Cavity Jahn-Teller polaritons in molecules

Jahn-Teller (JT) polaritons emerge when the two perpendicular, normal-incidence electromagnetic modes of a Fabry-Perot cavity interact with JT active systems. These JT polaritons are characterized by a mixed $(+/-)$–circular electromagnetic polarization mediated by the molecular JT vibronic coupling of the material subsystem. Consequently, the exchange of photonic and vibronic angular momenta can be very efficient. Due to the photonic-vibronic coupling, the magnitude and direction of the cavity polarization varies for different eigenstates of the cavity-molecule system. This type of light-matter coupling results in polarization inverted states in the polaritonic system—states that can be reached resonantly with either right or left circularly polarized light but which are characterized by a cavity-photon polarization opposite to the external fields used to excite the system.

Figure 1

Schematic of a JT active system situated inside the FP cavity. The symmetry axis of the JT system, represented by the triangular-shaped molecule, and the wave vector $\vec{k}$ of the $x\left(y\right)$-polarized cavity light point along the $z$ axis. The cavity is schematically represented by mirrors (in gray) separated by a distance $L$. The $x\left(y\right)$-polarized cavity mode interacts via dipole coupling with the $E_x\left(E_y\right)$ degenerate electronic excitation of the JT system.

Figure 2

Coupling of cavity modes (cyan) with $(+)$ and $(-)$ polarizations through molecular JT vibronic coupling (yellow): an initial one-photon state of $(+)$ polarization of the cavity-JT system, $p_{+}=1$, transfers angular momentum to the $E_{+}$ electronic state of the molecule (red) through light-matter coupling (step I). The $E_{+}$ electronic state couples to $E_{-}$ by virtue of the JT coupling (step II), involving angular momentum exchange with the vibrations: the vibrational pseudorotation increases $n_{+}$ by one unit [see Eq. (1)]. The negative electronic angular momentum in the $E_{-}$ state finally couples to the cavity mode with $(-)$ polarization via light-matter coupling, thus increasing $p_{-}$ by one (step III). Throughout the coupling mechanism, $j$ is conserved.

Figure 3

The absorption spectrum of the ($E\times e$) JT model of sym-triazine (in black) and the spectrum of the same system coupled to the FP cavity (in orange) in Fig. 1. Absorption lines are convoluted with a 44-meV Lorentzian shape. The spectrum corresponds to the absorption by RCP light propagating along the $z$ axis from right to left according to the schematic in Fig. 1. The ${\omega }_c$ is set at the energy of the most optically bright state of the bare JT spectrum (indicated with red arrow) of the triazine, which is lying below the CI energy $\epsilon$ (marked $\times$ on the energy axis). The expectation value of the photon polarization for each JT polaritonic eigenstate ${\mathcal{P}}_k^{-1}/\hslash$ is shown in blue (middle $y$ axis).

Figure 4

Expectation value of the cavity polarization for the most optically bright $k$ state within $j=-1$ block as a function of the cavity-molecule couplings ($\mathrm{\Omega }/2{\omega }_c$) at selected JT coupling ($\kappa /\omega$).