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arXiv:0710.2596

Sub-Poissonian laser emission from a single-electron permanently interacting with a single-mode cavity

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Published Oct 13, 2007• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0710.2596

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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.
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."
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 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 show that the injection of an external field in a laser helps to improve amplitude squeezing and sub-Poissonian light generation close to threshold, but spoils quantum noise reduction for very high pumping rates. A general nonlinear theory is developed for the resonant case (no detunings), without any assumption on the relative magnitudes of field and atomic decay constants, thus encompassing a large class of lasers. Several possible pumping schemes are accommodated, ranging from regular to Poissonian. We carry out a detailed stability analysis of the general equations of motion, relating it to the noise-reduction problem. Both the photon-number variance inside the cavity and the homodyne spectra of the output are discussed.
Shot noise sets a fundamental limit on the sensitivity of classical optical measurements, with coherent emitters achieving the lowest possible shot-noise level. Emission from sub-Poissonian light provides a pathway to surpass this limit, and single-photon sources provide a natural platform for generating such light. However, it is commonly assumed that continuously excited single-photon sources exhibit Poissonian statistics. In this work, a theoretical model of a continuously driven two-level single-photon source is developed, treating both excitation and radiative decay as stochastic processes. The analysis demonstrates that photon emission can display sub-Poissonian statistics when excitation and decay rates are comparable, showing that continuous excitation does not inherently preclude nonclassical emission. The model is further extended to include finite detection efficiency and detector dead time, illustrating how these practical non-idealities can affect the experimental observation of sub-Poissonian statistics.
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!