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arXiv:quant-ph/0703217

Semi-classical theory of quiet lasers. Short version

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Published Mar 23, 2007• 0 citations
arXivHTMLPDF

Abstract

This article is the shorten version of quant-phys/0610106 with a supplemented theory and new results concerning a single-electron laser driven by a constant-potentiel battery. "Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. We consider in the present paper two oscillators that should exhibit in principle the same property. First, a reflex klystron, a vacuum tube operating in the microwave range of frequency. Second a laser involving a single electron permanently interacting with the field. It is unnecessary to quantize the optical field, that is, the theory is semi-classical, yet exact. As an example, the battery-driven one-electron laser delivers a detected noise of 7/8 of the shot-noise level, and is therefore sub-Poissonian. Our calculations are related to resonance-fluorescence treatments but with a different physical interpretation. Previous theories considering excited-state atoms regularly-injected in low-loss resonators, on the other hand, do require light quantization. The theory presented here is restricted to above-threshold stationary single-mode oscillators. The paper is written in such a way that readers should be able to follow it without having to refer to quantum-optics texts."

DOI
10.48550/arxiv.quant-ph/0703217

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Reviews of Modern Physics•Jul 1, 1996•220 citations
This article is the shorten version of quant-phys/0610106 with a supplemented theory and new results concerning a single-electron laser driven by a constant-potentiel battery. "Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. We consider in the present paper two oscillators that should exhibit in principle the same property. First, a reflex klystron, a vacuum tube operating in the microwave range of frequency. Second a laser involving a single electron permanently interacting with the field. It is unnecessary to quantize the optical field, that is, the theory is semi-classical, yet exact. As an example, the battery-driven one-electron laser delivers a detected noise of 7/8 of the shot-noise level, and is therefore sub-Poissonian. Our calculations are related to resonance-fluorescence treatments but with a different physical interpretation. Previous theories considering excited-state atoms regularly-injected in low-loss resonators, on the other hand, do require light quantization. The theory presented here is restricted to above-threshold stationary single-mode oscillators. The paper is written in such a way that readers should be able to follow it without having to refer to quantum-optics texts."
Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. The purpose of this paper is to show that, as long as the laser-detector system is strictly stationary, quantization of the optical field is not required to explain such phenomena. The theory presented here is semi-classical, yet exact. Previous theories considering excited-state atoms regularly-injected in resonators, on the other hand, do require in principle light quantization. Specifically, we consider a laser involving a single electron permanently interacting with the field and driven by a constant-potential battery, and point out a similarity with reflex klystrons. The detected noise is found to be only 7/8 of the shot-noise level. It is therefore sub-Poissonian. Our calculations are related to resonance-fluorescence treatments but with different physical interpretations.
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.
When light originating from a laser diode driven by non-fluctuating electrical currents is incident on a photo-detector, the photo-current does not fluctuate much. Precisely, this means that the variance of the number of photo-electrons counted over a large time interval is much smaller that the average number of photo-electrons. At non-zero Fourier frequency ΩΩΩ the photo-current power spectrum is of the form Ω2/(1+Ω2)Ω^2/(1+Ω^2)Ω2/(1+Ω2) and thus vanishes as Ω→0Ω\to 0Ω→0, a conclusion equivalent to the one given above. The purpose of this paper is to show that results such as the one just cited may be derived from a (semi-classical) theory in which neither the optical field nor the electron wave-function are quantized. We first observe that almost any medium may be described by a circuit and distinguish (possibly non-linear) conservative elements such as pure capacitances, and conductances that represent the atom-field coupling. The theory rests on the non-relativistic approximation. Nyquist noise sources (in which the Planck term ℏω/2\hbarω/2ℏω/2 is being restored) are associated with positive or negative conductances, and the law of average-energy conservation is enforced. We consider mainly second-order correlations in stationary linearized regimes.
We call quiet a stationary laser that generates in detectors regular photo-electrons (sub-Poisson statistics). It follows from the law of conservation of energy that this is so when the laser power supply does not fluctuate. Various configurations are analyzed on the basis of the Planck (1907) semi-classical concept: am not seeking the meaning of light quanta in the vacuum but rather in places where emission and absorption occur, and I assume that what happens in the vacuum is rigorously described by Maxwell's equations. Exact agreement with Quantum Optics results is noted. Comments welcome!
We solve the problem of a laser with variable pumping statistics for any relative magnitude of the atomic- and cavity-decay constants, and obtain a different regime of sub-Poissonian light generation. We show that, even for Poissonian pumping, the noise in the amplitude quadrature outside the cavity can be reduced up to 50% below the shot-noise level when the polarization but not the populations can be adiabatically eliminated. Maximum noise reduction in this case is obtained when the lower level decays much faster than the upper one and occurs at a frequency given by the geometrical mean of the decay rates of the field and the lower-level population. Furthermore, the full consideration of atomic memory effects leads to a generalization of previous results on regularly pumped lasers. We find that, for regular pumping, maximum amplitude-noise reduction (up to complete quieting) still occurs at zero frequency in all cases. However, a long-living polarizaton leads to an increase in amplitude noise and may even eliminate the dip at zero frequency, at the same time leading to a significant quenching of the laser linewidth in the bad-cavity limit.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]