Cavity-Correlated Electron-Nuclear Dynamics from First Principles

The rapidly developing and converging fields of polaritonic chemistry and quantum optics necessitate a unified approach to predict strongly correlated light-matter interactions with atomic-scale resolution. Toward this overarching goal, we introduce a general time-dependent density-functional theory to study correlated electron, nuclear, and photon interactions on the same quantized footing. We complement our theoretical formulation with the first ab initio calculation of a correlated electron-nuclear-photon system. For a ${\mathrm{CO}}_2$ molecule in an optical cavity, we construct the infrared spectra exhibiting Rabi splitting between the upper and lower polaritonic branches, time-dependent quantum-electrodynamical observables such as the electric displacement field, and observe cavity-modulated molecular motion. Our work opens an important new avenue in introducing ab initio methods to the nascent field of collective strong vibrational light-matter interactions.

Figure 1

Infrared spectra in vibrational strong coupling for ${\mathrm{CO}}_2$. Black spectrum refers to the spectrum outside the cavity. We explicitly depict the two infrared-active vibrational modes of the ${\mathrm{CO}}_2$ molecule. Blue spectra correspond to the electron-nuclear spectrum. Importantly, we capture the Rabi splitting between the lower and upper polariton branches.

Figure 2

Vibrational excitation at $2430{\mathrm{cm}}^{-1}$. Initial displacement of the C atom of 0.01 Å, (a) dipole moment ${\mathrm{CO}}_2$ outside the cavity, (b) dipole moment ${\mathrm{CO}}_2$ under strong light-matter coupling for ${\lambda }_{\alpha }=0.05$, (c) the photon displacement coordinate $q_{\alpha }(t)$ as defined in Eq. (5) for ${\lambda }_{\alpha }=0.05$.

Figure 3

Spinning molecule. From top to bottom: infrared spectrum after 5 ps for a ${\mathrm{CO}}_2$ molecule under strong light-matter coupling with ${\lambda }_{\alpha }=0.05$. Center: time-evolution of the expectation value of $q_{\alpha }(t)$. Bottom: snapshots of the nuclear positions of the spinning molecule for $t=(0,1205,4000)\mathrm{fs}$. The blue area indicates the polarization direction of the photon mode.