Formulae for entanglement in a linear coherent feedback network of multiple nondegenerate optical parametric amplifiers: the infinite bandwidth case

TL;DR

This paper derives formulas for EPR entanglement in a lossless, infinite bandwidth chain of multiple NOPAs with adjustable phases, providing insights into the maximum achievable entanglement in such quantum optical networks.

Contribution

It introduces explicit formulas for EPR entanglement in a linear chain of NOPAs under idealized conditions, advancing understanding of quantum entanglement limits in these systems.

Findings

Maximum EPR entanglement achievable in the idealized scenario.

Effectiveness of phase adjustments in optimizing entanglement.

Approximation accuracy of infinite bandwidth limit at low frequencies.

Abstract

This paper presents formulae for Einstein-Podolsky-Rosen (EPR) entanglement generated from $N$ nondegenerate optical parametric amplifiers (NOPAs) interconnected in a linear coherent feedback (CFB) chain in the idealized lossless scenario and infinite bandwidth limit. The lossless scenario sets the ultimate EPR entanglement (two-mode squeezing) that can be achieved by this linear chain of NOPAs while the infinite bandwidth limit simplifies the analysis but gives an accurate approximation to the EPR entanglement at low frequencies of interest. Two adjustable phase shifts are placed at the outputs of the system to achieve the best EPR entanglement by selecting appropriate quadratures of the output fields.