Multiphoton absorption cross section and virtual-state spectroscopy for the entangledn-photon state

Using a microscopic theory, we determine the entangled $n$-photon state generated both by the nonlinear process of spontaneous $n$-photon parametric down-conversion and in a cascade of $n-1$ crystals with two-photon parametric down-conversions. Expressions for the entangled $n$-photon absorption cross sections are also obtained. The absorption cross sections exhibit a linear dependence on the photon flux density, and depend on the entanglement times characterizing photons. The effect of relative path delay in the beams is discussed. It forms the basis for extracting the quadrupole moments between states involved in the interaction from the absorption cross section measured as a function of path delay. Effects competitive with entangled three-photon absorption are discussed.