The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by quantum fluctuations. We utilize the positive-
P phase-space method to investigate the dynamics of the atoms and counterpropagating emissions. The light field intensities are calculated, and the signal-idler correlation function is studied for different optical depths of the atomic ensemble. A shorter correlation time scale for a denser atomic ensemble implies a broader spectral window needed to store or retrieve the idler pulse.
We theoretically investigate the spectral entanglement of a multiphoton source generated from the cascade emissions in cascaded cold atomic ensembles. This photon source is highly directional, which is guaranteed under the four-wave mixing condition, and is also highly frequency correlated due to finite driving pulse durations and superradiant decay constants. We utilize Schmidt decomposition to study the bipartite entanglement of the biphoton states projected from the multiphoton ones. This entropy of entanglement can be manipulated by controlling the driving parameters and superradiant decay rates. Moreover, the projected biphoton states in the cascaded scheme can have larger entanglement than the one produced from only one atomic ensemble, which results from larger capacity in multipartite entanglement. This cascaded scheme enables a multiphoton source useful in quantum-information processing. It also allows for potential applications in multimode quantum communication and spectral shaping of high-dimensional continuous frequency entanglement.