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.Comment: 13 pages, 4 figure