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Multi-mode entanglement is one of the critical resource in quantuminformation technology. Generating large scale multi-mode entanglement state bycoherently combining time-delayed continuous variables Einstein-Podolsky-Rosenpairs with linear beam-splitters has been widely studied recently. Here wetheoretically investigate the multi-mode quantum correlation property of theoptical fields generated from an unbalanced SU(1,1) interferometer pumpedultra-short pulses, which generates multi-mode entangled state by using anon-degenerate parametric processes to coherently combine delayedEinstein-Podolsky-Rosen pairs in different frequency band. The covariancematrix of the generated multi-mode state is derived analytically for arbitrarymode number $M$ within adjacent timing slot, which shows a given mode ismaximally correlated to 5 other modes. Based on the derived covariance matrix,both photon number correlation and quadrature amplitude correlation of thegenerated state is analyzed. We also extend our analyzing method to the schemeof generating entangled state by using linear beam splitter as a coherentcombiner of delayed EPR pairs, and compare the states generated by the twocoherently combining schemes. Our result provides a comprehensive theoreticaldescription on the quantum correlations generated from an unbalanced SU(1,1)interferometer within Gaussian system range, and will offer more perspectivesto quantum information technology.

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