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Journal of Experimental and Theoretical Physics

Inversionless superradiance of an ensemble of three-level atoms in a high-Q cavity

А. И. Зайцев, Igor Viktorovich Ryzhov, Evgenii Dmitrievich Trifonov, Victor A Malyshev

Published Feb 1, 1999• 9 citations
Publisher

Abstract

We analyze the possibility of superradiance in an ensemble of three-level atoms in the absence of population inversion. We show that in the case of a Λ configuration of the active transitions this effect can occur for an initially coherent superposition of the states of the lower doublet. We also study how splitting of the lower levels influences this effect and discuss ways of creating low-frequency coherence.

DOI
10.1134/1.558795

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We analyze the possibility of superradiance in an ensemble of three-level atoms in the absence of population inversion. We show that in the case of a Λ configuration of the active transitions this effect can occur for an initially coherent superposition of the states of the lower doublet. We also study how splitting of the lower levels influences this effect and discuss ways of creating low-frequency coherence.
Superradiance of three-level optical systems with a doublet in the ground state (Λ-scheme) placed in a high- Q cavity is studied theoretically. The conservation laws are obtained, which allow to considerably reduce the dimension of the phase space of the examined model (R 11 →R 5 ). In the particular case of a degenerate doublet, a mapping that makes it possible to reduce the problem of the three-level superradiance to a Duffing oscillator model (R 5 →R 2 ) is found. It is shown the possibility to initiate the superradiance generation even in the case when the population of the upper level is smaller than the total population of the lower doublet, i.e., without population inversion on the whole.
Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (ℝ 11 → ℝ 5 ) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.
The article reports the results of a theoretical study of superradiance of three-level optical systems with a doublet in the ground state (Λ-scheme) placed in a high-quality cavity. Hyperbolic chaos and unpredictable dynamic movements of the system appear on the surface of a multidimensional torus without dissipative losses in the conditions of superradiance without population inversion. The study resulted in the development of conservation laws to reduce the dimension of the phase space. An analytical result is obtained for the special case of a degenerate doublet.