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arXiv:1704.01558 · Physical review. B./Physical review. B

Collective two-boson decay of excitons in a Bose-Einstein condensate and generation of coherent photon-phonon radiation

H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, B. R. Avchyan

Published Jul 27, 2017• 1 citation
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Abstract

The collective decay of excitons from initial Bose-Einstein condensate state is investigated theoretically. As a practically more interesting case we consider excitons of the yellow series in the semiconductor cuprous oxide where we have collective photon and phonon-assisted decay of excitons. It is shown that because of intrinsic instability of recoilless two-boson decay of Bose-Einstein condensate, the spontaneously emitted bosonic pairs are amplified, leading to an exponential buildup of a macroscopic population into the certain modes. The collective decay rate has a nonlinear dependence on the excitonic density being comparable or larger than the Auger recombination loss rate up to the high densities, which makes obtainable its observation. The phenomenon considered can also be applied for the realization of a phonon laser.

DOI
10.1103/physrevb.96.045206

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The collective decay of excitons from initial Bose-Einstein condensate state is investigated theoretically. As a practically more interesting case we consider excitons of the yellow series in the semiconductor cuprous oxide where we have collective photon and phonon-assisted decay of excitons. It is shown that because of intrinsic instability of recoilless two-boson decay of Bose-Einstein condensate, the spontaneously emitted bosonic pairs are amplified, leading to an exponential buildup of a macroscopic population into the certain modes. The collective decay rate has a nonlinear dependence on the excitonic density being comparable or larger than the Auger recombination loss rate up to the high densities, which makes obtainable its observation. The phenomenon considered can also be applied for the realization of a phonon laser.
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Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.
Superfluorescence (SF) is the emission from a dense coherent system in population inversion formed from an initially incoherent ensemble. This is characterized by an induction time (${\ensuremath{\tau}}_{\mathrm{D}}$) for the spontaneous development of the macroscopic quantum coherence. Here we report detailed observation of SF on an ultrafast timescale from a quantum ensemble of coherent excitons in highly excited intrinsic-bulk ZnTe single crystal at 5 K, showing a characteristic ${\ensuremath{\tau}}_{\mathrm{D}}$ from 40 ps to 10 ps, quantum noise and fluctuations, and quantum beating and ringing. From this clear observation of SF from a spontaneous coherence of excitons bound to impurities and defect states, we infer that this is indicative of the formation of a spontaneous Bose-Einstein condensation (BEC) of excitons on an ultrafast timescale. The population density and dephasing time (T2{T}_{2}T2​ or T2∗{T}_{2}^{*}T2∗​) of exciton are two controlling factors in the generation of SF from the BEC.
Introduction. Polaritons and Semiconductor Microcavities As we have mentioned previously, BEC of excitons or biexcitons and lasing can be seen as two limits of the same theory. Lasing occurs in the case of strong electron-photon coupling (recombination rate fast compared with interparticle-scattering rate) while excitonic BEC occurs in the case of weak electron-photon coupling (recombination rate slow compared with the interparticle-scattering rate.) A laser can be seen as a Bose condensate in which the long-range phase coherence exists in the photon states [1], while in the exciton condensate the coherence exists in the electronic states. This is one of the reasons for some of the confusing debates in the early history of excitonic Bose condensation – in many systems there is not a sharp distinction between an excitonic condensate and supperradiance, i.e., luminescence with enhanced intensity due to stimulated emission [2-4]. In the previous chapters, we have so far considered a laser light source only as a source of excitons by means of quantum transitions. In Chapter 6, the laser radiation was taken into account as a given external factor. This chapter is dedicated to phenomena related to a strong and noticeable exciton-photon interaction, when the light significantly influences the energy spectrum of the high-density excitons [5-9]. As we will see, this leads to many fascinating effects related to instabilities. A strong exciton-photon interaction implies a strong polariton effect, in which photon and exciton states are mixed (as in Fig. 1.3). When this mixing is strong, it is not obvious how to define the ground state of the system.