Enhancing Two-Photon Absorption of Green Fluorescent Protein by Quantum Entanglement

Exploring the electronic states of molecules through excitation with entangled and classical photon pairs offers new insights into the nature of light-matter interactions and stimulates the development of quantum spectroscopy. Here, we address the importance of temporal entanglement of light in two-photon absorption (TPA) upon the S₀ → S₁ transition by the green fluorescent protein (GFP)─a key molecular unit in the bioimaging of living cells. By invoking a two-level model applicable when permanent dipole pathways dominate the two-photon transition, we derive a convenient closed-form analytical expression for the entangled TPA strength. For the first time, we disclose specific molecular properties that cause classical and entangled two-photon absorptions to be qualitatively different when exciting the same state. We reveal a new nonclassical contribution to the TPA strength, which is defined by the magnitude and directional alignment of permanent dipole moments in the initial and final states. Using high-level electronic structure theory, we show that the nonclassical contribution is intrinsically larger than the classical counterpart in GFP, leading to an enhancement of the TPA strength due to quantum entanglement by several orders of magnitude. We also present evidence that the classical and quantum TPA strengths can be modulated differently by the protein environment and demonstrate how to control the outcome by alterations in the local electric field of the protein caused by a single amino acid replacement. Our findings establish physical grounds for enhancing TPA in photoactive proteins by quantum entanglement, facilitating the rational design of high-efficiency biomarkers for future applications that utilize quantum light.