Quantum theory of all-optical switching in nonlinear Sagnac interferometers

Recently, our group demonstrated an ultrafast, low-loss, fiber-loop switch based on a nonlinear Sagnac-interferometer design, using which entangled photons were shown to be routed without any measurable degradation in their entanglement fidelity (Hall et al 2011 Phys. Rev. Lett. 106 053901). Such a device represents an enabling technology for a rich variety of networked quantum applications. In this paper, we develop a comprehensive quantum theory for such switches in general, i.e. those based on nonlinear Sagnac interferometers, where the in-coupling of quantum noise is carefully modeled. When applied to the fiber-loop switch, the theory shows good agreement with the experimental results without using any fitting parameter. This theory can serve as an important guiding tool for configuring switches of this kind for future quantum networking applications.