Cooperative Emission from an Ensemble of Three-Level Λ Radiators in a Cavity: An Insight from the Viewpoint of Dynamics of Nonlinear Systems

Igor V. Ryzhov, Nikolai N. Vasil'ev, Irina S. Kosova, Maria D. Shtager, V.A. Malyshev

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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 (ℝ11 → ℝ5) 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.
Original languageEnglish
Pages (from-to)683-700
Number of pages18
JournalJournal of Experimental and Theoretical Physics
Issue number5
Publication statusPublished - May-2017

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