Inversionless Superradiance and the Duffing Model

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 (R¹¹→R⁵). 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 (R⁵→R²) 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.