Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Arxiv, 23/03/2007

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. »

LIEN VERS  L’ARTICLE : SEMI-CLASSICAL THEORY OF QUIET LASERS SHORT VERSION

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

arXiv:quant-ph/0703217v1 

22/01/2007

ABSTRACT

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 Ω the photo-current power spectrum is of the form Ω2/(1+Ω2) and thus vanishes as Ω→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 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.

LIEN VERS  L’ARTICLE : SEMI-CLASSICAL THEORY OF QUIET LASERS I. PRINCIPLES 

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

J. Phys. IV France, Volume 119, November 2004, pp. 155-156

ABSTRACT

L’étude de la statistique des photons dans des lasers monomodes de classe A ou B pompés proche du seuil est conduite par la simulation Monte Carlo d’un processus markovien négligeant les éventuels états de superposition. Pour des paramètres usuels, le calcul montre un excès de probabilité de trouver un photon et un seul dans la cavité comparé aux théories classiques de Scully, Lamb et Loudon. L’origine de ce résultat reste mystérieuse mais pourrait correspondre à l’hypothèse de linéarisation des théories classiques.

LIEN VERS  L’ARTICLE : ETUDE MONTE CARLO DE LA STATISTIQUE DES PHOTONS D UN LASER PROCHE DU SEUIL

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Arxiv, 2 juin 2003, Version 2

ABSTRACT

Quantum heat engines employ as working agents multi-level systems instead of gas-filled cylinders.

We consider particularly two-level agents such as electrons immersed in a magnetic field. Work is produced in that case when the electrons are being carried from a high-magnetic-field region into a low-magnetic-field region. In watermills, work is produced instead when some amount of fluid drops from a high-altitude reservoir to a low-altitude reservoir . We show that this purely mechanical engine may in fact be considered as a two-level quantum heat engine, provided the fluid is viewed as consisting of n molecules of weight one and N−n molecules of weight zero. Weight-one molecules are analogous to electrons in their higher energy state, while weight-zero molecules are analogous to electrons in their lower energy state. More generally, fluids consist of non-interacting molecules of various weights. It is shown that, not only the average value of the work produced per cycle, but also its fluctuations, are the same for mechanical engines an d quantum (Otto) heat engines. The reversible Carnot cycles are approached through the consideration of multiple sub-reservoirs.

LIEN VERS  L’ARTICLE : A SIMPLE QUANTUM HEAT ENGINE

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Optics and Spectroscopy, May 2003, Volume 94, Issue 5, pp. 746-754

ABSTRACT

Single-mode cavity laser light statistics is considered within the framework of rate equations. According to this approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is simple, allowing analytical expressions for the intracavity Fano factor and the photocurrent spectral density to be obtained. Poissonian, quiet, and optical pumps are considered. The results are verified by comparison with Monte Carlo simulations. An essentially exhaustive investigation of sub-Poissonian light generation by classical laser schemes, two-mode lasers, and semiconductor lasers is proposed.

LIEN VERS  L’ARTICLE : RATE EQUATION APPROACH TO LASER LIGHT STATISTICS

J.  Arnaud, L. Chusseau, F. Philippe

in Proc. 22èmes Journées Nationales d’Optique Guidée, Valence, 2003.

ABSTRACT

Un laser naturellement bi-mode constitue la source de choix pour les applications de photomélange, par exemple pour produire des fréquences térahertz. Nous étudions dans cette communication le bruit optique d’instensité généré sur chacun des deux modes et sur leur somme. Les sauts quantiques des atomes émetteurs et détecteurs sont la seule source de bruit physique prise en compte. Les résultats détaillent le bruit de partition se produisant entre les deux modes de la cavité. Les calculs analytiques sont supportés par une simulation Monte Carlo d’un processus de naissance et de mort.

LIEN VERS  L’ARTICLE : BRUIT DE PARTITION ET STATISTIQUE DES PHOTONS D UN LASER BI-MODE

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

15/11/2002

ABSTRACT

The statistical properties of non-interacting bosons and fermions confined in rapping potentials are most easily obtained when the system may exchange

energy and particles with a large reservoir (grand-canonical ensemble). There are

circumstances, however, where the system under consideration may be Considered as being isolated (micro-canonical ensemble). This paper first reviews results relating to micro-canonical ensembles. Some of them were obtained a long time ago, particularly by Khinchin in 1950. Others were obtained only recently, often motivated by experimental results relating to atomic confinement. A number of formulas are reported for the first time in the present paper. Formulas applicable to the case where the system may exchange energy but not particles with a reservoir (canonical ensemble) are derived from the micro-canonical ensemble expressions. The differences between the three ensembles tend to vanish in the so-called Thermodynamics limit, that is, when the number of particles and the volume go to infinity while the particle number density remains constant. But we are mostly interested in systems of moderate size, often referred to as being mesoscopic, where the grand-canonical formalism is not applicable. The mathematical results rest primarily on the enumeration of partitions of numbers.

LIEN VERS  L’ARTICLE : STATISTICS OF NON-INTERACTING BOSONS AND FERMIONS IN MICRO-CANONICAL, CANONICAL AND GRAND-CANONICAL ENSEMBLES – A SURVEY

Jacques Arnaud, Laurent Chusseau

Optical and Quantum Electronics, October 2002, Volume 34, Issue 10, pp 1007-1023

ABSTRACT

When laser diodes are driven by high-impedance electrical sources, the variance of the number of photo-detection events counted over large time durations is less than the average number of events (sub-Poissonian light). This paper presents a Monte-Carlo simulation that keeps track of each level occupancy (0 or 1) in the conduction and valence bands, and of the number of light quanta in the optical cavity. When there is good electron–lattice thermal contact, the electron and hole temperatures remain equal to that of the lattice. In that case, the elementary laser-diode noise theory results are accurately reproduced by the simulation. But when the thermal contact is poor (or, almost equivalently, at high power levels), new effects occur (spectral-hole burning, temperature fluctuations, statistical fluctuations of the optical gain) that are difficult to handle theoretically. Our numerical simulation shows that the frequency domain over which the photo-current spectral density is below the shot-noise level becomes narrower as the optical power increases.

LIEN VERS  L’ARTICLE : MONTE-CARLO SIMULATION OF LASER DIODE SUB-POISSONNIAN LIGHT GENERATION

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

05/06/2002

Journal de Physique, J. Phys. IV France 12 (2002) Pr5-337

ABSTRACT

Les lasers conventionnels à 4 niveaux peuvent délivrer de la lumière de statistique sous-Poissonienne même lorsqu’ils sont soumis à un pompage optique. Nous retrouvons exactement ces prédictions de l’optique quantique en supposant simplement que les atomes ont des niveaux d’énergie quantifiés interagissant avec un champ électromagnétique classique, la source du bruit optique étant les sauts quantiques entre niveaux. Des formules analytiques sont obtenues pour les deux paramètres clefs de la statistique des photons du laser: le facteur de Fano et la densité spectrale des photons émis.

LIEN VERS  L’ARTICLE : STATISTIQUE DES PHOTONS D’UN LASER A 4 NIVEAUX SOUMIS A UN POMPAGE OPTIQUE

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Physical Review A66,06/03/2002

ABSTRACT

We consider three- and four-level atomic lasers that are either incoherently (unidirectionally) or coherently (bidirectionally) pumped, the single-mode cavity being resonant with the laser transition.

The intra-cavity Fano factor and the photo-current spectral density are evaluated on the Basis of rate equations. According to that approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is considerably simpler than the one required by Quantum-Optics treatments.

Whenever a comparison can be made, the expressions obtained coincide. The conditions under which the output light exhibits sub-Poissonian statistics are considered in detail. Analytical results, based on linearization, are verified by comparison with Monte Carlo simulations. An essentially exhaustive investigation of sub-Poissonian light generation by three- and four-level atoms lasers has been performed. Only special forms were reported earlier.

LIEN VERS  L’ARTICLE : RATE-EQUATION APPROACH TO ATOMIC-LASER LIGHT STATISTICS