Temporal dynamics of zero-delay second order correlation function and spectral entanglement of two photons emitted from ladder-type atomic three-level systems.

We theoretically investigate temporal dynamics of the second order cross correlation function at zero delay time (12(2)()) and spectral entanglement of two photons emitted from an atomic three-level cascade. In Heisenberg's picture, a closed set of quantum kinetic equations of motion for 12(2)() is derived within density matrix formalism with cluster expansion rule. 12(2)() shows qualitatively distinctive features depending on the spectral entanglement of two photons. Although incoherent photon pairs generated from spontaneous radiation of the excited electron are not entangled, their correlation and anti-correlation properties can be found in 12(2)() depending on the radiative decay rates. In the coherent excitation regime where the light emitter is located in a high Q-cavity, and its atomic polarizations are predominantly initialized, spectral entanglement between two coherent photons is established. We show that 12(2)() is well fitted by the entanglement criterion by Duan-Giedke-Cirac-Zoller and explain the close relationship between them by means of the optically forbidden transition in the three-level cascade.