Ultrafast optical techniques are crucial for probing the dynamics of various excitations in complex materials. Advances in pulse shaping and two-photon absorption with photon entanglement have significantly improved the efficiency of populating higher excited states by suppressing intermediate state relaxation. Entangled photon states offer additional control over molecular relaxation and radiative processes, enabling sub-picosecond time-resolved studies. While stimulated Raman and pump-probe spectroscopies have shown enhanced resolution via photon entanglement, the ultrafast dynamics of electronic coherence remains challenging due to its rapid decay. This work aims to leverage the unique properties of entangled photons to overcome these limitations and develop a new spectroscopic technique for high-resolution, ultrafast studies of electronic and vibrational coherences in molecules.

Previous research has highlighted the potential of entangled photons in enhancing spectroscopic techniques. Studies have demonstrated the use of entangled photons in two-photon absorption, suppressing intermediate state relaxation and improving the efficiency of populating higher excited states. Work on stimulated Raman and pump-probe spectroscopies has shown improved resolution through model calculations using entangled photons. Recent advancements in semiconductor quantum-light sources have shown promise in generating high photon flux and scalability for ultrafast optical probing of nanostructures and low-dimensional materials. Ultrafast multi-photon coincidence counting and manipulation of temporal and spectral profiles of entangled photons have enabled super-resolved imaging and surpassed standard quantum limits, indicating the potential of quantum-light spectroscopy for novel applications.

The authors present Quantum FAST CARS (Q-FAST CARS) using entangled photons. In this setup, a pair of entangled photons are generated via spontaneous parametric down-conversion (SPDC). One photon serves as a Raman probe, interacting off-resonantly with molecules, while the idler photon acts as a reference. The field-molecule interaction is described by equation (1), where the Raman polarizability and electric fields are defined. The Heisenberg equation of motion for emitted photons (equation 3) is solved using perturbation expansion (equation 4). The four-point field correlation function is crucial for understanding the spectral properties. Joint detection of spectral-resolved transmissions in two arms yields the intensity-correlated signal (equation 5) and ultimately equation (6) which is the Quantum FAST CARS signal. The spectral resolution is analyzed by comparing signals from entangled photons, Fock states, and pseudo-thermal light. To monitor ultrafast electronic coherence in excited states, a resonant photoexcitation precedes the Raman probing (Fig. 1d). Equation (7) and (8) describe the intensity-correlated QFRS signal incorporating the electronic polarizability α(t). The Fröhlich-Holstein model (equation 10) describes the electronically excited-state dynamics coupled to nuclear motions. Equation (11) gives the intensity-correlated QFRS signal, accounting for vibronic coupling and dephasing. The heterodyne-detected QFRS uses a Mach-Zehnder interferometer to record interference between s-arm photons (serving as a local oscillator) and emitted photons, resulting in equation (12) and (13).

The study demonstrates that using entangled photons in femtosecond time-resolved coherent Raman spectroscopy significantly enhances spectral resolution. Quantum FAST CARS signals (equation 6) show a spectral resolution governed by photon entanglement, allowing independent control and improvement compared to classically shaped pulses. The comparison with Fock states and pseudo-thermal light highlights the unique advantages of entangled photons. The intensity-correlated QFRS (equations 7-9) reveals ultrafast electronic coherence dynamics, resolving vibronic couplings and revealing slower decay of peaks at ωei + nνi due to weaker influence from low-frequency vibrations (Fig. 2a). Classical pulses and uncorrelated photons produce significantly poorer resolutions (Fig. 2c,e). The heterodyne-detected QFRS (equations 12-13) provides a method to obtain phase information about the excited states, complementing the intensity-correlated measurements. The highly time-frequency resolved nature of QFRS is due to the spectral-resolved idler photons, offering independent control over temporal and spectral resolutions.

The results demonstrate the superior capabilities of QFRS compared to classical techniques. The enhanced spectral and temporal resolution achieved through photon entanglement provides detailed information about electronic and vibrational coherences, resolving vibronic couplings and ultrafast dynamics inaccessible with classical pulses. The independent control of spectral and temporal resolution offered by entangled photons overcomes a long-standing limitation in ultrafast Raman spectroscopy. The comparison between intensity-correlated and heterodyne-detected QFRS signals highlights the complementary nature of these methods, suggesting a more comprehensive understanding of molecular dynamics can be achieved by combining these techniques.

This work introduces Quantum Femtosecond Raman Spectroscopy (QFRS), a new technique utilizing entangled photons to achieve unprecedented time-frequency resolution in Raman spectroscopy. The improved resolution allows detailed study of electronic and vibrational coherences, including vibronic couplings and ultrafast dynamics. Both intensity-correlated and heterodyne-detected QFRS methods are presented, offering complementary information. Future research can explore further applications of QFRS to study a wider range of materials and complex molecular systems, and to develop more sophisticated quantum light sources to optimize this technology.

The current study focuses on specific model systems. Extending the applicability to more complex and diverse molecular systems requires further investigation. While the theoretical framework is well-established, experimental validation and refinement of the QFRS techniques are necessary to optimize the signal-to-noise ratio and expand the range of measurable parameters. The computational cost associated with the modeling of complex molecular systems can be high.