Quantum Description of Cavity Raman Elucidates "Anomalous" anti-Stokes SERS

Gold nanospheres, (~90 nm in diameter), plasmonically confine and enhance incident radiation sufficient to approach the limit of single-molecule Raman detection. In this regime, we record the power-dependent anti-Stokes-to-Stokes (AS-to-S) ratio of a BPE molecule and find that there is no satisfactory map to the canonical quantum model with vibrational pumping + laser-induced heating. Non-thermal anti-Stokes exceed three orders of magnitude enhancement over conservative estimates of the pumping effect. With impetus from this anomalous AS behavior, we revisit optomechanical models of Raman both with explicit numerical simulation as well as a perturbation algorithm to generate analytical expressions for higher-order scattering terms. These tools let us characterize novel pathways that harness the heterodyning effect of the cavity luminescence spectrum. We show that these channels may far exceed the feeble pumping component, thus elucidating the anomaly. Notably, the novel pathways are second order in the pump but only first order in the Raman cross-section, a unique attribute that is reflected in the data.