The Quantum Properties Of Certain Quantum States And Mesoscopic Rlc Circuit

This thesis presents my main research work carried out during my master course.In this thesis,the quantum properties of some quantum states and mesoscopic RLC circuit are investigated.Significant new results as shown below:1.Using the coherent state representation of Wigner operator and the technique of integration within an ordered product(IWOP) of operators,the Wigner functions of the even and odd binomial states(EOBSs) are obtained.Using the Radon transform between the Wigner operator and the projection operator of intermediate coordinate-momentum state,the tomograms of the EOBSs calculated.By virtue of numerical computation,the nonclassical properties of the EOBSs are studied,then the physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions.2.The properties of the even and odd negative binomial states(NBSs) are investigated. Mainly we concentrate on the nonclassical properties for such the states where we consider the quadrature squeezing,antibunching effect and the phase probability distributions. Using the Pegg-Barnett formalism of phase operator,the phase probability distributions of the states are discussed,and also the phase and number squeezing with different parameters are studied.Using the coherent state representation of Wigner operator and the IWOP technique,the Wigner functions of the even and odd NBSs are obtained.And,the physical meaning of the Wigner functions for the even and odd NBSs is discussed.Then, by virtue of intermediate coordinate-momentum representation,the tomograms of the even and odd NBSs are obtained,and their nonclassical properties exhibited are discussed in detail.3.Using the IWOP technique,the coherent state representation of Wigner operator and the intermediate coordinate-momentum representation,the Wigner functions and the tomograms of the Klauder-Perelomov(K-P) coherent states for the pseudoharmonic oscillator(PHO) are obtained.The nonclassical properties of the K-P coherent states for the PHO are discussed.Moreover,the physical meaning of the Wigner functions for the K-P coherent states for the PHO is given by means of their marginal distributions.4.By means of the Weyl correspondence,Wigner theorem and the coherent thermo state representation theorem we show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature,we show that the quantum fluctuations of both charge and current increase with the rising temperature and the resistance value,the physical meaning of its marginal distributions'statistical average is discussed.