Photonic Entanglement In Nonlinear Waveguide Array And Its Application In Photonic Quantum Simulation

The new nonlinear waveguide array, adding spontaneous parametric down-conversion into traditional waveguide array, brings some novel effects on the manipulation of spatial correlation of photon pair. What is more, the application of the nonlinear waveguide array in photonic quantum simulation and quantum computation is increasingly significant and important. This thesis focuses on this nonlinear waveguide array, giving an analysis of the spatial correlation of the photon pair generated in the array and the parameters effects the correlation, and discusses the application of this nonlinear waveguide array in photonic quantum simulation. The main results of this thesis are demonstrated as follows:1. By discussing the photon pair state and its spatial correlation in nonlinear waveguide array, we found both the pump condition and the length of the array have an effect on the spatial correlation and these new photon pair states which also entitled the quantum walk brand new properties, In details, the pump condition offering the anti-correlated in momentum space, together with the variety of the array length which changes the bandwidth of phase match function, make the spatial correlation varies from anti-correlated, near uncorrelated and correlated. After further analysis, we found that the spatial correlation is actually affected by the ratio of relative array length and pump condition, namely L/Lz/N. And this phenomenon can also be observed by the Schmidt number. When the ratio is equal to 0.15, the photon pair is near uncorrelated and the Schmidt number is 1.8533. And when it is smaller than 0.15, the spatial correlation is anti-correlated and the Schmidt number is 3.7652. While if the ratio is larger than 0.15, the spatial correlation is correlated and the Schmidt number reaches 4.6484. Different spatial correlation stand for different quantum walk of photon pair, which makes the design of related algorithm possible.2. The engineering of the second order nonlinear coefficient is considered in the spatial correlation of photon pair. It turns out that when the transverse engineering is linear and all the waveguides in array are pumped, the high entangled photon pair bunching state in position space is generated in the array. The Schmidt number arrives at 8.51 which is much larger than that of photon pair spatial correlation manipulated only by the ratio of array length and pump condition. What’s more, if the slope of the linear engineering changes, the bunching state is reproduced periodically. For parabolic engineering, the photon pair is focused after it propagates a distance out of the array. The engineering of the second order nonlinear coefficient not only generates some new spatial correlation of photon pair, but also shed a new way for quantum walk research and the output of photon pair state in the array.3. The photon pair state of cos curved nonlinear waveguide array with positive and negative coupling constant is discussed. The cos curved waveguide array varies the dispersion of the array, which influences the phase match function and the pairing way of the photon pair’s reduced transverse wave vector. This new pairing way is much similar to the way how and 4H superfluid and the cooper pair generated. The comparability between the Hamiltonians of photon pair and 4H superfluid make the photonic quantum simulation of 4H superfluid by photon pair in this kind of nonlinear array possible. And the counter propagating signal and idle photon can also simulates the cooper pair. What is more important, the phase transition of these two particles is simulated by increasing the temperature of the spontaneous parametric down-conversion.4. Based on the above theoretical analysis, the experimental scheme of quantum walk in nonlinear waveguide array is given and some early experimental results are given. The design of waveguide array includes input area, periodically poled area (where the photon pair generated) and the output area for photon pair after quantum walk. This single chip realize the generation of photon pair from classical light and quantum walk of this photon pair simultaneously. And by measuring the spatial correlation of photon pair outside the array, the properties of this quantum walk can be described. The design for pump condition, sample preparation and experimental measurement are given for two typical quantum walk, namely bunching quantum walk and anti-bunching quantum walk. In experimental measurement, the generation of photon pair and single photon coupling in periodically poled lithium niobate waveguide array is observed.