Initialization with a Fock State Cavity Mode in Real-Time Nuclear--Electronic Orbital Polariton Dynamics

TL;DR

This work probes whether a quantized cavity mode initialized in a Fock state can reveal polariton dynamics that require quantum electrodynamics beyond semiclassical models. By comparing mean-field quantum (mfq-RT-NEO) and full-quantum (fq-RT-NEO) real-time NEO TDDFT methods, the authors show that mfq-RT-NEO yields no polariton formation due to the lack of light–matter entanglement, while fq-RT-NEO exhibits substantial entanglement and polariton-like dynamics, evidenced by oscillations in the von Neumann entropy $S(t)$ and in even powers of the cavity coordinate and nuclear dipole operators. The observed spectra feature a Rabi frequency $\Omega_{\rm R}$ and side peaks near $2\omega_{\rm c}$, which align qualitatively with quantum Rabi-model predictions and require a larger, beyond-Jaynes–Cummings basis to capture. Overall, the results demonstrate quantum-cavity phenomena that cannot be captured by classical or simple two-level models, motivating first-principles quantum electrodynamics simulations for polariton chemistry under vibrational strong coupling.

Abstract

Molecular polaritons have drawn great interest in recent years as a possible avenue for providing optical control over chemical dynamics. A central challenge in the field is to identify physical phenomena that require a quantum rather than a classical treatment of electrodynamics. In this work, we use our recently developed mean-field quantum (mfq) and full-quantum (fq) real-time nuclear--electronic orbital (RT-NEO) time-dependent density functional theory methods to simulate polaritonic dynamics for a molecule under vibrational strong coupling when a quantized cavity mode is initialized in a Fock state rather than a coherent state. Our previous work showed that a coherent state initial condition for the cavity mode leads to polariton formation for both the mfq-RT-NEO and fq-RT-NEO methods. Herein, we show that the mfq-RT-NEO method, which does not allow light--matter entanglement, does not predict polariton formation for a Fock state initial condition. Similar to the mfq-RT-NEO method, the fq-RT-NEO method does not predict oscillations of the cavity mode coordinate and molecular dipole operator expectation values for a Fock state initial condition. However, the fq-RT-NEO method does predict oscillations of the expectation values of even powers of these operators as well as light--matter entanglement, implicating polariton formation with a Fock state initial condition. All these observations can be explained with model systems. These results suggest that using a quantized cavity mode initial condition that does not have a direct analogy to an initial condition in classical electrodynamics can lead to physical phenomena that can only be described by a quantum treatment of the cavity mode.

Figures (4)

• Figure 1: Comparison of time-dependent properties computed with mfq- and fq-RT-NEO dynamics applied to HCN. (a) mfq-RT-NEO dynamics of $\mu_{{\rm n}, x}(t)$ and $q(t)$. No significant oscillations are observed. No units are given on the $y$-axis because these observables have different units. (b) fq-RT-NEO dynamics of $\mu_{{\rm n}, x}(t)$ and $q(t)$, as well as $S(t)$, $\mu^2_{{\rm n}, x}(t)$ and $q^2(t)$. No units are given on the $y$-axis because these observables have different units. (c) fq-RT-NEO dynamics of $S(t)$. The maximum computed value of $S(t)$ is $\sim$ 0.67.
• Figure 2: Power spectrum of $q^2(t)$ obtained with fq-RT-NEO dynamics applied to HCN for the (a) 400 - 1000 cm-1 region and (b) 4500 - 6500 cm-1 region. In both spectra, the largest signal amplitude has been scaled to a value of 1.
• Figure 3: fq-RT-NEO dynamics of $q^n(t)$ for $n = 1, ..., 8$. No units are given on the $y$-axis because these observables have different units.
• Figure 4: Structure of the trees corresponding to the Jaynes-Cummings (left) and counterrotating (right) blocks of $\textbf{H}$. Each tree is shown up to the first layer with more than one node.