Multidimensional Pump-probe Spectroscopy with Entangled Twin-photon States

We show that entangled photons may be used in coherent multidimensional nonlinear spectroscopy to provide information on matter by scanning photon wave function parameters (entanglement time and delay of twin photons), rather than frequencies and time delays, as is commonly done with classical pulses. Signals are expressed and interpreted intuitively in terms of products of matter and field correlation functions using a diagrammatic close time path loop formalism which reveals the entangled quantum pathways of the fields and matter. The pump-probe signal measured when the pump and the probe are in a twin entangled state shows two-photon resonant contributions which scale linearly rather than quadratically with the incident beam intensity and reveal frequencies of off-resonant transitions. Two-dimensional spectrograms obtained by double Fourier transform of the signal with respect to the entanglement time and delay of the twins could provide detailed information on correlations among states and dynamical processes with high temporal resolution. The analogy with multidimensional time-domain optical techniques which use sequences of short classical pulses and pulse shaping algorithms is pointed out.