Spectroscopy and sensing using quantum light sources have gained significant attention across various research fields. Quantum states of light, particularly those exhibiting different types of entanglement, offer novel ways to control light-matter interactions and enable more precise measurements. This opens up possibilities for manipulating atomic and molecular motions at the microscopic level. For example, photon entanglement has facilitated the control of multi-photon transitions, a hallmark of nonlinear optical processes. Recent research highlights the potential of entangled photons in quantum simulations and their integration with molecular spectroscopy. Studies of multi-photon interactions with complex molecules using quantum-light spectroscopy have shown promising results. Experiments have demonstrated the ability of entangled two-photon absorption (ETPA) to circumvent inhomogeneous line broadening, leading to efficient population of highly-excited molecular states. While multi-photon interactions have been extensively studied in atoms, their investigation in molecules remains a significant challenge due to the coupling of electrons to numerous degrees of freedom. Despite these challenges, experiments have showcased the power of entangled photons in probing and controlling electronic structures with unprecedented precision. Time-resolved ETPA studies have further revealed the remarkable cancellation of molecular correlation functions inaccessible by classical pulses. Entangled photons offer potential for substantial background suppression and improved signal-to-noise ratios. The entanglement-refined interactions can induce nonlinearities that resonate with excited-state relaxation and many-particle couplings, underscoring the need to understand quantum-light interactions with complex molecules at ultrafast timescales. The Raman process, a key aspect of multi-photon interactions, is intrinsically linked to quantum light fields. Research has shown the quantum advantage of entangled light in spectroscopy, with the time-frequency entanglement of photons potentially enabling super-resolution beyond the classical limits of Raman spectroscopy. This paper focuses on the unique time-frequency scales achieved by explicitly including quantum-light interactions with molecules, a crucial step toward advancing spectroscopy and sensing.

Coherent Raman spectroscopy, encompassing various techniques, is a valuable tool in quantum physics and materials characterization. Recent advancements include a femtosecond coherent anti-Stokes Raman spectroscopy (CARS) using entangled photon pairs to monitor ultrafast electronic coherence dynamics and conical intersections. Another study demonstrated CARS with squeezed photons in a nonlinear interferometer, achieving quantum-enhanced measurements beyond the shot-noise limit. Stimulated Raman scattering, another approach, provides sensitivity to molecular populations crucial for understanding cooperative effects and multi-exciton correlations. These populations can be effectively monitored using entangled photons and nonlinear interferometry. Previous work has also investigated time-frequency entanglement in photon pairs before and after up-conversion, laying the groundwork for understanding the time-frequency capabilities of entangled photons in spectroscopy. These studies underscore the potential for quantum-enhanced Raman techniques to surpass the limitations of classical methods.

This article proposes an ultrafast stimulated Raman spectroscopy (USRS) technique employing entangled photons. A microscopic theory is developed using a molecular trimer model. In this model, the molecules actively participate as beam mixers for the Raman pump and probe fields, rather than passively scattering light. The entangled photons, shaped into short pulses, are jointly scattered by molecular excited states, inducing the stimulated Raman process. Coincidence counting of the emitted photons is used to measure the Raman signal, eliminating the need for spectrometers. The Raman interaction between molecules and entangled photons is described by the Hamiltonian V(t) = α(t)Es(t)Ei(t) + h.c., where Es(t) and Ei(t) represent the pump and probe fields respectively, and α(t) is the Raman polarizability operator. The Q-USRS signal, S(Ts, Ti), is defined as the coincidence counting of transmissions along the s and i arms. Equation (2) in the paper gives the detailed expression of S(Ts, Ti) which involves six-point field correlation functions, CI and CII, representing parametric and dissipative processes respectively. Importantly, CI = CII for both quantum and classical fields; however, the entangled photon states lead to a cancellation of these correlation functions, achieving selectivity in the molecular correlation functions not obtainable with classical pulses. To analyze the quantum field correlations from entangled photons, an entangled state of photons is considered with a two-photon wave function Φ(ωs, ωi) that incorporates phase matching. This specific form of the two-photon wave function leads to CI = CII = 0, a consequence of the Hong-Ou-Mandel (HOM) effect. This results in the survival of only the parametric component (loop diagram I) while the dissipative component (loop diagram II) vanishes. The spectral lines are shown to be dependent on the molecular dynamics. Equations (7) and (8) describe the Q-USRS signal, highlighting the time-frequency resolution capabilities enabled by entangled photons. In the case where the time delay between the entangled photons is zero, a simplified expression (equation 9) shows the direct relationship between the Q-USRS signal and the population dynamics of the excited state. The molecular dynamics are modeled using a molecular aggregate model. The Hamiltonian for the molecular trimer includes exciton energies (ωi), intermolecular coupling (Vij(t)), and exciton-vibration coupling. The time evolution of the density matrix is described by an equation of motion that considers radiative and nonradiative relaxation processes. Finally, simulations of the Q-USRS are performed using a Photosystem (PS) trimer model to illustrate the impact of entangled light on stimulated Raman spectra.

The use of entangled photons in ultrafast stimulated Raman spectroscopy (Q-USRS) offers several key advantages over traditional methods. The theoretical framework demonstrates that the entangled nature of the photons leads to a remarkable selectivity in accessing molecular correlation functions. This selectivity is a direct result of the Hong-Ou-Mandel (HOM) interference, which suppresses the dissipative component of the Raman signal while retaining the parametric component. This selective enhancement of specific pathways provides unprecedented access to information about molecular dynamics. The Q-USRS technique achieves a time-frequency resolution beyond the limitations of classical Raman spectroscopy. The analytical expressions derived for the Raman signal clearly show that entangled photons enable the simultaneous determination of both temporal and spectral characteristics, a feat usually limited by the time-bandwidth product. This increased time-frequency resolution allows for a more detailed and precise measurement of molecular relaxation dynamics. Simulations using a molecular trimer model corroborate the theoretical predictions. The simulations show that entangled photons effectively probe the excited-state population dynamics of the molecules. The resulting spectra exhibit a super-resolved nature, offering significantly enhanced information compared to classical Raman approaches. The simulations confirm the suppression of background noise and improved signal-to-noise ratio, thus leading to a more efficient and reliable molecular spectroscopy technique. The research suggests a new paradigm for Raman spectroscopy, which extends the capabilities beyond the limitations of classical light. The use of an unconventional interferometer in the experimental design allows for the selective observation of molecular interactions, thus improving the overall capability to study complex molecular systems.

The findings of this research directly address the challenge of achieving high time-frequency resolution and selectivity in Raman spectroscopy. By demonstrating the effectiveness of entangled photons in achieving both of these characteristics, this study significantly advances the field. The time-frequency entanglement of photons, as shown in the presented theoretical model and confirmed in simulations, offers a substantial improvement over classical Raman techniques which struggle to resolve both fast dynamics and spectral details simultaneously. The selectivity, due to the HOM interference, allows researchers to focus on specific molecular correlation functions, reducing the complexity of analyzing intricate spectral patterns and thereby extracting more meaningful information from complex molecular systems. The implications of this work extend to various fields that rely on spectroscopic techniques for studying molecular structure and dynamics. The ability to obtain more precise and selective information about molecular interactions holds particular relevance for researchers studying complex materials such as photosynthetic complexes, semiconductors, and other systems exhibiting strong many-body interactions. The significant reduction in background noise allows the study of weaker signals that previously were difficult to resolve. The enhanced signal-to-noise ratio also makes this technique more robust and less susceptible to experimental noise, leading to a more reliable and sensitive method for molecular characterization.

This paper presents a novel approach to ultrafast stimulated Raman spectroscopy using entangled photons. The theoretical framework, supported by simulations, demonstrates that this technique offers unprecedented time-frequency resolution and selectivity in probing molecular dynamics. The Hong-Ou-Mandel interference plays a crucial role in enabling selective access to molecular correlation functions, enhancing the signal-to-noise ratio and providing a detailed real-time monitoring of the molecular processes. This study paves the way for more advanced spectroscopic investigations of complex molecular systems and opens up new possibilities for studying ultrafast dynamics in various fields. Future work could explore different types of entangled photon sources and investigate the application of this technique to a wider range of molecules and materials.

While this study presents a compelling theoretical framework and supporting simulations, experimental validation is needed to fully confirm the predicted performance. The molecular trimer model, while useful for illustrating the key principles, might not fully capture the complexity of real-world molecular systems. Further investigations could focus on expanding the model to larger and more complex molecular structures to assess the generality of the proposed method. The sensitivity of the Q-USRS to experimental parameters, such as the photon source characteristics and the molecular environment, requires further detailed analysis and optimization.