“Regular” form of the Sudarshan-Glauber representation of the density matrix

Ravinder Nath

S. Chaturvedi, G. S. Agarwal, Venkatraman Srinivasan

It is shown that, to any quasiprobability distribution corresponding to a given density operator, one can associate a class of positive distributions in an extended space. In situations where the quasiprobability distributions are singular, these distributions are shown to provide regularized versions thereof. The positive distribution introduced by Drummond and Gardiner (1981) in the context of the Glauber-Sudarshan P-representation is shown to arise as a special case. One can thus associate a positive distribution to the Wigner function such that its moments give the averages of Weyl-ordered operators with respect to the given density operator. It is also found that one can associate to the Glauber-Sudarshan P-function, a distribution in the extended space which, though not positive, interestingly, involves the Wigner function (1932). A measurement scheme which directly yields these positive distributions is presented.

G. Ramachandran, M. V. N. Murthy

Jan Sperling

Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.

G. Ramachandran, M. V. N. Murthy

A.V. Vikentyev, V. Yu. Goryainov, Ларионов Николай Владимирович

We consider the model of a single-emitter laser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. In the stationary regime using normally-ordered diagonal representation of the density matrix over the coherent states we derive equation for the phase-averaged Glauber-Sudarshan P function. In the strong-coupling regime between atom and cavity mode the asymptotic solution of this equation is obtained. This solution is a linear combination of two basis solutions. We analyze one of them which was ignored in previous work without any discussions.