Perturbative approach in the frequency domain for the intensity correlation spectrum at electromagnetically induced transparency

Correlation spectroscopy has been proposed as a spectroscopic technique for measuring the coherence between the ground states in electromagnetically induced transparency (EIT). While in time domain the steep dispersion in EIT condition accounts for the robustness of the correlation linewidth against power broadening, such physical insight was not directly established in the frequency domain. We propose a perturbative approach to describe the correlation spectroscopy of two noisy lasers coupled to a $\Lambda$-transition in cold atoms, leading to EIT. Such approach leads to an analytical expression that maps the intensity correlation directly in terms of the absorption and dispersion of the light fields. Low and high perturbative regimes are investigated and demonstrate that, for coherent light sources, the first oder term in perturbation expansion represents a sufficient description for the correlation. Sidebands resonances are also observed, showing the richness of the frequency domain approach.