Dynamics in Open Quantum Systems: strong Dissipation and Integrability

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Quantum systems in and out of equilibrium have drastically different properties. In a non-equilibrium setting in which the system experiences a controlled dissipation, the time evolution becomes non-unitary and the dynamics irreversible. Usually the long-time evolution then brings the quantum system into a state with properties that do not depend on time, the so-called non-equilibrium steady state (NESS). The steady state properties are robust with respect to temporal initial conditions and incidental perturbations along the way, thus opening dissipative quantum systems as an attractive path to quantum states engineering. Furthermore, the properties of a NESS are usually completely different from those of a Gibbs ensemble of states, e.g. the NESS of a quantum spin chain can carry macroscopic stationary currents accompanied by long-range correlations, or be unexpectedly sensitive to boundary conditions at the edges of the chain. The interplay between coherent and dissipative dynamics thus renders novel quantum states accessible which are otherwise unreachable in the usual unitary dynamics. Our objective is the study of chiral states in quantum magnets as they have recently been experimentally prepared in systems of cold atoms. We want to understand the stability of these states of spin-helix type and are interested in their dissipative generation. These states have unusual physical properties like strong spin currents which we are going to compute by analytical and numerical means. Analytically we will make use of the recently discovered structure of "phantom'' Bethe states. We plan to show how to dissipatively generate mixtures of chiral states using dissipation acting just locally at the edges and to construct the respective NESS via so-called matrix product states (MPS). In the dissipative setting the MPS are constructed from rectangular Lax matrices which is qualitatively different from the MPS appearing in equilibrium physics. In the Zeno limit we will compute NESS and its properties using the integrability of effective Zeno dynamics governed by integrable open Heisenberg and Hubbard type systems.