Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems

Abstract

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.

Interaction of subsystems in nonlinear dynamics problems. Various phases of chaos

“…Among them of special interest are: 2D supercrystals of semiconductor quantum dots (Evers et al 2013) and super crystals synthesized on the basis of aromatic 2D polymers (Liu et al 2017). To date, the optical properties of these objects, especially nonlinear ones, including chaotic dynamics, are a promising and little-studied avenue of research (Ryzhov et al 2017;2021). In these nonlinear dynamical systems, under conditions of a degenerate doublet state, the problem can be reduced (if there are appropriate conservation laws) to the Duffing equation.…”