Manipulations And Applications Of Position-correlation Of Entangled Photons

In recent years, quantum information is developing rapidly with showing many attractive prospects. Integrated photonic chips becomes a new direction of development of quantum information science, as its integration makes the quantum information processing more stable and scalable. As an important physical resource of the quantum information science, entangled photons and its generation and manipulating attract a lot of research. While spatial characteristic is an important and fundamental freedom of entangled photons. Along the direction of the development of quantum information science, integratively generating and manipulating the entangled photons represent the general trend. Optical superlattice acts as one of the most widely used materials for generation of entangled photons with high efficiency by flexible domain engineering. This dissertation is constructed as follows:1. We experimentally realized the two-photon entangled state with correlated-momentum and anti-correlated position, namely the counter-Einstein-Podolsky-Rosen (CEPR) state from spontaneous parametric down-conversion process in a long periodically poled lithium tantalate (PPLT) crystal with a tightly focused pump beam. The CEPR state is identified by measuring the momentum and position correlations at the Fourier plane and imaging plane of the PPLT crystal end face, respectively, showing a variance product (△x+)2(Ap_)2= 0.14 ± 0.02h2, which fulfils the entanglement criterion.2. We present a theoretical analysis on the properties of quantum ghost imaging on account of photon pairs with different types of momentum correlations generated by spontaneous parametric down conversion. We derive the analytical form of the two-photon amplitude at the detection planes, which gives the magnification and resolution of ghost imaging under different two-photon momentum correlations. The intrinsic magnification can be applied as the entanglement criterion. In addition the analytical form shows the influence of pump beam waist and crystal length on imaging resolution under different types of momentum correlations, indicating crystal length plays an important role on the resolution. Also a vivid numerical simulation of ghost imaging is given. This work gives applicable references to the applications of quantum ghost imaging and may stimulate the development of new types of quantum technologies.3. The Fresnel zone plate (FZP) was introduced into optical superlattice. The nonlinear FZP sample was fabricated by poling lithium niobate crystal as FZP structure. And we experimentally demonstrated that the nonlinear FZP crystal could realize second harmonic generation (SHG) and imaging of SHG. Furthermore, the FZP structure was introduced into the transverse modulation ofthe optical superlattice. With this structure, we can realize the lensless ghost imaging with multi focus, which makes the manipulating of spatial correlation of the entangled photos more convenient and integrative.4.We proposed two schemes of quantum error correctiing codes (QECC) on multiple degrees of freedom of photons. One proposal is coding on the multiple degrees of freedom of a single photon, which can efficiently realize QECC, and reduce the request on the numbers of photon. Also we completely designed a feasible experimental setup for such scheme. Additionally, another proposal is coding on the multiple degrees of freedom of two photons, which can cover the potential shortage ofthe former scheme in further applications. These two schemes may help us to broaden our mind in QECC...