Multi-mode quantum correlation generated from an unbalanced SU(1,1) interferometer using ultra-short laser pulses as pump

TL;DR

This paper provides a theoretical analysis of multi-mode quantum correlations generated from an unbalanced SU(1,1) interferometer pumped by ultra-short laser pulses, revealing detailed covariance properties and correlations in the generated entangled states.

Contribution

It introduces an analytical derivation of the covariance matrix for multi-mode states from an unbalanced SU(1,1) interferometer and compares it with linear beam splitter schemes.

Findings

Maximal correlation of a mode with five others.

Analytical covariance matrix for arbitrary mode number.

Comparison between SU(1,1) interferometer and linear beam splitter schemes.

Abstract

Multi-mode entanglement is one of the critical resource in quantum information technology. Generating large scale multi-mode entanglement state by coherently combining time-delayed continuous variables Einstein-Podolsky-Rosen pairs with linear beam-splitters has been widely studied recently. Here we theoretically investigate the multi-mode quantum correlation property of the optical fields generated from an unbalanced SU(1,1) interferometer pumped ultra-short pulses, which generates multi-mode entangled state by using a non-degenerate parametric processes to coherently combine delayed Einstein-Podolsky-Rosen pairs in different frequency band. The covariance matrix of the generated multi-mode state is derived analytically for arbitrary mode number $M$ within adjacent timing slot, which shows a given mode is maximally correlated to 5 other modes. Based on the derived covariance matrix, both photon number correlation and quadrature amplitude correlation of the generated state is analyzed. We also extend our analyzing method to the scheme of generating entangled state by using linear beam splitter as a coherent combiner of delayed EPR pairs, and compare the states generated by the two coherently combining schemes. Our result provides a comprehensive theoretical description on the quantum correlations generated from an unbalanced SU(1,1) interferometer within Gaussian system range, and will offer more perspectives to quantum information technology.