Minimization of Mixing Time in Rudner–Levitov Chains by Optimizing the Initial State

Abstract

The mixing process in Rudner–Levitov chains, which are a one-dimensional lattice of bosonic modes with designed losses in every second mode, has been studied. The mixing time could be significantly reduced by choosing the initial excitation in the system in a special way. An eigenvector of the effective Hamiltonian corresponding to a non-zero eigenvalue of the effective Hamiltonian with the smallest absolute value of the imaginary part must be chosen for the class of single-mode excitations. An initial state localized in two or more modes must be chosen so that it is orthogonal to this eigenvector.