Superradiant cascade emissions in an atomic ensemble via four-wave mixing

We investigate superradiant cascade emissions from an atomic ensemble driven by two-color classical fields. The correlated pair of photons (signal and idler) is generated by adiabatically driving the system with large-detuned light fields via four-wave mixing. The signal photon from the upper transition of the diamond-type atomic levels is followed by the idler one which can be superradiant due to light-induced dipole-dipole interactions. We then calculate the cooperative Lamb shift (CLS) of the idler photon, which is a cumulative effect of interaction energy. We study its dependence on a cylindrical geometry, a conventional setup in cold atom experiments, and estimate the maximum CLS which can be significant and observable. Manipulating the CLS of cascade emissions enables frequency qubits that provide alternative robust elements in quantum network.