Entangled Photon Resonance Energy Transfer in Arbitrary Media

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.