Studies On Spatial Correlations Of Hybrid Entangled States Based On Double-slit Interference

Interference is a concept of the classic wave theory. In quantum me-chanics, quantum interference describes the situation that a quantum state is superimposed by a number of different states in the same system. We can get some information about the state by investigating the coherence effects of the state. As we all know, the double-slit interference is a powerful way to study the coherence effects of optical field. In this thesis, we study higher-order double-slit interference for two types of hybrid entangled states and to inves-tigate fundamental problems in quantum mechanics and quantum informa-tion, such as multi-photon de Broglie wavelength and quantum entanglement detection. The two types hybrid entangled states studied in this thesis in-clude the continuous-discrete-variablc entanglement αNNα and macroscopic-microscopic entangled state α0β1. We calculate the higher-order correlation functions and visibility double-slit interference for two types of hybrid entan-gled states. We reveal the relation between their degree of entanglement and visibility of double-slit interference of hybrid entangled states, and show a new method to detect their degree of entanglement. We also indicate the reduction of multi-photon de Broglie wavelength caused by the higher-order double-slit interference, and find the different reduction of multi-photon de Broglie wave-length if the photon detector is put in some special positions. This thesis includes the following main results.(1) We find that higher-order double-slit interference αNNα state exists sub-wavelength interference effect. It is shown that the first-order correlation function of this state is a single-photon interference while the second-order correlation function interference includes the two-photon interference with the two-photon sub-wavelength interference, and the third-order interference con-tains the three-photon interference with the three-photon sub-wavelength in-terference characteristics. It is predicted that the nth-order correlation func-tion may contain n-photon interference with n-photon sub-wavelength inter-ference characteristics.(2) We get the correlation between the quantum entanglement and the visibility of interference fringes for the hybrid entangled state αNNα. It is found that quantum entanglement is a necessary condition for observing in- terferencc fringes in the quantum double-slit system for the αNNα state. In general, when sin2θ>0, the degree of entanglement;the visibility of first-and second-order interference of αNNα state increase with sin2θ. when a<<1and N>>1. We also find that the visibility of the second-order interference of hybrid entangled state αNNα is bigger than the visibility of the first-order interference, and the interference visibility is proportional to the entanglement degree, which implies a new method to detect the entanglement degree of the state αNNα by measuring the visibility of the interference fringes.(3) We get the general analytical expression of the nth-order correlation function of the macro-micro hybrid entangled state α0β1state wherever the detector is set, from which we find that the nth-order interference just behaves as a single-photon interference when the detector is set in the same place, we couldn’t observe multi-photon interference. This reveals the microscopic characteristics of the α0β1state.(4) When α=-β and|α|2>>1and the detectors placed at x1=rx, x2=sx (r and s are Integers), we find that the second-order correlation function reflects|r-s photons sub-wavelength interference effect. This interference effect reveals macroscopic characteristics of α0β1state.(5) When α=-β and the detectors placed at the same place, the en-tanglement disappears, but the single-photon higher-order interference is still alive. This means that higher-order interference reveals the single-photon co-herence characters of the α0β1state under this condition.(6) We study the second-order interference of α0β1state when two detec-tors placed at different position, under the condition of α=β3and|α|2>>1and the detectors placed at x1=rx,x2=sx (r and s are Integers), we get the correlation between the visibility of the second-order interference and the quantum entanglement of α0β1state. It is shown that the visibility increase with the entanglement but decrease with the macroscopic parameter α.