Superradiance of three-level optical systems with a doublet in the ground state ( -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 (). 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 ( ) 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 twolevel 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.
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