Quantum Statistical Properties Of Two Non-classical Optical Fields

In the field of quantum optics, application of the quantum properties of non-classical states in quantum information science and exploitation of the advantages of the low quantum noise of quantum states in precise optical measurement have aroused much attention in the scientific community. There have been many new types of quantum states created according to the basic principles of quantum mechanics, which can give us a better understanding of the nature of light. Once they are created experimentally they will have significant applications. Quantum states have great potential in the major high-tech quantum science and technology fields, such as weak signal detection, quantum communication, quantum computing, and so forth. It is therefore of real practical importance to construct as many non-classical states as possible, and to investigate their quantum properties, characteristics, and evolution of their quasi-probability distribution functions.In this paper, two new types of quantum states are constructed: by repeatedly applying the operator b↑= v * a +μ* a↑"m"times on the coherent states we create the so-called generalized excited coherent states, then by further applying the unitary displacement operator ( )D g(β) = expβb↑-β↑bwe obtain the displaced generalized excited coherent states. Using quantum statistics, we have investigated the non-classical properties of these two types of states in detail, including the fluctuations of the quadrature components, field intensity and photon number, and the quasi-probability distribution functions (P function and Wigner function). We find that, for certain parameters, the quadrature components of the field may become squeezed, the photons may exhibit antibunching, their distribution may be sub-Poissonian, and the Wigner function may assume minus values. In particular, the characteristics of these two types of states and the evolution of their Wigner functions are compared. We show that the second type of state is a more general class of quantum states.