Energy-time entanglement and intermediate-state dynamics in two-photon absorption

It is well known that energy-time entanglement can enhance two photon absorption (TPA) by simultaneously optimizing the resonance and coincidence rate of photons at absorber. However, precise relation between TPA depends on coherences intermediate states involved in transition, making it a rather challenging task to identify universal features processes. In present paper, we show theory be simplified greatly separating from temporal dynamics levels. The result description role process one-dimensional coherence Hilbert space defined arrival time difference photons. Transformation into frequency basis results Kramers-Kronig relations for process, off-resonant contributions virtual levels resonant contributions. particular, shown are insensitive frequencies associated states, indicating virtual-state spectroscopy above final excited state not possible.