Interaction free and decoherence free states

Abstract

An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.Dedicated to Margarita and Volodia Man'ko for their 150th birthday

Interaction-free evolution in the presence of time-dependent Hamiltonians

“…This notion, which has been introduced in Ref. [1], is somehow related to the concept of decoherence-free subspaces (DFS) [2][3][4][5][6]. In spite of such connection, it should be stressed that the two concepts are still different in many aspects.…”