Collective Jahn-Teller Interactions through Light-Matter Coupling in a Cavity

The ultrafast nonradiative relaxation of a molecular ensemble coupled to a cavity mode is considered theoretically and by real-time quantum dynamics. For equal coupling strength of single molecules to the cavity mode, the nonradiative relaxation rate from the upper to the lower polariton states is found to strongly depend on the number of coupled molecules. The coupling of both bright and dark polaritonic states among each other constitutes a special case of (pseudo-)Jahn-Teller interactions involving collective displacements the internal coordinates of the molecules in the ensemble, and the strength of the first order vibronic coupling depends exclusively on the gradient of the energy gaps between molecular electronic states. For $N>2$ molecules, the $N-1$ dark light-matter states between the two optically active polaritons feature true collective conical intersection crossings, whose location depends on the internal atomic coordinates of each molecule in the ensemble, and which contribute to the ultrafast nonradiative decay from the upper polariton.

Figure 1

Single-molecule photodissociation probability $P_{\mathsf{dis}}(t)=⟨\mathrm{\Psi }(t)|\mathrm{\Theta }(R_1-R_b)|\mathrm{\Psi }(t)⟩$ as a function of time for an ensemble of different size interacting with a laser pulse of photon energy $\hslash {\omega }_L=3.9\mathrm{eV}$. $R_b=15$ au. The dashed curves correspond to fitted first order rate expressions.

Figure 2

Polaritonic PES obtained by the diagonalization of Hamiltonian [Eq. (4)] for the case of $N=5$ molecules. Upper and lower solid curves correspond to the nominally bright polaritons whereas the dashed curves correspond to the nominally dark states.