Time Dependent Quadratic Hamiltonians,SU(1,1), SU(2), SU(2,1) and SU(3)
Abstract
Description
The properties of SU(1,1) SU(2),SU(2,1) and SU(3) have often been used in quantum optics. In this paper we demonstrate the use of these symmetries. The group properties of SU(1,1) SU(2), and SU(2,1) are used to find the transition probabilities of various time dependent quadratic Hamiltonians. We consider Hamiltonians representing the frequency converter,parametric amplifier and raman scattering.These Hamiltonians are used to describe optical coupling in nonlinear crystals.
This paper is a replacement, new, appendix, sections and references have been added. A version of this paper has been accepted by 'Physics Letters A' on 17th of febuary 2006. It is available from http://www.sciencedirect.com. Title of paper 'Time dependent quadratic Hamiltonians SU(2) and SU(2,1)' author Paul Croxson 19 pages
This paper is a replacement, new, appendix, sections and references have been added. A version of this paper has been accepted by 'Physics Letters A' on 17th of febuary 2006. It is available from http://www.sciencedirect.com. Title of paper 'Time dependent quadratic Hamiltonians SU(2) and SU(2,1)' author Paul Croxson 19 pages