Statistical properties of light and the Sudarshan representation

Sobhan Kumar Sounda, Koushik Mandal

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.

Arne Skov Jensen

Eiichi Hanamura, Yutaka Kawabe, Akio Yamanaka

Arindam Kumar Chatterjee, Anik Rudra, Soham Chakraborty

The diagonal representation and optical equivalence theorem are the E. C. G. Sudarshan's mid 20th century adventures in non-classical optics. It basically deals with a quantum mechanical description of photons to explain the quantum properties of light. Inspired by Sudarshan's pioneering work we try to explain the every minute mathematical details of his paper "Equivalence of semi-classical and quantum mechanical descriptions of statistical light beams". In this article we are going to go through some of the basics in developing quantum optics, then land up in E.C.G's original work and try to present it as rigorous as possible. We show some of its important applications in various classes of physics problems.

Edward L. Hill

Max Schubert

Abstract In the present paper the attributes of nonclassical light with respect to the theoretical basis, the experimental verification, and the applications are discussed and compared. If one ore more of the corresponding statistical measures (fluctuation excess, bunching excess, Poisson excess) attain negative values, surprising new properties of photon states occur. The analysis shows that under certain temporal and interaction conditions squeezing, antibunching, and sub‐Poisson behavior can accompany one or more of the other attributes. Also the connection of the attributes with the Glauber‐Sudarshan P‐representation of the corresponding states is studied and yields important assertions.