Biphoton Hofstadter's Butterfly and Entanglement Engineering in a Synthetic Photonic Lattice

Abstract Based on a coupled resonator array, we theoretically construct and numerically simulate a nonlinear quantum optics platform to dynamically control the Bloch wavevector. By scanning the modulation parameters (α, k y ), we reproduce the Hofstadter's butterfly structure in the biphoton energy spectrum and reveal clear correspondences among the eigenenergy spectrum, transmission spectrum, and biphoton joint spectral intensity (JSI). Further research demonstrates that screening the pump wavelength can effectively tailor the JSI profile and the Schmidt number of the quantum state, enabling flexible manipulation of frequency entanglement characteristics. This work provides a theoretical framework for exploring quantum state generation and manipulation in nonlinear topological photonic systems and demonstrates the potential for realizing programmable quantum light sources in integrated quantum photonic circuits.