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Physical Review A

Role of internal degrees of freedom in laser-light coherence

Alexander M. Khazanov, Gennady A. Koganov, R. Shuker

Published Feb 1, 1993• 2 citations
Publisher

Abstract

Conditions for noise minimization in laser systems are studied and formulated as a principle. It involves the correlation of the internal degrees of freedom of the system and the relative rates of transitions between them. The minimization principle proposed is appropriate for a variety of lasing schemes including nonunidirectional pump processes. It allows one to interpret a wide scope of experimental results. It is expected to be serviceable in further exploring of the squeezing phenomenon.

DOI
10.1103/physreva.47.1274

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Conditions for noise minimization in laser systems are studied and formulated as a principle. It involves the correlation of the internal degrees of freedom of the system and the relative rates of transitions between them. The minimization principle proposed is appropriate for a variety of lasing schemes including nonunidirectional pump processes. It allows one to interpret a wide scope of experimental results. It is expected to be serviceable in further exploring of the squeezing phenomenon.
The intrinsic property of laser systems with many internal degrees of freedom to generate a squeezed light is studied. The dressed-atom approach to fluctuations, described in the preceding paper [Khazanov, Koganov, and Shuker, Phys. Rev. A 48, 1661 (1993)], is employed. A minimization principle which governs noise quenching in laser systems is described comprehensively. This principle allows one to avoid complicated quantum-mechanical calculations to assess the squeezing capacity of the system. It is shown that noise in a laser system can be decomposed into noise states. These states interact coherently. For instance, each nonactive level in a multilevel lasing scheme may represent separate noise states under certain conditions while both lasing levels make only one noise state. The squeezing capacity of the system is determined by a quantity called the noise dimension. The theory is extended to laser schemes with many photons (two-photon generation, more than one lasing transition, etc.). The validity of the minimization principle is established for this type of system. Some consequences from the theory, which are relevant to the experiment, are discussed.
It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.
Considerable attention has been directed recently to the study of lasing without the need of population inversion. The optical coherence and quantum interference associated with the light amplification may lead to interesting statistical properties in inversionless lasers. Here we analyze a laser model that consists of an ensemble of closed multi-level (three or four levels) atoms driven by a single coherent field. Unlike conventional lasers where population inversion is maintained and kept at the threshold value for arbitrary laser output, the multi-level laser analyzed here can start lasing from population inversion and evolves from population inversion into non-inversion with the increasing atomic pumping. In other words, the system makes transition from light amplification by population inversion into light amplification by coherence. On the other hand, the system can be also made to start lasing without population inversion in any state basis. In both cases, initial inversion and non-inversion, which are controlled by the ratio of spontaneous decay rates, the laser well above threshold is always maintained by lasing without inversion (light amplification by coherence), and the laser intensity fluctuations may drop below the shot noise limit. Two factors contribute to the noise reduction: first, the disappearance of the population inversion leads to the depleted atomic population in the upper lasing state, which reduces the spontaneous emission noises; second, the fast coherent cycling of electrons between excited states leads to the highly regulated absorption and emission processes. We found that the combination of these two mechanisms can lead to the noise reduction in the laser output more than 50% below the shot-noise limit.
We present a detailed analysis of the noise properties of a potential lasing scheme employing a coherently driven three-level system in the \ensuremath{\Lambda} configuration inside an optical cavity. We derive expressions for the steady-state laser intensity and the width of the intensity fluctuations and show that the output fields exhibit sub-Poissonian statistics for suitable operating conditions. The fundamental mechanism responsible for noise suppression is identified as increased intensity dissipation inside the cavity through emission and absorption by the atoms, which counteracts the intensity fluctuations.
We summarize the basic problems in laser coherence and the concepts and techniques needed to solve them. Special techniques needed to handle partition noise in semiconductor lasers will be touched on. We address the problem of how a self-sustained oscillator works. Why is the laser line so narrow? Why does a small amount of noise produce a broadening of the line as opposed to additive side bands? What is the role of zero point oscillations and spontaneous emission in determining the line width? In what sense can the transition to a lasing state be described as a phase transition? The concepts used to deal with the response of a laser system involve a quasi-Markoffian description. This in turn validates a quantum regression theorem which relates the spectrum of the noise to the transport response even in a system far from equilibrium. A significant simplification is made by introducing non-commuting (quantum) noise sources. The techniques required in the solution of laser noise problems involve a multi-time correspondence between quantum variables and c-number random variables that reduces a quantum stochastic problem to a classical stochastic problem. Adiabatic elimination is used to eliminate the fast variables to obtain a reduced problem for the fields alone or the fields and some total atomic variables (total inversion and polarization). Reduction to a rotating wave version of the van der Pol oscillator and numerical solution of the Fokker-Planck equation yields (a) the line shape (b) the spectrum of intensity fluctuations and (c) the distribution of photocounts observed over some time interval. Comparison of theoretical results with later experiments will be presented.