Theory for Entangled-Photons Stimulated Raman Scattering versus Nonlinear Absorption for Polyatomic Molecules

Abstract

Quantum entanglement offers an incredible resource for enhancing the sensing and spectroscopic probes. Here we develop a microscopic theory for the stimulated Raman scattering (SRS) using entangled photons. We demonstrate that the time-energy correlation of the photon pairs can optimize the signal for polyatomic molecules. Our results show that the spectral-line intensity of the entangled-photon SRS (ESRS) is of the same order of magnitude as the one for the entangled two-photon absorption (ETPA); the parameter window is thus identified to do so. Moreover, the vibrational coherence is found to play an important role for enhancing the ESRS against the ETPA intensity. Our work paves a firm road for extending the schemes of molecular spectroscopy with quantum light, based on the observation of the ETPA in experiments.

Figures (5)

• Figure 1: Level scheme of molecular system. $g,~e,~f$ represents different electron levels, the group of solid black lines are vibrational modes, $\delta_\omega$ between the dashed lines represents the detuning between real energy state and virtual touched one. (a) ETPA process, the molecule absorbs idler photon first to the $e$ state, and then absorbs signal photon to the final $f$ state. (b) ESRS process, the molecule absorbs idler photon first to the $e$ state, and then stimulated emits a photon with the same frequency of signal photon back to the $g$ state. (c) Joint spectral intensity $|F_{PDC}|^2$ of entangled photon pair. Correlated photons $\Omega_m=0.05\text{fs}^{-1},~\Omega_p=0.3\text{fs}^{-1}$ for ESRS. (d) Frequency anti-correlated photon pairs with $\Omega_p=0.05\text{fs}^{-1},~\Omega_m=0.3\text{fs}^{-1}$ for ETPA. (e) Experimental setup for the proposed ETPA and ESRS measurement. A pump photon is down-converted into two photons with frequencies $\omega_s$ and $\omega_i$. Both photons are then directed to the molecule sample.
• Figure 2: TPA/SRS ratio with the same input entangled photon pairs. $\tilde{D}$ stands for a global decay rate of high-frequency vibrations, as induced by low-frequency vibrational modes. (a) $\tilde{D}=3$ as a comparable result for the probability of ETPA and ESRS. (b) $\tilde{D}=300$ case when ETPA signal is way more stronger than ESRS.
• Figure 3: The signal strength of ETPA, ESRS and their comparison under central frequency sum and difference. (a) Signal distribution for ETPA. The central peak is at $\omega_+=7.5\text{eV},~\omega_-=0\text{eV}$. (b) Signal distribution for ESRS. The first SRS signal peak is at $\omega_+=8.14\text{eV},~\omega_-=\pm 0.17\text{eV}$. (c) The ratio of ETPA over ESRS in the magenta rectangular region. $\delta\omega_+$ and $\delta\omega_-$ are the relative frequency compared with the central peak of the signals. ($\delta\omega_+^{\text{TPA}}, \delta\omega_-^{\text{TPA}}$)=($\omega_+^{\text{TPA}}-7.5$eV,$\omega_+^{\text{TPA}}$), ($\delta\omega_+^{\text{SRS}},\delta\omega_-^{\text{SRS}}$)=($\omega_+^{\text{SRS}}-8.14$eV, $\omega_+^{\text{SRS}}-0.17$eV). The image shows the logarithmic value.
• Figure 4: (a) ETPA/ESRS intensity via high frequency coupling strength $F_j$ and low frequency decay rate $\tilde{D}$. The Black solid line represents the conditions where ETPA signal is an order of magnitude higher than ESRS.(b) ETPA and ESRS signal strength via the change of middle state detunings. The x-label is the variety of detuning for ETPA, and the y-label is the change of detuning for ESRS. The black solid line is the curve when ETPA is tenfold of ESRS, and the black dashed line describes when ESRS is tenfold of ETPA. The central red circle represents the region where both detunings are small. Both images show the logarithmic value.
• Figure 5: The ratio of ETPA and ESRS under their optimal conditions via different temperature.