Raman scattering with strongly coupled vibron-polaritons

Strong coupling between cavity photons and molecular vibrations can lead to the formation of vibron-polaritons. In a recent experiment with PVAc molecules in a metal-metal microcavity [Shalabney et al., Angew. Chem., Int. Ed. 54, 7971 (2015)], such a coupling was observed to enhance the Raman scattering probability by several orders of magnitude. Inspired by this, we theoretically analyze the effect of strong photon-vibron coupling on the Raman scattering amplitude of organic molecules. This problem has recently been addressed by del Pino, Feist, and Garcia-Vidal [J. Phys. Chem. C 119, 29132 (2015)] using exact numerics for a small number of molecules. In this paper we derive compact analytic results for any number of molecules, also including the ultrastrong-coupling regime. Our calculations predict a division of the Raman signal into upper and lower polariton modes, with some enhancement to the lower polariton Raman amplitude due to the mode softening under strong coupling.

Figure 1

(a) Schematic illustration of the vibronic energy levels in the two electronic manifolds (left) and their hybridization with photon number states (right) to form a ladder of polariton states (middle). (b) Cartoon of molecules placed at the antinode of an optical cavity.

Figure 2

Transition probability to the upper and lower polariton in the RWA. Plotted for ${\omega }_c={\omega }_v, S=0.3, N={10}^6$ molecules, and $\mathrm{\Delta }={\omega }_v$. Note that, as discussed in the text, such a value of $\mathrm{\Delta }$ is far smaller than experimentally relevant, and thus exaggerates the size of any effect.

Figure 3

Transition probability to the LP and UP dependence on the vibron-cavity photon detuning in RWA. Red lines: lower polariton, blue lines: upper polariton. Solid lines correspond to $G\sqrt{N}=0.1{\omega }_v$, and dashed lines to $G\sqrt{N}=0.2{\omega }_v$.

Figure 4

Transition probability to the upper and lower polariton beyond the RWA, including $A^2$ terms. Thick lines plotted for $\delta {\omega }_v=0$, thin lines for $\delta {\omega }_v=-0.5{\omega }_v$. Other parameters as for Fig. 2.