Studies About The Photonic Simulation And Quantum Walk In Waveg- Uide Arrays

The traditional information processing based on semiconductor integrated circuit, has achieved great progress in the 20th century and changed our daily life deeply. How-ever, further development of the traditional integrated circuit is limited by the quantum tunneling effect, the heating and power consumption problem, which are caused by the further reducing the size of electronic components. Quantum information processing with its extraordinary properties has opened up a new direction for the development of information processing science. More efficient quantum computation is achieved by utilizing the quantum superposition principle of quantum states. The quantum non-cloning theorem guarantees the absolutely secure quantum communication. The quan-tum metrology can break the limitation of classical measurement and achieve more precise measurement. Great efforts have been dedicated to the quantum information processing in various physical systems in the recent 30 years. There are many can-didate systems for quantum information processing, including linear optics, ion trap, superconducting Josephson junction, cold atoms, nuclear magnetic resonance, quan-tum dot and diamond color centre. Among all the systems, photon system becomes a formidable competitor for quantum information processing. Photon system has a good coherence property which can help achieve high fidelity of state manipulation. The information can be transmitted with the light velocity, and the photonics technology has been very mature.However, there are many problems for photon-based quantum information pro-cessing in traditional space optical circuits. The space optical circuit occupies a large room, which limits its scalability. It has a strict requirement for the stability of the environment, including the temperature, vibrations and airflow. Inspired by the de-velopment of integrated electronic circuits, people put forward to integrating all the linear optical components into a tiny photonic chip. The photonic chip has a tiny size, good stability and scalability, which overcomes the drawbacks of the traditional space optical circuits. Optical waveguide is the elementary unit of photonic chip. The waveguide array consists of multiple waveguides which are arranged in some regular way. The propagation of light in waveguide array is complex. This thesis is dedicated to study the quantum information processing in waveguide arrays. On one hand, we compare the similarity between the paraxial wave function in waveguide array and the Schrodinger equation in quantum mechanics, and propose a scheme to simulate some relativistic quantum effects. On the other hand, the essence of photon propagation in the waveguide array is the continuous-time quantum walk. We propose several ways to manipulate the single photon and two-photon quantum walk in the waveguide array by engineering the structure of the waveguide array. We also achieve an experimental re-alization of quantum search algorithm based on quantum walk in the waveguide array. The dissertation is constructed as follows:(1) We introduce several ways to manipulate the optical simulation and quantum walk in waveguide arrays. We demonstrate the equivalence between the propagation of photons in the waveguide array and the continuous-time quantum walk. We analyze the quantum walk of single photon and two-photon with various initial states. We sum-marize several common structures of waveguide arrays. We compare the relations and differences of quantum walk in the linear waveguide array and the nonlinear waveguide array.(2) We propose a scheme to simulate the Schwinger effect via light propagation in a circular-curved binary waveguide array. We demonstrate the similarity between the dynamical equations in such waveguide array and 1-d Dirac equation, the similarity between the dispersion relation in the Brillouin edge and that of the relativistic elec-tron. We numerically simulate the propagation of a broad Gaussian beam incident into such a binary waveguide array in a tilted angle. The split of the Gaussian wavepacket corresponds to the generation of positron-electron pairs. We analyze the influence of the geometrical parameters to the generation rate of positron.(3) We theoretically analyze the quantum walk in the passive-PT-symmetric waveg-uide array with loss in every second site. We derive the dispersion relation in such waveguide array. We deduce the formation of intensity distribution with different ini- tial situations. We analyze the reason for the asymmetry of the intensity distribution. We calculate the associated similarity function of intensity distribution with differen-t loss parameters. We also study the two-photon quantum walk in such waveguide array. If two photons are injected into two lossy or two lossless waveguides, their two-photon correlations are asymmetric. A mode filter is achieved by designing the geometric structures of passive-PT-symmetric waveguide arrays. A similar asymmet-ric two-photon quantum walk occurs in the passive-PT-symmetric quadratic waveguide array.(4) We theoretically investigate the Anderson localization effect in a disordered quadratic waveguide array. The Anderson localization gets enhanced compared with that in the linear waveguide array. It exhibits a reduced pattern similar to that of the uniform case in the weak disorder regime. For the strong disorder parameter, the single-photon intensity is strongly localized around the excited waveguides and two-photon correlation turns to be bunching distributed indicating that two photon tend to emerge in the same waveguide. Such two-photon bunching correlation for a strong disorder pa-rameter is caused by the intrinsic feature of nonlinear parametric process, independent of pumping condition and geometrical structure of waveguide arrays.(5) We analyze the experimental requirements of the waveguide array to real-ize the glued-binary-tree problem. We design the template which consists of several waveguide arrays with different waveguide spacings. We test the intensity ratio in the two output ports of the directional coupler with different propagation distances. We de-rive the coupling coefficients by fitting the experimental data. We find the waveguide array which meets the requirements of the glued-binary-tree problem. We try several different ways to observe the propagation of light in the surface of the waveguide ar-ray. We measure the intensity distribution in the output face of the waveguide array preliminarily.