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

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Optics Communications, Elsevier, 2002, 213, pp.325

ABSTRACT

The statistics of the light emitted by two-level lasers is evaluated on the basis of generalized rate equations. According to that approach, all fluctuations are interpreted as being caused by the jumps that occur in active and detecting atoms. The intra-cavity Fano factor and the photo-current spectral density are obtained analytically for Poissonian and quiet pumps. The algebra is simple and the formulas hold for small as well as large pumping ates. Lasers exhibit excess noise at low pumping levels.

LIEN VERS  L’ARTICLE : TWO-LEVEL LASER LIGHT STATISTICS

Jacques Arnaud

Optical and Quantum Electronics, 34, 393-410, 2002

ABSTRACT

Lasers essentially consist of single-mode optical cavities containing two-level atoms with a supply of energy called the pump and a sink of energy, perhaps an optical detector. The latter converts the light energy into a sequence of electrical pulses corresponding to photo-detection events. It was predicted in 1984 on the basis of Quantum Optics and verified experimentally shortly thereafter that when the pump is non-fluctuating the emitted light does not fluctuate much. Precisely, this means that the variance of the number of photo-detection events observed over a sufficiently long period of time is much smaller than the average number of events.

Light having that property is said to be “sub-Poissonian”. The theory presented rests on the concept introduced by Einstein around 1905, asserting that matter may exchange energy with a wave at angular frequency ω only by multiples of ~ ω. The optical field energy may only vary by integral  multiples of ~ ωas a result of matter quantization and conservation of energy. A number of important results relating to isolated optical cavities containing two-level atoms are first established on the basis of the laws of Statistical Mechanics. Next, the laser system with a pump and an absorber of radiation is treated. The expression of the photo-current spectral density found in that manner coincides with the Quantum Optics result.

The concepts employed in this paper are intuitive and the algebra is elementary. The paper supplements a previous tutorial paper (Arnaud, 1995) in establishing a connection between the theory of laser noise and Statistical Mechanics.

LIEN VERS  L’ARTICLE : RATE EQUATION THEORY OF SUB-POISSONIAN LASER LIGHT

J. Arnaud, L. Chusseau, F. Philippe

European Journal of Physics, 23, pp. 489-500, 2002

ABSTRACT

Carnot established in 1824 that the efficiency of cyclic engines operating between a hot bath at absolute temperature T hot and a bath at a lower temperature T cold cannot exceed 1−T cold/T hot. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as in the classical regime. The expression of the work performed is derived from a simple prescription. Reversible and non-reversible cycles are illustrated. The paper begins with historical considerations and is essentially self-contained.

LIEN VERS  L’ARTICLE : CARNOT CYCLE FOR AN OSCILLATOR

J. Arnaud,  F. Philippe

Journal of Physics A : Math Gen, 34 (2001) L473-L77

ABSTRACT

We consider a strictly isolated single-mode optical cavity resonating at angular Frequency ω containing atoms whose one-electron level energies are supposed to be : ~ ω, 2 ~ ω … B ~ ω, and m photons.

If initially the atoms are in their highest energy state and m= 0, we find that at equilibrium: variance(m) / mean(m) = (B+ 1)/6, indicating that the internal field

statistics is sub-Poissonian if the number of atomic levels B does not exceed 4. Remarkably, this result does not depend on the number of atoms, nor on the number of electrons that each atom incorporates. Our result has application to the statistics of the light emitted by pulsed lasers and nuclear magnetic resonance. On the mathematical side, the result is based on the restricted partitions of integers.

LIEN VERS  L’ARTICLE : PHOTON NUMBER VARIANCE IN ISOLATED CAVITIES

Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

Physical  Review B 62, number 20, novembre 2000

ABSTRACT

Systems containing few fermions (e.g., electrons) are of great current interest. Fluorescence occurs when electrons drop from one level to another without changing spin. Only electron gases in a state of equilibrium are considered. When the system may exchange electrons with a large reservoir, the electron-gas fluorescence is easily obtained from the well-known Fermi-Dirac distribution. But this is not so when the number of electrons in the system is prevented from varying, as is the case for isolated systems and for systems that are in thermal contact with electrical insulators such as diamond. Our accurate expressions rest on the assumption that single-electron energy levels are evenly spaced, and that energy coupling and spin coupling between electrons are small. These assumptions are shown to be realistic for many systems. Fluorescence from short, nearly isolated, quantum wires is predicted to drop abruptly in the visible, a result not predicted by the Fermi-Dirac distribution. Our exact formulas are based on restricted and unrestricted partitions of integers. The method is considerably simpler than the ones proposed earlier, which are based on second quantization and contour integration.

LIEN VERS  L’ARTICLE : FLUORESCENCE FROM A FEW ELECTRONS

Jacques Arnaud

Eur. J. Physics, 21 (2000) L15-L16

ABSTRACT

Pulsating Gaussian wavepackets are constructed from complex trajectories.

LIEN VERS  L’ARTICLE : PULSATING GAUSSIAN WAVEPACKETS AND COMPLEX TRAJECTORIES

Am. J. Phys. 67, 215 (1999)

ABSTRACT

The distribution of electrons in small one-dimensional systems is obtained under the assumption of evenly spaced energy levels. The method consists of considering isolated systems and shifting electrons from their zero-temperature location. The distribution is then expressed in terms of the number of partitions of integers. When the system is in thermal contact with an electrical insulator, the electron distribution is obtained by averaging the previous result with the Boltzmann factor as a weight. Finally, when the system is in thermal and electrical contact with a large medium, the Fermi–Dirac distribution emerges through averaging over the number N of electrons. The statistics of light emitted or absorbed by the electron gas is obtained without quantization of the optical field. Our rigorous though elementary treatment helps clarify concepts employed in statistical mechanics.

LIEN VERS  L’ARTICLE : ILLUSTRATION OF THE FERMI-DIRAC STATISTICS

J. Arnaud

Quantum Semiclass. Opt. 9 507-518, 1997

ABSTRACT

Essentially closed-form formulae are given for the linewidth of inhomogeneously broadened lasers, with arbitrary cavity detuning and pumping statistics (Poissonian or quiet pumps). The so-called `bad-cavity’ mode of operation is treated. The general formula is obtained from a semiclassical theory first derived from a linearized symmetrically ordered quantum theory in the limit of a large number of atoms. This semiclassical theory is most easily explained in terms of independent quantum jumps performed by emitting and absorbing atoms. The effect of inhomogeneous broadening on linewidth is found to be negligible for some pumping schemes, but when the atoms are independently pumped the linewidth is proportional (at some constant power level) to the gain-medium spectral width. We consider, in particular, an intermediate situation in which the rate at which atoms are promoted from the lower to the upper level (pump rate) is proportional to the lower-state population for each atom class. For that particular model, pump fluctuations do not affect the linewidth, even when the cavity is detuned from the centre of the atomic transition frequency distribution.

LIEN VERS  L’ARTICLE : DETUNED INHOMOGENEOUSLY BROADENED LASER LINEWIDTH

J. Arnaud

Tutorial Review, Optical and Quantum Electronics, November 1996, Volume 28, Issue 11, pp 1589-1615

ABSTRACT

The classical theory of light fluctuations rests on the intuitive concept that jumps between atomic states occur at independent times when the optical field has a prescribed value. The statistical properties of phase-noise sources are obtained in the present paper by applying this principle to detuned atoms. Formulae for amplitude and phase fluctuations coincide with quantum-theory results even when ‘non-classical’ states of light are generated. Theories employing semiclassical or quantum concepts are reviewed. We consider particularly the linewidth of laser oscillators operating below and above threshold when the atomic polarization cannot be adiabatically eliminated. Quantum-theory results by Lax (1966) are recovered from classical theory in a straightforward manner. More general results are given for dispersive loads, applicable to external-cavity lasers and relevant to gain guidance. It is emphasized that the K-factor as calculated by Petermann is applicable only below threshold. When more than one emitting element is present, population rate equations need to be considered and the linewidth decreases when the pump fluctuations are suppressed. The role of gain compression relating to semiconductor lasers is discussed. It is shown that at low and moderate powers gain compression reduces the effective phase-amplitude coupling factor, α. But at high power a number of mechanisms contribute to linewidth rebroadening. One of them is the statistical (quasi-thermal equilibrium) fluctuation of the refractive index. General concepts applicable to broadband light are outlined in an appendix.

LIEN PAYANT VERS  L’ARTICLE : CLASSICAL THEORY OF LASER LINEWIDTH