[Paper Review] A quantum optics approach to photoinduced electron transfer in cavities

David Wellnitz, Guido Pupillo+1 more|arXiv (Cornell University)|Nov 12, 2020

Strong Light-Matter Interactions4 citations

TL;DR

This paper develops a quantum optics framework using a Lindblad master equation to model photoinduced electron transfer in cavity-coupled donor-acceptor pairs, employing adiabatic elimination to derive an effective rate equation. It reveals that cavity-induced enhancement of electron transfer rates can occur even in the weak coupling regime, driven by dissipative dynamics and incoherent excitation, with the rate depending non-trivially on the time-varying number of ground-state pairs.

ABSTRACT

We study a simple model for photoinduced electron transfer reactions for the case of many donor-acceptor pairs that are collectively and homogeneously coupled to a photon mode of a cavity. We describe both coherent and dissipative collective effects resulting from this coupling within the framework of a quantum optics Lindblad master equation. We introduce a method to derive an effective rate equation for electron transfer, by adiabatically eliminating donor and acceptor states and the cavity mode. The resulting rate equation is valid both for weak and strong coupling to the cavity mode, and describes electronic transfer through both the cavity coupled bright states and the uncoupled dark states. We derive an analytic expression for the instantaneous electron transfer rate that depends non-trivially on the time-varying number of pairs in the ground state. We find that under proper resonance conditions, and in the presence of an incoherent drive, reaction rates can be enhanced by the cavity. This enhancement persists, and can even be largest, in the weak light-matter coupling regime. We discuss how the cavity effect is relevant for realistic experiments.

Motivation & Objective

• To understand how collective light-matter coupling in optical cavities modifies photoinduced electron transfer rates in molecular ensembles.
• To address the challenge of modeling dissipative effects—such as cavity losses, radiative decay, and incoherent excitation—alongside coherent dynamics in polaritonic chemistry.
• To develop a tractable theoretical framework that captures both strong and weak coupling regimes in a unified, effective rate equation.
• To demonstrate that cavity-induced rate enhancement is not limited to strong coupling, but can be significant even in the weak coupling regime.

Proposed method

• Formulates a Lindblad master equation to describe a many-body system of donor-acceptor pairs collectively coupled to a cavity mode, including incoherent excitation and decay channels.
• Applies adiabatic elimination to the cavity mode and excited donor/acceptor states, reducing the full quantum dynamics to an effective, purely dissipative master equation with zero effective Hamiltonian.
• Derives an analytic expression for the instantaneous electron transfer rate that depends on the time-varying number of donor-acceptor pairs in the ground state.
• Uses quantum trajectory simulations to efficiently model the full dynamics and validate the effective rate equation, treating pair loss as emission into a final state.
• Introduces a simplified 3-level model per pair (ground, donor excited, acceptor excited) and treats final-state relaxation as effective pair loss.
• Validates the effective rate equation by comparing numerical simulations of the full and effective dynamics, showing quantitative agreement under appropriate conditions.

Experimental results

Research questions

• RQ1 Can cavity-induced modifications to electron transfer rates be understood beyond the strong coupling regime, particularly in the presence of dissipation?
• RQ2 How does the instantaneous electron transfer rate depend on the number of donor-acceptor pairs in the ground state in a cavity environment?
• RQ3 What role do dark states, bright states, and superradiant states play in mediating electron transfer under collective coupling?
• RQ4 Under what conditions does incoherent excitation lead to rate enhancement in cavity-modified electron transfer?
• RQ5 Can adiabatic elimination yield a valid, effective rate equation that captures both coherent and dissipative effects in a single, analytically tractable form?

Key findings

• The effective rate equation derived via adiabatic elimination is purely dissipative, with no coherent Hamiltonian term, and accurately describes electron transfer dynamics across both weak and strong coupling regimes.
• Electron transfer occurs through two distinct channels: cavity-coupled bright states and uncoupled dark states, with the latter contributing significantly to the overall rate.
• Rate enhancement due to the cavity is most pronounced under resonance conditions and in the presence of incoherent excitation, even in the weak coupling regime.
• The instantaneous transfer rate depends non-trivially on the time-varying number of pairs in the ground state, capturing the dynamic interplay between population and decay.
• Numerical simulations confirm that the effective rate equation accurately reproduces the full dynamics, validating its use for predicting reaction rates in realistic experimental setups.
• Cavity losses, which occur on a femtosecond timescale, play a critical role in shaping the dynamics and can dominate over coherent effects in certain regimes.