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.
The general expression of the output-light Mandel parameter out 5 obtained in case of purely absorptive bistability, for arbitrary value of of incident light (theparameter measures the deviation of the photon-flow statistics from Poisson statistics). Calculations are based on stochastic rate equations. No adiabatic elimination of atomic variables is made; the coherent nature of "incoming" of incident photons into a cavity is correctly taken into account. On condition of bistability, although the strongly sub-Poisson input-photon statistics ( = -1) generally reduces the output noise as compared to the case of coherent input ( = 0), the inequality tout > 0 still holds near the switching points.
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