Environmentally induced effects and dynamical phase transitions in quantumsystems

Abstract

The dynamics of open quantum systems is determined by singularities in thecontinuum of scattering wavefunctions which are related to avoided and true crossingsof eigenvalue trajectories of a non-Hermitian Hamiltonian. The phases of theeigenfunctions are not rigid in approaching the crossing points so that environmentallyinduced spectroscopic redistribution processes may take place and a dynamicalphase transition may occur. Due to the formal equivalence between the quantummechanical Schrödinger equation and the optical wave equation in symmetric lattices, the dynamics of the system is determined also in this latter case byavoided and true crossings of eigenvalue trajectories of the non-Hermitian Hamiltonian. Incontrast to the eigenvalues characterizing an open quantum system, the eigenvaluesdescribing the symmetric optical lattice are real as long as the influence of the environment (lattice) onthe optical wave equation is small. In the regime of avoided level crossings, the symmetry isbroken, the eigenvalues become complex and a dynamical phase transition occurs, similaras in the open quantum system. These results can be proven experimentally by tracingthe phase rigidity of the eigenfunctions of the Hamiltonian and its correlationwith the transparency. The redistribution processes in the regime of avoided levelcrossings allow us to design systems with desired properties in a broad parameterrange.