Non-additive dynamical Casimir atomic phases

We discuss a fundamental property of open quantum systems: the quantum phases associated with their dynamical evolution are non-additive. We develop our argument by considering a multiple-path atom interferometer in the vicinity of a perfectly conducting plate. The coupling with the environment induces dynamical corrections to the atomic phases. In the specific example of a Casimir interaction, these corrections reflect the interplay between field retardation effects and the external atomic motion. Non-local open-system Casimir phase corrections are shown to be non-additive, which follows directly from the unseparability of the influence functional describing the coupling of the atomic waves to their environment. This is an unprecedented feature in atom optics, which may be used in order to isolate non-local dynamical Casimir phases from the standard quasi-static Casimir contributions.