About fifty years ago E. Wolf and L. Mandel developed the theory of partial coherence into a systematic theory. Wolf showed that coherence propagates as a wave; and Mandel gave the formalism for photo-counting.

In March 1963, Sudarshan formulated the quantum theory of light beams and gave a formula that makes it very similar in form to the classical wave theory. This is called the Quantum Optical Equivalence Theorem. The novel and crucial feature was that the distribution of weights in the beam could become negative. This is the signature of the quantum nature of the optical field. It can lead to anti-correlation (anti Hanbury-Brown, Twiss effect) for intensity correlations and can also lead to photon antibunching. Both of these have been experimentally verified. (The much advertised treatment by R. Glauber did not contain any quantum signature. It only used Dirac’s quantum notation for the coherence functions and reproduced the earlier Mandel-Wolf theory). Independent of the intensity, the quantum signatures are present only when the weight functions are non-positive definite. In addition to the original letter in Physical Review Letters, a comprehensive theory was presented by Sudarshan in a later paper; and a rigorous definition of the weight function as the Fourier transform of an easily computed quantity by Mehta and Sudarshan. These results and a comprehensive treatment of the subject can be found in the book Quantum Optics by Klauder and Sudarshan.

Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams, Phys. Rev. Lett. 10, 277-279 (1963).

Relation between Quantum and Semiclassical Descriptions of Optical Coherence; with C. L. Mehta, Phys. Rev. 138, B274 (1965).

Time Evolution of Coherent States; with C. L. Mehta, Phys. Lett. 22, 574 (1966).

Dynamics of Coherent States; with C. L. Mehta, P. Chand and R. Vedam, Phys. Rev. 157, 1198 (1967).

Fundamentals of Quantum Optics; with J.R. Klauder, W. A. Benjamin, Inc., New York (1968). [BOOK]

Quantum Theory of Partial Coherence, J. Math. and Phys. Sci. 3, 121 (1969) Madras, India.

Many-time Photocount Distributions; with S. K. Srinivasan and S. Sukavanam, J. Phys. and Math. 6, 1910 (1973).

New Light on the Optical Equivalence Theorem and a New Type of Discrete Diagonal Coherent State Representation; with N. Mukunda, Pramana 10, 227 (1978).

Quantum Theory of Radiative Transfer, Phys. Rev. A 23, 2802 (1981).

Diagonal Harmonious State Representations, Int. J. Theor. Phys. 32, 1069 (1993).

Photon Distribution in Nonlinear Coherent States

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