Glauber–Sudarshan P-representation

The Glauber-Sudarshan P-representation is a suggested way of writing down the state of any type of light using the coherent states as a basis. It was developed by George Sudarshan and later adopted by Roy J. Glauber (see the references below). It was the subject of a controversy when Glauber was awarded a share of the 2005 Nobel Prize in Physics for his work in this field and George Sudarshan's contribution was not recognized.

In this representation, the density matrix $\widehat{\rho}$ is written as:

$\widehat{\rho} = \int P(\alpha) |{\alpha}\rangle \langle {\alpha}|\ d^{2}\alpha, \qquad d^2\alpha \equiv d\, {\rm Re}(\alpha) \, d\, {\rm Im}(\alpha) \,$

where $\scriptstyle|\alpha\rangle\,$ are the coherent states and $\scriptstyle P(\alpha) \,$ is a quasi-probability distribution.

The matter is not quite simple. According to Mandel and Wolf: "The different coherent states are not [mutually] orthogonal, so that even if $\scriptstyle P(\alpha) \,$ behaved like a true probability density [function], it would not describe probabilities of mutually exclusive states."

References

Citation bibliography

Mandel, L.; Wolf, E. (1995), Optical Coherence and Quantum Optics, Cambridge UK: Cambridge University Press, ISBN 0-521-41711-2 

General references

• E. C. G. Sudarshan, Phys. Rev. Letters 10, 277 (1963)
• Roy J. Glauber, Physical Review 131, 2766 (1963)

See also

• Nonclassical light
• Wigner quasi-probability distribution
• Husimi Q representation
• Nobel Prize controversies