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Soviet Journal of Quantum Electronics

Quantum and quasiclassical lasing regimes

Vladimir P Bykov, G V Shepelev

Published Sep 30, 1982• 1 citation
Publisher

Abstract

The Scully-Lamb quantum-mechanical laser theory is generalized to the case of active atoms situated in superposed upper and lower active states. In this case, a laser emits a field of nonzero average intensity. If there is no interference between the active levels of the active atoms, a state of the field may be found for which the average quantum-mechanical intensity is zero. An investigation is made of pumping in a molecular oscillator and in gas lasers. It is shown in which cases pumping causes interference between the active levels of the active atoms. An interference experiment which can distinguish between fields having zero and nonzero average intensities is discussed.

DOI
10.1070/qe1982v012n09abeh005988

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Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
The Scully-Lamb quantum-mechanical laser theory is generalized to the case of active atoms situated in superposed upper and lower active states. In this case, a laser emits a field of nonzero average intensity. If there is no interference between the active levels of the active atoms, a state of the field may be found for which the average quantum-mechanical intensity is zero. An investigation is made of pumping in a molecular oscillator and in gas lasers. It is shown in which cases pumping causes interference between the active levels of the active atoms. An interference experiment which can distinguish between fields having zero and nonzero average intensities is discussed.
A comprehensive review is given of investigations, both theoretical and experimental, that demonstrate interference to take place even when the fields involved are produced by independent sources. The physical situation is rather different for coherent and incoherent fields. In the first case, where the sources are lasers, a conventional interference pattern can be observed which is adequately described by the classical theory. In the present paper, special attention is paid to the question of whether this interference persists when the two laser beams become strongly attenuated. In the second case, the sources are individual atoms excited by a pumping mechanism, that emit spontaneously and, hence, independently from each other. In those circumstances, no interference pattern can show up. However, it becomes evident from both the classical and the quantum-mechanical theory that interference effects can still be established by observing intensity correlations rather than the intensity itself. This point is discussed in greater detail. The pioneering experiments of Forrester, Gudmundson and Johnson, and Brown and Twiss are reviewed in this context. Especially interesting from the theoretical point of view is the case of two emitting atoms, since then the classical and the quantum-mechanical description differ significantly, the quantum theory predicting the intensity correlations to be distinctly stronger than those following from classical considerations. This specific quantum-mechanical feature is shown to be intimately connected with the corpuscular aspect of light.
A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.
We discuss a generalized version of the Scully-Lamb laser master equation for a collection of driven multilevel atoms in a lambda-type configuration. We are especially interested in the effect of the external driving field on the laser process with or without a population inversion between the lasing levels. We provide an exact solution of the photon probability distribution in steady state and discuss regimes of operation that can lead to sub-Poissonian statistics, as measured by the ratio between the variance and the average photon number. We solve the field master equation in the transient regime and analyze the effects of the external driving field on the linewidth of the emitted radiation. The largest reduction of the photon variance relative to the mean number corresponds to the injection into the cavity of atoms prepared in the nonlasing level. Injection of atoms in an incoherent mixture of the three energy states normally leads to super-Poissonian statistics.
Abstract This present paper is an attempt to describe the operation of a laser by a method patterned closely after the classical theory of dispersion. There, the electromagnetic field is treated as a classical system interacting with a collection of classical harmonic oscillators which are at rest. In the present case the radiation field is still treated classically, but, in accordance with the correspondence principle, the oscillators are now virtual oscillators associated with the up-and-down transitions in effective two-state atoms which are described quantum mechanically. The atoms carrying these virtual oscillators are not at rest but move with different velocities. We show how the Lorentz averaging can be performed for such systems, and derive a closed set of equations linking the average electric field E, with the average polarization density P„ and the average population inversion density Mp associated with atoms moving with the velocity v. Next, we investigate the conditions for the existence of a steady state if pumping is present, and if the electric field is represented by a standing wave, or a travelling wave of a single frequency (single-mode case). It turns out that, notwithstanding the nonlinear nature of the equations, the steady-state conditions give a simple complex dispersion relation; moreover, the real and imaginary part of this dispersion relation are equivalent to the usual heuristic expressions which specify the operating frequency in terms of the index of refraction and cavity length, and which balance the gain against the losses. The single-mode case is analysed in detail without any smallness assumptions for the resultant intensity. The small-intensity case gives the usual results exhibiting the tuning dip. For high intensities the relative depth of the dip tends to zero. At the end of the paper we discuss proposed extensions and additional applications.
Summary form only given.The behavior of a laser intensity as a function of a pump rate is studied. We consider a three-level lasing scheme with two different types of pumping. In the first case, the lower lasing level is depleted to the ground state, and then the pumping is used to excite the atom from the ground state to the upper lasing level. In the second case the pumping is used to excite the atom directly from the lower lasing level to one of the excited states, which is then depleted to the upper lasing level. We refer these two types of pumping as type 1 and type 2, respectively. It is shown that although these two schemes are equivalent mathematically, i.e., they are formally described by the same set of equations, physically their dynamical properties are completely different. It is noted that the pumping of the type 1 does not affect either of lasing levels directly, whereas the pumping of the type 2 does connect the lower lasing level with one of the excited states. It is this difference of the two ways of pumping which is responsible for the crucial difference in the dynamic behavior of the lasing schemes of types 1 and 2.