Cavity-Controlled Chemistry in Molecular Ensembles

The demonstration of strong and ultrastrong coupling regimes of cavity QED with polyatomic molecules has opened new routes to control chemical dynamics at the nanoscale. We show that strong resonant coupling of a cavity field with an electronic transition can effectively decouple collective electronic and nuclear degrees of freedom in a disordered molecular ensemble, even for molecules with high-frequency quantum vibrational modes having strong electron-vibration interactions. This type of polaron decoupling can be used to control chemical reactions. We show that the rate of electron transfer reactions in a cavity can be orders of magnitude larger than in free space for a wide class of organic molecular species.

Figure 1

(a) Nuclear potentials for a single molecule along the reaction coordinate $q$. Excited states $|e⟩$ and $|f⟩$ are shifted with respect to the ground state by $q_0^{(e)}$ and $q_0^{(f)}$ in free space. A cavity field $\widehat{a}$ couples to the transition $|g⟩\leftrightarrow |e⟩$ with a detuning ${\mathrm{\Delta }}_e$ and Rabi frequency ${\mathrm{\Omega }}_e$. For large enough ${\mathrm{\Omega }}_e$, the cavity effectively shifts the potential minimum in state $|e⟩$ to coincide with $|g⟩$ (right gray arrow). State $|f⟩$ does not couple to the cavity. (b) Cavity-dressed spectrum for an ensemble of $N$ molecules with vibronic coupling showing the splitting of the permutation-symmetric collective dressed states $|\pm ,\tilde{m}⟩$ from the cavity-free polaron eigenstates $\mathcal{Q}|{\mathrm{\Psi }}_N⟩$. ${\omega }_v$ is the vibrational frequency.

Figure 2

Cavity-induced polaron decoupling. (a) Probability $P_0$ for the lowest many-body dressed state to be decoupled from molecular vibrations, as a function of the number of molecules $N$ in a linear lattice. Several values of the Rabi frequency are shown: ${\mathrm{\Omega }}_{\mathrm{e}}/{\omega }_v=4$ (curve $a$) and ${\mathrm{\Omega }}_e/{\omega }_v=2$ (curve $b$). ${\omega }_v$ is the vibrational frequency. (b) $P_0$ as a function of ${\mathrm{\Omega }}_e/\sigma$ for a linear array of size $N=10$ and disorder width $\sigma$. 2500 disorder realizations are included in the shaded area. Dashed lines in both panels correspond to $P_0=\exp [-{\lambda }_e^2/4N]$, with ${\lambda }_e^2=1$.

Figure 3

ET rate $k_{\mathrm{ET}}$ in an optical cavity. (a) Ratio $k_{\mathrm{ET}}/k_0$ as a function of $N$. $k_0$ is the ET rate in free space. Curves are shown for $\mathrm{\Delta }E=0$ (curve $a$), $\mathrm{\Delta }E=2{\gamma }_v$ (curve $b$), and $\mathrm{\Delta }E=5{\gamma }_v$ (curve $c$). We set ${\lambda }_D=-{\lambda }_A=\sqrt{2}$. (b) $k_{\mathrm{ET}}/k_0$ as a function of ${\lambda }_D/{\lambda }_A$ for $N={10}^4$ molecules with ${\lambda }_A=\sqrt{2}$ and $\mathrm{\Delta }E=0$ (circles). The solid line is the analytical bound in Eq. (7). In both panels, the vibrational linewidth is $\hslash {\gamma }_v=0.01\hslash {\omega }_v$, where ${\omega }_v$ is the vibrational frequency, and $k_{B}T=0.1\hslash {\omega }_v$. $\mathrm{\Delta }E\ll {\omega }_v$ is the donor-acceptor electronic transition frequency taken to be the same in the cavity and in free space.