Quantum Transport And Correlation Of Photons In One-dimensional Coupled Waveguide Arrays

Controlling and molding the flow of light by waveguide arrays have numerous ap-plications in various areas, such as in optical signal processing, optical communication, and optical computing. Due to the similarities between equation describing the wave propagation in waveguide array and the Schrodinger equation in quantum mechanics, the waveguide arrays enable direct observation of optical analogues of many funda-mental quantum effects. The waveguide arrays are versatile to manipulate the flow of light, and have been studied widely in the framework of classical light. Recently, the propagation of nonclassical light and quantum particles in waveguide arrays have also attracted lots of attention.This thesis focuses on the quantum properties of photons evolving in one-dimensional waveguide arrays with defect, disorder, and even in the PT-symmetric arrays, respec-tively.In Chapter1, we give a brief introduction on the related background. The state of art on the study of optical analogies of quantum effects has been reviewed, sever-al examples also given. Then the study on nonclassical light in waveguide arrays is introduced. At last, we give the main contents of this thesis.In Chapter2, we introduce the basic concepts and theory we employed in this thesis, which include the one-dimensional waveguide array, the coupled mode theory, the Heisenberg equation for the creation operator of photons, the classical and quantum correlation functions, and the PT-symmetric non-Hermitian systems.In Chapter3, We study the quantum correlation of path-entangled states of two photons in coupled one-dimensional waveguide arrays with lattice defects. Both off-diagonal and diagonal defects are considered, which show different effects on the quan-tum correlation of path-entangled two-photon states. Two-photon bunching or anti-bunching effects can be observed and controlled. Defect modes may play an important role on the two-photon correlation of path-entangled states in the waveguide arrays. Due to the quantum interference effect, intriguing evolution dynamics of the two-photon cor- relation matrix elements with oscillation frequencies being either twice of or the same as that of a classical light wave, depending on the position of the correlation matrix element, is observed. Our results show that it is possible to manipulate the two-photon correlation properties of path-entangled states in waveguide arrays with lattice defects.In Chapter4, we study the quantum properties of photons evolving in off-diagonal-disordered waveguide arrays. Photon localization can be observed during the photon propagation in waveguide arrays when disorders are introduced into such systems. Fur-thermore, if we introduce some lattice defects into such disordered arrays, the localiza-tion will be influenced dramatically. With different types of defects, the localization can be enhanced, weaken, or even becomes delocalized.In Chapter5, we study the quantum behaviors and quantum correlations of pho-tons evolving in the quasi-PT-symmetric systems formed by coupled waveguide arrays. Our results show that, the phase transition point will be influenced by the disorder level. With increasing off-diagonal disorder, the transition point of the transmittance will de-crease, and the loss enhanced transmission of such non-Hermitian system will be further enhanced.In Chpter6, we give the conclusions of this dissertation and then present our plans for the further research.