Research On The Nonclassicality Of Non-Gaussian Quantum States Prepared Through Beam Splitter Or M-times Photon Addition-subtraction Operation

Nonclassical character of quantum light field is one of the important topics in quantum optics and quantum information science. In general, nonclassical light field can show some quantum properties, such as anti-bunching effect, sub-Poissonian photon statistics, squeezed effects and the negative distribution of Wigner function, etc. Not only the research of these nonclassical behaviors will help prove the correctness of quantum theory, but also these nonclassical properties have been applied in quantum communication, quantum cryptography, gravitation wave detection and so on. Negative Wigner function is an important sign of non-classical quantum states. The quantum state is called non-Gaussian quantum state, whose Wigner function show non-Gaussian type distribution. Many people have been proposed many programs to construct a number of new nonclassical states. Using the quantum mechanics principle of superposition to induce new nonclassical quantum states is the most common way.Using non-Gaussian operator acting on the quantum state is also one of the way to obtain a new non-Gaussian quantum states. For example, squeezing operator operation, photon subtraction operation, photons addition operation or photon addition-subtraction coherent superposition operation on quantum states can obtain some nonclassical states. Studies have shown that the use of continuous variable quantum states can achieve the preparation and handling of quantum state, can complete the transfer and processing of quantum information. Non-Gaussian state as a new source of information in the field of teleportation, cloning, storage and quantum computers will play an important role. Thus, the non-classical nature of non-Gaussian quantum states is beginning to attract many experimental and theoretical physicists’ attention. In this paper, some new non-Gaussian quantum states will obtained through any times coherent addition-subtraction operators operation on some quantum states and optical devices(such as a beam splitter). The main contents are as follows:In Chap.1, theoretical basis of quantum optics will be introduced briefly, including the technique of integration within ordered product of operators(IWOP), production and properties of common quantum states, the criterion of non classical light field, and so on.In Chap.2, nonclassicality and decoherence in a thermal environment of the variable arcsine state are studied, which is generated through a variable beam splitter. Beam splitter is an effective way to obtain nonclassical light fields.In Chap.3, the nonclassicality and decoherence of m-times photon subtractionaddition coherent superposition operated odd-Schródinger-cat states are discussed. After obtaining its normalized constant by IWOP technology, we discuss the nonclassical properties of the new state in terms of Mandel’s Q-parameter, quadrature squeezing properties, photocount distribution and so on. We derive the analytical expression of Wigner function and use it to discuss the characteristics of Wigner function’ negative region, as well as the decoherence in the thermal environment.In Chap.4, the nonclassicality of coherent photon-subtracted two single-modes squeezed vacuum state is studied. After obtaining its normalized constant, we discuss the nonclassical properties in terms of cross-correlation function, anti-bunching effect, photon-number distribution, wave function and Wigner function in details.