Wegener Function And Chromatogram Function Of Several Quantum States

Wigner functions are an important tool in quantum mechanics for expressing evolutions of quantum states and estimating non-classical properties of them.Tomography theory is an effective way to reconstruct Wigner functions using measurable tomogram functions,and has widespread applications in quantum optics,quantum communications and so on.In this paper,a series of investigation and study surrounding the evolutions of Wigner functions and tomogram functions were carried out with the help of the technique of integration within the ordered product of operators(IWOP technique).The main work of this paper includes:1.Using IWOP technique,we investigated how displaced thermal states(DTSs)evolve in a laser channel.And the normal ordering product of density operator of the DTS in the laser channel leads to obtaining the analytical time-evolution expressions of the photon number,Wigner function and von Neumann entropy.Also,some interesting results are presented via numerically investigating these explicit time-dependent expressions.2.By introducing the explicit expression of the intermediate state,a convenient method to obtain optical tomograms for multiple-photon-added Gaussian states was presented.And we calculated the specific optical tomograms for multiple-photon-added coherent states,thermal states and displaced thermal states.3.We presented new forms of Legendre polynomials and Jacobi polynomials using photon-subtracted squeezed vacuum states and two-mode photon-added squeezed vacuum states.Also,new forms of their generating functions were given in an exponential form.As applications,the normalization factors of photon-added and subtracted squeezed chaotic states were obtained in a compact form related to these two polynomials.