Research on entangled photon characteristics based on spontaneous parametric down conversion

With the vigorous development of quantum information technology, quantum entanglement as its core resource has shown tremendous application potential in quantum communication, quantum computing, and quantum measurement fields. Therefore, the efficient preparation of entangled photon pairs plays a key role in advancing quantum information technology. This paper thoroughly investigates the theoretical model analysis of entangled photon pair generation based on cascaded second-harmonic generation and spontaneous parametric down-conversion effects in periodically poled lithium niobate crystals. The paper uses quantum field theory methods to derive the interaction Hamiltonian of the system, obtains the analytical expression of the biphoton wave function, and analyzes the biphoton wave function using the Schmidt decomposition method. Through quantitative indicators such as Schmidt number, entanglement entropy, and single-photon purity, the paper systematically studies the influence of different crystal lengths on entanglement characteristics in the cascaded system. Research shows that as crystal length increases, the Schmidt number and entanglement entropy increase, enhancing entanglement dimension; however, single-photon purity decreases with increasing crystal length, reflecting the trade-off relationship between entanglement degree and purity.