# Entangled Photon Resonance Energy Transfer in Arbitrary Media

## TL;DR

This paper introduces a new theoretical framework for entangled two-photon resonance energy transfer (E2P-RET) in complex media, showing significant rate enhancements due to quantum entanglement effects and proposing a way to characterize this process.

## Contribution

The authors develop a comprehensive F"orster-type model for E2P-RET in arbitrary media, incorporating quantum entanglement and media inhomogeneity, and introduce an effective rate coefficient for characterization.

## Key findings

- E2P-RET rate can be enhanced by over three orders of magnitude due to entanglement.
- The new formulation accounts for media with arbitrary dielectric properties.
- A method to quantify E2P-RET via an effective rate coefficient $K_{E2P}$ is proposed.

## Abstract

Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive F\"orster-type formulation for entangled two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor particle. The temporal entanglement leads to frequency anticorrelation in the virtual photon's field, and vanishing of one of the time-ordered excitation pathways. The underlying mechanism leads to more than three orders of magnitude enhancement in the E2P-RET rate compared with the uncorrelated photon case. With the power of our new formulation, we propose a way to characterize E2P-RET through an effective rate coefficient $K_{E2P}$, introduced here. This coefficient shows how energy transfer can be enhanced or suppressed depending on rate parameters in the radiative cascade, and by varying the donor-acceptor frequency differences.