The Barut-Girardello states (the eigenstates of the SU(1, 1) lowering generator K - are considered in the harmonic oscillator Hilbert space. They are found to have sub-Poissonian photon statistics. By using these states, the diagonal P-representation of the density operator is constructed, and it is shown to be well behaved for non-classical photon states.
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Brif et al. (1994) studied this question.
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