Nonclassicality and photon number distributions in quantum Optics

Abstract

The nonclassical oscillations in photon number distribution exhibits collapses and revivals similar to those exhibited in the Jaynes-Cumming's model. These oscillations are considered as a qualitative signature of nonclassicality; Squeezing, Sub-Poissonian are of qualitative signature of statistics, involving the lower order moments of the diagonal R-distribution, provides quantitative conditions for nonclassicality. The nonclassicality is studied as coded in photon number distribution as Pn. The Gaussian states of the radiation field are studied in this thesis. A comprehensive analysis of the characterization, spectral decomposition, and entropy for General Gaussian states of a system with arbitrary finite number of Bosonic degrees of freedom N is presented in this thesis. The Fock state representation and photon number distribution of a general Gaussian state are also discussed. Techniques and results from the classical Stieltjes moment problem are exploited for the thorough analysis of nonclassicality of a state p as coded in the photon number distribution. The present approach to nonclassicality of the photon number distribution is local in 'n' - unlike in terms of normal ordered moments mn. It is dual to the traditional approach in terms of pn. The complete equivalence between the present approach to nonclassicality in terms of local conditions on pn and the traditional approach in terms of conditions on the moments mn is established, using the techniques of Laplace transform. The two model squeezed coherent state with complex squeeze and displacement parameters is studied. It is found that the two-mode squeeze operator is a rotated version of the product of reciprocal single-mode squeezings. The second order coherent properties of the two-mode squeezed coherent state, the phase distribution, and the correlation functions associated with it are also studied.