  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.
