Non-local double-path Casimir phase in atom interferometers

We present a quantum open 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. Such a non-local phase arises from the coarse-graining over the quantized electromagnetic field and internal atomic degrees of freedom, yielding a non-Hamiltonian evolution of the atomic waves moving in presence of correlated quantum dipole and field fluctuations. We develop a diagrammatic interpretation of this phase, and estimate it for realistic experimental parameters.