Non-adiabatic quantum electrodynamic effects on electron–nucleus–photon systems: Single photonic mode vs infinite photonic modes

The quantum-electrodynamic non-adiabatic emission (QED-NAE) is a type of radiatively assisted vibronic de-excitation due to electromagnetic vacuum fluctuations on non-adiabatic processes. Building on our previous work [Tsai et al., J. Phys. Chem. Lett. 14, 5924 (2023)], we extend the theory of the QED-NAE rate from a single cavity photonic mode to infinite photonic modes and calculate the QED-NAE rates of 9-cyanoanthracene at the first-principles level. To avoid the confusion, the quantum electrodynamic internal conversion process is renamed as "QED-NAE" in our present work. According to our theory, we identify three key factors influencing the QED-NAE processes: light-matter coupling strength (mode volume), mass-weighted orientation factor, and photonic density of states. The mode volume is the primary factor causing rate differences between the two scenarios. In a single cavity with a small mode volume, strong light-matter coupling strength boosts QED-NAE rates. In contrast, in free space with infinite photonic modes, weak coupling strength significantly reduces these rates. From a single cavity photonic mode to infinite photonic modes, the mass-weighted orientation factor only causes an 8π/3-fold increase in the QED-NAE rate. In free space, the photonic density of state exhibits a flat and quadratic distribution, which slightly reduces the QED-NAE rate. Our study shows that cavities can significantly enhance non-adiabatic QED effects while providing a robust analysis demonstrating that QED vibronic effects can be safely ignored in free space.