High Gain More Spontaneous Parametric Process Photon Correlation Effect

Quantum entanglement is the core resource for quantum information and quantumcomputation. In experiments, the source of quantum entanglement is often acquired fromthe spontaneous parametric down-conversion (SPDC) process of a nonlinear crystal. Sincethe quantum efficiency of SPDC is very low, it is reasonable to think that the convertedbeam contains two correlated photons, the signal photon and idler photon, which areconverted from a pump photon. The two entangled photons can be regarded as in a puretwo-photon entangled state. However, in a real SPDC process, the nonlinear crystal canradiate a large number of photons, and these photons can manifest effects of quantumentanglement and thermal light correlation. From this point of view, the pure two-photonentangled state does not work in the high-gain SPDC process. In this thesis, we calculatehigh-order correlation function of multi-photon interference in the case of high-gain SPDCwith field input-output relation of the nonlinear crystals. We find the effects of quantumentanglement and thermal light correlation can interfere, or be coupled with each other. Inthe theoretical analysis of two-photon correlation in Hong-Ou-Mandel (HOM)interferometer, we find that thermal light correlation contributes a background term to thequantum entanglement effects. When the SPDC gain increases, the background termincreases, too. We calculate the arbitrary Nth-order photon correlation function ofquantum lithography with SPDC light, and the simulation shows that the fringe visibilitydecreases when the SPDC gain increases. A compensative way is to increase thecorrelation order N. Our analysis also shows that one can never surpass the two-photondiffraction limit with N photon measurement. We further investigate the double slitinterference with SPDC light beams, by calculating the second-order, third-order andfourth-order correlation functions. We find that the effects of entanglement and thermallight correlation interfere each other when the order N>2. According to the simulations onthe quantum entanglement effects in the fourth-and sixth-order correlation functions, wefind multi-photon subwavelength interference patterns can be obtained in a certain type ofmeasuring style. This means that the two-photon diffraction limit now can be surpassed by multi-photon measurement. The idea is confirmed when we examine the arbitraryeven-order correlation functions in multi-photon process. The specific experimentalmethod is proposed to obtain arbitrary even-order subwavelength interference patterns. Wehope our theoretical studies can be realized soon.