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Journal of the Optical Society of America B

Higher-order sub-Poissonian photon statistics in terms of factorial moments

Daniel B. Erenso, Reeta Vyas, Surendra Singh

Published Jun 1, 2002• 37 citations
Publisher

Abstract

We introduce the concept of higher-order super-Poissonian and sub-Poissonian statistics and show that higher-order sub-Poissonian statistics is a signature of a nonclassical field. Fields generated in intracavity second-harmonic generation and single-atom resonance fluorescence are shown to exhibit higher-order sub-Poissonian statistics.
DOI
10.1364/josab.19.001471

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In the present paper we study higher-order sub-Poissonian photon statistics in interaction of a single mode radiation initially in the coherent state Ŧα〉 with an assembly of two excited two-level atoms using the Hamiltonian, H=ω(a+a+Sz)+g(aS++a+S.), in the natural system of units. Here, α=|α|eiθα, a is the annihilation operator for radiation, Sz and S± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and the energy difference between the two atomic levels. We solve it exactly and conclude that higher-order sub-Poissonian photon statistics can be obtained for an arbitrary order by choosing suitably the square root of mean photon number |α| of the coherent radiation and coupling time gt. Variations of higher-order sub-Poissonian photon statistics with parameters |α| and gt have also been discussed.
The quantum statistical equations for the field produced in the process of second-harmonic generation (SHG) are expressed, based on a method proposed for four-wave mixing.1 We start from the following assumptions: 1) the field absorption in the nonlinear medium may be neglected; 2) the amplitude of the fundamental field is much greater than that of the SH field; 3) the Wigner function associated with the density operator of the field depends significantly only on the variables of the SH field. The coefficients of the Fokker–Planck equation thus obtained depend on the Laplace transforms of the correlation functions of the atomic polarization operator. The moments of the Wigner function2 are related to the moments of the SH field photon number; consequently, we impose the condition for sub-Poissonian photon-statistics and derive the corresponding relationships satisfied by the atomic correlation functions. A numerical interpretation is given.