Non-local double-path Casimir phase in atom interferometers

We present an open quantum system theory of atom interferometers evolving in the quantized electromagnetic field bounded by an ideal conductor. Our treatment reveals an unprecedented feature of matter-wave propagation, namely the appearance of a non-local double-path phase coherence. In the standard interpretation of interferometers, one associates well-defined separate phases to individual paths. Our non-local phase coherence is instead associated to pairs of paths. It arises from the coarse-graining over the quantized electromagnetic field and internal atomic degrees of freedom, which play the role of a common reservoir for the pair of paths and lead to a non-Hamiltonian evolution of the atomic waves. We develop a diagrammatic interpretation and estimate the non-local phase for realistic experimental parameters.