Signatures of Narrowband and Ultrashort-Pulse-Like Probing in Coherent Anti-Stokes Raman Scattering Using Twin Beams and Sum-Frequency Generation Readout

Abstract

We theoretically investigate coherent anti-Stokes Raman scattering (CARS) driven by bright twin beams with sum-frequency generation (SFG) readout. Expressing the SFG output in terms of quantum-field correlation functions yields multiple correlation structures with distinct properties associated with different interaction pathways on the bra and ket sides. Among them, frequency correlations between the CARS probe and SFG gating fields enable the two fields to act collectively as an effective narrowband probe, avoiding probe-induced spectral convolution. When this behavior appears on either the bra or ket side, the other retains Raman relaxation information as if probed by an ultrashort pulse.

Can bright twin beams support Raman spectroscopy that resolves both intrinsic spectral structure and relaxation dynamics? This paper analyzes coherent anti-Stokes Raman scattering (CARS), with the signal beam supplying pump and probe fields and the idler supplying Stokes and sum-frequency-generation (SFG) gating fields. It asks whether contributions without probe-induced spectral convolution can also retain temporal information. The SFG photon-number signal is derived from a Bogoliubov model of parametric down-conversion and decomposed into 24 field-correlation terms, grouped by their frequency constraints. Probe–gate frequency anticorrelation on both bra and ket pathways yields a contribution proportional to $|\chi(\omega_{\rm sfg}-\Omega_e)|^2$, multiplied by spectral and delay-dependent factors. This contribution avoids probe-bandwidth convolution but does not resolve Raman relaxation. Interference terms with probe–gate anticorrelation on only one pathway instead contain an un-convolved susceptibility factor multiplied by a time-dependent response. For a single Lorentzian Raman resonance, high gain ($\mu\approx\nu$), Gaussian beam spectra, and matched probe/gate delays, the latter response becomes a convolution of exponential relaxation with a short temporal overlap function. When that overlap is short compared with $1/\Gamma$, its delay dependence approaches $e^{-\Gamma\tau}$. The treatment neglects dispersive propagation phases and assumes independently controllable probe and gate delays. Although delay-independent backgrounds can in principle be subtracted using long-delay measurements, isolating the interference contribution from other SFG contributions remains unresolved and is left for future work. No experimental demonstration of this combined spectral–temporal readout is presented.