Optomechanical Collective Effects in Surface-Enhanced Raman Scattering from Many Molecules

The interaction between molecules is commonly ignored in surface-enhanced Raman scattering (SERS). Under this assumption, the total SERS signal is described as the sum of the individual contributions of each molecule treated independently. We adopt here an optomechanical description of SERS within a cavity quantum electrodynamics framework to study how collective effects emerge from the quantum correlations of distinct molecules. We derive analytical expressions for identical molecules and implement numerical simulations to analyze two types of collective phenomena: (i) a decrease of the laser intensity threshold to observe strong nonlinearities as the number of molecules increases, within very intense illumination, and (ii) identification of superradiance in the SERS signal, namely a quadratic scaling with the number of molecules. The laser intensity required to observe the latter in the anti-Stokes scattering is relatively moderate, which makes it particularly accessible to experiments. We treat the system on the basis of the individual molecules and demonstrate that for ideal systems with identical molecules this approach is equivalent to a description based on collective modes. The basis of individual molecules also allows for describing in a straightforward manner more general systems where the molecules might have different vibrational properties or suffer from pure-dephasing processes. Our results show that the collective phenomena can survive in the presence of the homogeneous and inhomogeneous broadening that might influence experimental results.