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Physical Review A

Sub-Poissonian statistics and squeezing in fluorescence fromNatoms in a cavity

P. L. Knight, Tran Quang

Published Jun 1, 1990• 17 citations
Publisher

Abstract

The sub-Poissonian statistics and squeezing in the fluorescence field from N two-level atoms in a cavity are considered for the case for which the cavity mode is so intense that it can be treated as a classical field. It is shown that sub-Poissonian statistics of sidebands are present for a large number of atoms. Moreover, the sidebands become more sub-Poissonian with increasing number of atoms. The condition for obtaining a large degree of squeezing in the sidebands is discussed.

DOI
10.1103/physreva.41.6255

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The sub-Poissonian statistics and squeezing in the fluorescence field from N two-level atoms in a cavity are considered for the case for which the cavity mode is so intense that it can be treated as a classical field. It is shown that sub-Poissonian statistics of sidebands are present for a large number of atoms. Moreover, the sidebands become more sub-Poissonian with increasing number of atoms. The condition for obtaining a large degree of squeezing in the sidebands is discussed.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
We have discussed the photon statistics of the spectral components of N-atom time-dependent resonance fluorescence. It is shown that in contrast to the stationary limit, sub-Poissonian photon statistics in the sidebands occur for any number N of atoms including the case N\ensuremath{\gg}1. Reduction in Mandel's parameters Q+1{\mathit{Q}}_{+1}Q+1​ is found with increasing numbers of atoms. The typical time for the presence of sub-Poissonian statistics is proportional to 1/N.
We study the conditions for sub-poissonian photon statistics and squeezed states in the field of resonance fluorescence of a two-state atom. These conditions as a function of the detuning from resonance, the linewidth and the Rabi frequency have some overlap, but they are largely complementary. Super-poissonian statistics arise for small linewidths and large detunings, irrespective of the Rabi frequency. Squeezed states require small linewidths and either low or moderate Rabi frequencies, or large detunings from resonance.
We study sub-Poissonian photon statistics of light in interaction of a single mode radiation, initially either in a coherent state or in a superposed coherent state with an assembly of two-level atoms using the Hamiltonian, H = ω(a+a + Sz) + g(aS+ + a+ S–) in natural units, where a+ and a are creation and annihilation operators, Sz, S ± are the collective Dicke operators, g is the coupling constant, and ω is the energy of the photons and also the separation between the two atomic levels. We study the cases of (i) a single two-level and (ii) of two two-level atoms interacting with a single mode coherent or superposed coherent radiation. We find that for large coupling time gt, Fano factor shows collapses and revival phenomena, and that the variation is large for small mean number of photons. We also find that in the case of two two-level atoms, photon statistics shows larger sub-Poissonian than the case of a single two-level atom, and that there is no definite relationship between squeezing and sub-Poissonian photon statistics of light.