Entanglement in a linear coherent feedback chain of nondegenerate optical parametric amplifiers

TL;DR

This paper investigates the generation and stability of entanglement in linear chains of nondegenerate optical parametric amplifiers, revealing that longer chains can achieve desired entanglement with less pump power and exhibit internal entanglement synchronization.

Contribution

It provides a detailed analysis of stability, entanglement properties, and the effects of losses and delays in NOPA networks, extending previous work on dual-NOPA systems to chains of up to six amplifiers.

Findings

More NOPAs in the chain reduce the pump power needed for the same entanglement

Entanglement synchronization occurs between cavity modes inside the network

Longer chains can achieve target entanglement with less total pump power

Abstract

This paper is concerned with linear quantum networks of $N$ nondegenerate optical parametric amplifiers (NOPAs), with $N$ up to 6, which are interconnected in a coherent feedback chain. Each network connects two communicating parties (Alice and Bob) over two transmission channels. In previous work we have shown that a dual-NOPA coherent feedback network generates better Einstein-Podolsky-Rosen (EPR) entanglement (i.e., more two-mode squeezing) between its two outgoing Gaussian fields than a single NOPA, when the same total pump power is consumed and the systems undergo the same transmission losses over the same distance. This paper aims to analyze stability, EPR entanglement between two outgoing fields of interest, and bipartite entanglement of two-mode Gaussian states of cavity modes of the $N$-NOPA networks under the effect of transmission and amplification losses, as well as time delays. It is numerically shown that, in the absence of losses and delays, the network with more NOPAs in the chain requires less total pump power to generate the same degree of EPR entanglement. Moreover, we report on the internal entanglement synchronization that occurs in the steady state between certain pairs of Gaussian oscillator modes inside the NOPA cavities of the networks.