Some studies in coherent states and squeezed coherent States.

Abstract

This thesis deals with certain aspects of coherent states and Squeezed coherent states and their applications. Coherent states for harmonic oscillator, originally discovered by Schrodinger and then rediscovered by Sudharshan and Glauber, provides a good description in quantum theory of optical coherence, for various optical fields, especially for laser light. This thesis gives a detailed discussion of generalised coherent states. (i) In Lie algebra, the Harmonic Oscillator Algebra(Heisenberg-Weyl Algebra), used to define coherent state; Coherent states for angular momentum, the algebra as per Radcliffe and Arecchi et al., is used. Using group contraction procedure the harmonic oscillator coherent state could be obtained as a certain limit of angular momentum coherent state. In this thesis it is shown that the group contraction procedure merely means a well known concept of limiting distributions in probability theory. These concepts are used to associate a probability distribution with an arbitrary Lie algebra; And further the contraction of Lie algebras is shown to be contraction of probability distributions. The coherent states of phase operator in quantum mechanics in finite dimensions, and its results are discussed in this thesis. The results in this thesis, generalize the concept of squeezed coherent states, and discuss about their bunching and non-bunching properties, throwing some more light on Squeezing operators. Also extension to other quantum mechanical systems like hydrogen atom are studied.