent decay in multiple quantum-dot setups, and (B) spintronic exchange effects in quantum-dot spin valves, both of which are important problems characterizing the response of nanoelectronic systems to external control and driving.In subproject (A), we will calculate the decay modes of composite quantum-dot systems driven out of equilibrium, and determine how the current through one constituent quantum dot can be used to measure the decay modes of the others. This understanding of the time-dependent response is of key importance to physical and technological applications of externally driven quantum-dot devices, e.g., in sensitive electron-counting and qubit readout, respectively. We will establish measurement setups and protocols accounting for the effects of quantum-fluctuations. In particular, we will study how one can measure the recently predicted fermion-parity decay mode of a quantum dot, which is strikingly insensitive to Coulomb interaction and other local effects due to a fundamental superselection rule of quantum mechanics.In subproject (B), we will calculate the transport through a quantum dot coupled to biased noncollinear ferromagnets, accounting for the competition of the exchange field induced by spin-dependent confinement and the exchange field induced by tunneling and Coulomb interaction. These mechanisms are fundamental to the quest for time-dependent control over single spins in nanostructures for spintronics and quantum information. We will make predictions for stationary as well as time-dependent measurements that aim to detect and disentangle these two effects. In particular, we will predict how the exchange fields develop in time after switching on the tunneling between the quantum dot and the noncollinear ferromagnets.For both problems we will apply a causal superfermion formulation of the real-time diagrammatic technique. This approach reveals novel fundamental aspects of nonequilibrium processes and allows us to obtain the time-evolution of the reduced density operator of the quantum dot in a more efficient way, complementary to the physically more transparent quantum-kinetic equations for coupled observables.A feature central to both proposed subprojects is that we can systematically treat -- within a single approach - higher-order perturbations to the complementary limits of arbitrary interaction and weak tunneling, and, on the other hand, arbitrary tunneling and weak interaction. In general, the approach simplifies many of the required calculations. It has already led to new exact results for strongly interacting quantum dots, e.g., establishing the fermion-parity decay mode, and it shows great potential for successfully realizing the proposed research program. Each proposed subproject involves an external researcher who brings in expertise on modeling devices in close collaboration with leading experimental efforts.