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Optics and Spectroscopy

Inversionless Superradiance and the Duffing Model

Igor Viktorovich Ryzhov, N. A. Vasil’ev, I. S. Kosova, M. D. Shtager, Viktor A. Malyshev

Published Mar 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x1603019x

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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.
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.
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 two-level quantum model proposed by Preparata, according to which the interaction of a material system with a electromagnetic field can cause the loss of stability of the lower level, is examined. As a result of this instability, the role of the ground state is played by a periodic process generating superradiance (in contrast to laser radiation induced by overpopulation of the upper level). A classical analogue of a super-radiant quantum transition, a system of van der Pol-Duffing oscillators (generators) weakly coupled via a linear oscillator, is for the first time described. Such an analogue is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. It is shown that a necessary condition for the transition to intense energy exchange in the classical system is the instability of one of the nonlinear normal modes, similar to how the condition for a superradiant transition to occur is the instability of the ground state of a two-level quantum system coupled with a resonant electromagnetic field.