Inversionless Superradiance and the Duffing Model

Abstract

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

“…It can be seen from Fig. 4 that for the initial population α = 1 of the third level, the Poincaré maps are closed curves that never pass through the origin (separatrix) [45]. The fact that the curves in Poincaré maps are closed indicates quasi-periodicity of the given motion or the motion of the representative point over the surfaces of two five-dimensional tori, lying in the left (right) cavity of the dumbbell.…”

“…Our attention is mainly focused on analysis of the system with a nondegenerate doublet. The case with a degenerate doublet was investigated in detail in our previous publication [45]. We derive the equation for the SR field strength, which determines the stationary points of the system in the ℝ 5 phase space.…”

“…It should be noted that the dimension of the phase space in the case of a degenerate doublet (δ = 0) is ℝ 2 [45]. Even an infinitesimal splitting of the doublet transforms its dimension stepwise from ℝ 2 to ℝ 5 and is responsible for a complex behavior of the system's representative point in the phase space ( , ξ, ζ, η, χ) (see Fig.…”

“…It is well known that the necessary condition for SR [1] to occur is the existence of initial population inversion of the transition levels [2][3][4][5][6][34][35][36][37][38][39]. In the case of multilevel emitters (in particular, three level atoms with the Λ scheme of operating transitions considered here), this limitation is not necessary: SR is possible even when the initial population of the upper level is smaller than the population of the doublet (inversionless SR) [40][41][42][43][44][45][46][47][48][49][50]. A prototype of SR without the population inversion is the inversionless gain predicted for the first time in [51][52][53] (see also a review [54]).…”

Superradiance without inversion in a cavity: Effects of cavity losses and relaxation in the system of emitters

“…In the case of multilevel emitters (in particular, three-level atoms with the Λ-scheme of operating transitions considered here), this limitation is not crucial anymore: SR is possible even if the initial population of the upper level is smaller than the population of the doublet (SR without inversion, SRWI) [2][3][4]. In Ref.…”