The secular approximation is used to calculate an analytic expression for the intensity correlation function for two atoms undergoing cooperative decay. The analysis is valid for high incident field strengths and arbitrary frequency detuning.
We generalize our earlier formalism to treat the effects of both the finite-bandwidth excitations and finite arbitrary detunings, on the fluorescent spectra and second-order intensity correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom in cascade configuration. Under the conditions that one or both of these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity correlation functions which explicitly display the effects due to detunings and fluctuations.
The spectrum of resonance fluorescence and the second-order correlation function are calculated for a system of two identical two-level cooperative systems interacting via the dipole-dipole interaction. The results are valid for arbitrary incident-field strengths and for atomic separations much less than the resonant wavelength. The intensity of the sidebands at the Rabi frequency is diminished by the dipole interaction, whereas that of the sidebands at twice the Rabi frequency is enhanced. Both the cooperative behavior and the dipole-dipole interaction act to diminish the photon antibunching, as shown by the second-order correlation function.
We suggest that the intensity correlation function could be an important tool in the study of atomic cooperative behavior because it contains predominantly components at 0, $\ifmmode\pm\else\textpm\fi{}4\ensuremath{\Omega}$ in the limit of large Rabi frequency ($2\ensuremath{\Omega}$) and large cooperation number. This is in contrast with the single-atom prediction where the intensity correlation function contains only frequency components at 0, $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega}$. The master equation for the collective system is solved analytically in the secular approximation.