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

Abstract

Abstract. We investigate theoretically inversionless superradiance of an ensemble of three-level emitters (with Λ-scheme of operating transition), placed in a cyclic cavity. Effects of cavity losses and emitter's relaxation on the dynamics of superradiance are studied.The standard Dicke superradiance (SR) requires an initial population inversion of the operating transition to occur [1]. 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.[2], it has been found that SRWI of an assembly of three-level Λ-emitters in a high-Q cavity shows a rich optical dynamics (from regular to chaotic), depending on the population of the upper level α and splitting of the doublet ω21. These results have been obtained for a Hamiltonian system, i.e. neglecting the cavity losses and relaxation of coherence in the system of emitters. In reality, however, these factors are always present.In this paper, we investigate theoretically the influence of relaxation on the regimes of SRWI found in Ref.[2] (see Ref.[4b] for details). In the Hamiltonian case and at a small doublet splitting, the SRWI dynamics represents a comb of chaotically repeating pulses with a repetition time on the order of the period of oscillations of the low-frequency coherence, 2π/ω21 (see Fig. 1a). Just this regime of SRWI is the goal of our study.1. Cavity losses. This channel of SR relaxation is characterized by the SR lifetime in the cavity Tc. Figure 1b shows an example of the SRWI dynamics for Tc = 50Ω -1 , where Ω is the cooperative frequency introduced by Arecchi and Courtens [4b]; Ω determines the characteristic scale for the SR field and time. As is seen, the effect of cavity losses consists of, first, eliminating that part of the Hamiltonian SR pulse (shown in Fig.1a) which resides at times t > Tc, and second, decreasing the intensity of the remaining part. It should be noticed that the latter retains patterns of the Hamiltonian pulse.