Pump-Intensity Scaling of Two-Photon Absorption and Photon Statistics of Entangled-Photon Fields

We use a nonperturbative theoretical approach to the parametric down-conversion (PDC) process, which generates an entangled-photon field for an arbitrarily strong pump-pulse. This approach can be used to evaluate multipoint field correlation functions to compute nonlinear spectroscopic signals induced by a strong pump. The entangled-photon statistics is studied using Glauber's <i>g</i>⁽²⁾ function, which helps understand the significance of the photon entanglement-time and the pump-pulse intensity on spectroscopic signals. Under the nonperturbative treatment of the entangled field, the two-photon absorption (TPA) signal shows linear to strongly nonlinear growth with the pump intensity, rather than the linear to quadratic scaling reported previously. An increase in the range of pump intensity for the linear scaling is observed as the pump bandwidth is increased. We propose an experimental scheme that can select contributions to the TPA signal that arise solely from interactions with the entangled photons, and filter out unentangled-photon contributions, which are dominant at higher pump intensities, paving a way to explore the entanglement effects at higher intensities.