Case Studies of the Time-Dependent Potential Energy Surface for Dynamics in Cavities

TL;DR

This paper analyzes the structure and significance of the exact time-dependent potential energy surface in cavity quantum dynamics, highlighting its importance over simplified models for accurately describing nuclear behavior.

Contribution

It provides a detailed analysis of the exact potential energy surface in cavity systems, demonstrating its superiority over weighted polaritonic surfaces for nuclear dynamics.

Findings

Weighted polaritonic surfaces miss a key energy redistribution term.

Classical trajectories on the exact surface accurately reproduce wavepacket dynamics.

Simplified models fail to capture long-term nuclear behavior.

Abstract

The exact time-dependent potential energy surface driving the nuclear dynamics was recently shown to be a useful tool to understand and interpret the coupling of nuclei, electrons, and photons, in cavity settings. Here we provide a detailed analysis of its structure for exactly-solvable systems that model two phenomena: cavity-induced suppression of proton-coupled electron transfer and its dependence on the initial state, and cavity-induced electronic excitation. We demonstrate the inadequacy of simply using a weighted average of polaritonic surfaces to determine the dynamics. Such a weighted average misses a crucial term that redistributes energy between the nuclear and the polaritonic systems, and this term can in fact become a predominant term in determining the nuclear dynamics when several polaritonic surfaces are involved. Evolving an ensemble of classical trajectories on the exact potential energy surface reproduces the nuclear wavepacket quite accurately while evolving on the weighted polaritonic surface fails after a short period of time. The implications and prospects for application of mixed quantum-classical methods based on this surface are discussed.