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Acta Sinica Quantum Optica

Nonclassical Property of Inverse Coordinate Operator Excited Coherent States

YU Zhi-son

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this paper,we introduce a new nonclassical quantum state,an inverse coordinate operator excited coherent state.By using the IWOP technique,the normally ordering form of inverse coordinate operator and the normalization factor are derived.It is shown that the normally ordering form is related to Hermit polynomial.On the basis of the coherent state representation of the Wigner operator,the Wigner function is also calculated,whose negative property is used to discuss the nonclassical property of the nonclassical quantum state.

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In this paper,we introduce a new nonclassical quantum state,an inverse coordinate operator excited coherent state.By using the IWOP technique,the normally ordering form of inverse coordinate operator and the normalization factor are derived.It is shown that the normally ordering form is related to Hermit polynomial.On the basis of the coherent state representation of the Wigner operator,the Wigner function is also calculated,whose negative property is used to discuss the nonclassical property of the nonclassical quantum state.
Abstract In this work, we theoretically construct an orthogonal state of a coherent state where the orthogonalizer is based on the Hermite polynomial excited operation with H m ( x ) being a Hermite polynomial of order m and creation operator , called the Hermite-excite-orthogonalized coherent state (HEOCS). Then, in comparison with the Hermite polynomial excited coherent state (HPECS), we numerically investigate their different nonclassical properties by examining several measurable features, such as photon number distribution, sub-Poisson statistics, the antibunching effect, the quadrature squeezing effect, and the negative Wigner function. The results demonstrate that both HEOCS and HPECS are non-Gaussian quantum states with highly nonclassical characteristics by improving and modulating the order of the Hermite polynomial and coherent amplitude, which indicates that performing the Hermite-excited operation on given Gaussian states is an effective approach to generating non-Gaussian states.
An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text]. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.
We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that the normalized factor is related to the two-variable Hermite polynomials. We then investigate the nonclassical properties in terms of Mandel's Q parameter, quadrature squeezing, second correlation, and the negativity of Wigner function (WF). It is shown that all these properties are related to the amplitude of coherent state, catalysis number and unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced as catalysis number and keeps a constant for single-photon catalysis. In addition, we examine the effect of decoherence by Wigner function, which show that the negative region, characteristic time of decoherence and structure of WF are affected by catalysis number and unbalanced BS. Our work provides a general analysis about how to prepare theoretically polynomials quantum states.
Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter α the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state |β, m ⟩ o (or |β, m ⟩ e ) is more pronounced when m is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.