Preparing And Engineering Of Two-photon Spatial Modes Entanglement

1.Photons with complicated spatial mode structures can be applied for some new quantum information tasks.Here,we show the entanglement of photons with complex singularity patterns called Hermite-Laguerre-Gaussian(HLG)modes.Measuring one photon of the entangled pairs by HLG mode basis to define its singularity pattern,we can steer the singularity structure of its partner,while the initial singularity structure of the photons is undefined.We also calculate the HLG specific quantum-correlation function.It can be used to extend the quantum key distribution protocols and to tune experiments dealing with high order transverse modes.In addition we discuss orbital angular momentum properties of the HLG modes and summarize some features of singularity pattern of the HLG modes with varying angle parameter.2.The quantum spiral holographic imaging is introduced in this paper.We use spontaneous parametric down-conversion as a source of correlated photon pairs and analyze the joint orbital angular momentum spectrum of the reference photon and the photon encoding the object information.The first-order interference of the light beams in the common holographic imaging technique is replaced by the quantum interference of the two-photon probability amplitudes.It avoids the difficulty of retrieving the amplitude and phase structure of an unknown photon that cannot apply classical interferometric techniques such as optical holography.Our results show that the full information of the object's transmission function can be recorded in the spiral hologram,which originates directly from the joint orbital angular momentum spectrum.This presents a lateral demonstration of compressive imaging and can potentially be used for remote sensing.3.We discuss the HOM interference effect of photons with a vectorial field structure.By using specially designed q-plates together with the rotation operation,we can prepare various types of two-photon vector mode entangled states.These states include Bell states and their linear combination,hybrid polarization-OAM entangled states and high-dimensional ones.Our derivation results show that only the anti-symmetric components of the incident state can produce coincidence counts,while symmetric components will have no contributions.This effect can be employed to filter out the anti-symmetric components in the high-dimensional space encoded by the vector mode,and separate the vector modes with different orders.Our results show that the HOM interference can be used to generate and control the two-photon vector mode entangled states.4.Shaping light in second-order nonlinear interaction is a compact way of controlling both spatial structure and frequency at the output.Here we extend the nonlinear holography to spontaneous parametric down conversion process.The use of patterned nonlinear crystals,combining holographic methods can control the two-photon wave function generated by the SPDC.The transverse spatial correlation between the photon pair is controllable and conditional coincidence rate function with any desired distribution can be obtained.Based on these results,we propose a method to generate two-photon polarization-spatial mode hyperentanglement through the use of shaped crystals.