Distributed generation of entanglement between spatially separated propagating Gaussian fields via coherent feedback

In this paper we show how Einstein-Podolski-Rosen (EPR)-like entanglement between a pair of spatially separated propagating continuous-mode Gaussian fields can be generated via a coherent feedback loop that connects two spatially distant nondegenerate optical parametric amplifiers (NOPAs) over two transmission channels. In particular, the scheme generates entanglement in a distributed manner using spatially distributed resources. It is shown that similar to a single NOPA, the coherent feedback scheme has parameters that determine the achievable frequency dependent two-mode squeezing and entanglement bandwidth between the pair of continuous-mode fields. It is shown that in ideal scenarios, in the absence and presence of transmission losses, the feedback connection is able to provide a moderate increase in the quality of entanglement while achieving this in a more efficient manner by consuming less power, compared to conventional distribution of entanglement using a single NOPA.