Theory of four-wave mixing for biomolecular systems: Toward transduction of quantum information from fluorescent protein complexes to photonic readouts

The generation of photonic entanglement from fluorescent proteins (FPs) in aqueous solution has opened new opportunities for quantum-enhanced measurements in biomolecular environments. Theory suggests that quantum correlations in DNA and DNA-targeting enzymes can be probed on the spatial and temporal scales offered by these entangled photon experiments, which exploit nonlinear four-wave mixing (FWM) techniques. However, a clear theoretical framework describing the entangled outgoing signal and idler photons from the vibronic ground and excited state manifolds of the FPs is still lacking. We present a model for the FWM dynamics of two classical electromagnetic fields interacting with a matter density of FPs, each with two manifolds of states containing fine vibrational structure. Connecting the quantum state of the generated entangled photons to the internal molecular structure and dynamics of the statistical ensemble of FPs would lead to new experimental tests of our hypothesis that ultrashort pulses (~100 fs duration) can readout molecular correlations under ambient conditions. In the context of a warm and wet electrodynamic milieu, our results will be essential for designing bio-inspired quantum devices and robust quantum materials for room-temperature technology applications.