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arXiv:quant-ph/0107104 · Journal of Optics B Quantum and Semiclassical Optics

Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing

J. Bajer, Adam Miranowicz

Published Jul 23, 2001• 2 citations
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Abstract

Sub-Poissonian light generation in non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q -functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for the observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behaviour are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behaviour are found. Noise suppression levels in non-degenerate versus degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to the degenerate process.

DOI
10.1088/1464-4266/3/4/309

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Sub-Poissonian light generation in non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q -functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for the observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behaviour are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behaviour are found. Noise suppression levels in non-degenerate versus degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to the degenerate process.
Second-harmonic generation in the no-energy-transfer regime can be a source of quasi-stationary sub-Poissonian light as was recently shown by Bajer et al ( Bajer J, Haderka O and Perina J 1999 J. Opt. B: Quantum Semiclass. Opt. 1 529 ). We generalize their results for higher-harmonic generation by applying the numerical method of Hamiltonian diagonalization and the analytical semiclassical description of classical trajectories. The quasi-stationary behaviour of the sub-Poissonian photocount noise in the no-energy-transfer regime is explained. An approximate formula for the Fano factor is derived for arbitrary harmonics. It is predicted that the deepest quasi-stationary reduction of photocount noise in the no-energy-transfer regime is achieved in the third-harmonic generation.
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the third harmonic equal to 13/16.
The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
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.