Nonlinear quantum interferometric spectroscopy with entangled photon pairs

Abstract: We develop closed expressions for a time-resolved photon counting signal induced by an entangled photon pair in an interferometric spectroscopy setup. Superoperator expressions in Liouville-space are derived that can account for relaxation and dephasing induced by coupling to a bath. Interferometric setups mix matter and light variables non-trivially, which complicates their interpretation. We provide an intuitive modular framework for this setup that simplifies its description. Based on separation between the detection stage and the light-matter interaction processes. We show that the pair entanglement time and the interferometric time-variables control the observed physics time-scale. Only a few processes contribute in the limiting case of small entanglement time with respect to the sample response, and specific contributions can be singled out.