Collective Vibronic Cascade in Cavity-Coupled Jahn-Teller Active Molecules

Abstract

We study the polaritonic states and dynamics of multiple Jahn-Teller (JT) active molecules coupled to the modes of a Fabry-Perot cavity. We find that collective effects dramatically alter the interplay of electronic, vibrational and cavity angular momenta, giving rise to markedly different polaritonic spectra and dynamics even when going from one to two JT molecules. Starting from the ground vibronic state, we find that JT molecules collectively coupled to a common cavity can access a cascade of high-angular-momentum vibronic states in the presence of a single cavity photon, in sharp contrast to the single molecule case where the range of accessible vibronic angular momentum values are bounded. The observable consequences are a broadening of the cavity-molecular polariton spectrum and a suppression of photon polarization dynamics under broadband excitation of the system. Our results uncover new pathways for vibronic angular momentum transfer unique to collective molecular polaritonics with potential implications for cavity-assisted photo-physics and photo-chemistry.

Figures (4)

• Figure 1: (a) Schematic of $(E \times e)$ Jahn-Teller (JT) active molecules (represented here by sym-triazine systems) situated inside a Fabry-Perot cavity. The symmetry axis of the JT molecules and the wave vector $\vec{k}$ of the $x(y)$-polarized cavity light point along the $z$-axis. (b) JT coupled electronic $\ket{E_\pm}$ states and the ground $\ket{A}$ state of the molecules, sketched as a function of vibrational mode coordinate ($Q$), coupled via the cavity modes with frequency $\omega_c$ (red arrow). Two circularly polarized modes with angular momentum $\pm\hbar$ can be defined from the linearly polarized $x$ and $y$ modes of the cavity bar_12_013845.
• Figure 2: (a) Vibronic spectrum of a single JT molecule. The energy levels are grouped into different vibronic angular momentum sectors, labeled by $v$. (b) Collective vibronic angular momentum cascade: The mechanism of molecule-cavity coupling for the case of single JT molecule ($N$=1, shaded in orange) and for the case of two JT molecules ($N$=2, shaded in green) coupled to the cavity (cf. Fig. \ref{['fig:setup']}). In the latter case, starting from a single right-circularly polarized cavity photon and the two molecules in the ground state, the vibronic-photonic coupling leads to a proliferation of $v$ values for the two molecules. In contrast, the maximum value of accessible $v$ is restricted to $2$ in the $N$=1 case. The coupling mechanism follows the conservation of total vibronic-photonic angular momentum $j$ in both the cases.
• Figure 3: Polaritonic spectra for (a) $N$=1, (b) $N$=2, and (c) $N$= 4 and 8 JT molecules coupled to the FP cavity. The spectra are obtained by setting the cavity resonant with the most optically bright JT vibronic state (shown in (a), grey); the '$\textcolor{magenta}{\times}$' in (a) indicates the $\ket{A}\leftrightarrow\ket{E_\pm}$ energy separation $\epsilon$. The stick spectra in (a, b) are obtained by the diagonalization of the total Hamiltonian in Eq. (\ref{['eqn:ham_tot']}). The color of the sticks indicates the participation ratio of the vibronic sectors, which quantifies the range of accessible vibronic angular momenta $v$ for each JT molecule. The low-resolution spectra (solid curves) in all the panels are obtained using the MCTDH method mctdh_2.
• Figure 4: Cavity-polarization dynamics under broadband excitation. (a) Net cavity-polarizations associated with polaritonic states belonging to the $(1, -1)$ sector for $N$ = 1 (orange) and $N=$ 2 (black). (b) Time-dependent response of cavity-polarizations to an external RCP pulse for (b) $N$=1 and 2, and (c) $N$= 4 and 8. The polarizations are obtained by targeting the UP branch with a short $20$ fs pulse of bandwidth $\sim0.25$ eV (shaded in green, in (a)). Exactly the same time-dependent response, but with an opposite sign, can be triggered with an LCP pulse by targeting the $(1,1)$ sector.