E.C.G.Sudarshan and his Diagonal Representation in Quantum Optics

TL;DR

This paper revisits Sudarshan's 1963 work on the equivalence of semiclassical and quantum descriptions of light, emphasizing the diagonal representation of the density matrix using coherent states.

Contribution

It provides a clear, accessible exposition of Sudarshan's diagonal representation in quantum optics, making the original results understandable without expert guidance.

Findings

Reproduction of Sudarshan's original results from 1963.

Explanation of the diagonal representation of the density matrix.

Connection between harmonic oscillator algebra and quantum light states.

Abstract

The essential of this monograph is to reproduce the results of Sudarshans paper Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams published in 1963. To go in that direction we also describe the linear harmonic oscillator and its algebraic equivalence with a single-mode quantized beam of light. Coherent states and their overcompleteness properties along with the diagonal representation of the density matrix are essential as a prerequisite to reproduce the result. Most of the textbooks meant for graduate students describe linear harmonic oscillators in great detail but they cryptically mention coherent states and their associated properties. So it is difficult for the students to understand the essence of Sudarshans paper which contains only seven equations. This monograph is written in such a lucid manner that without the help of experts one can understand it.