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arXiv:1107.5273 · Physical Review B

Observation of superfluorescence from a quantum ensemble of coherent excitons in a ZnTe crystal: Evidence for spontaneous Bose-Einstein condensation of excitons

D. C. Dai, Andrew P. Monkman

Published Sep 19, 2011• 65 citations
arXivHTMLPDF

Abstract

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 (${T}_{2}$ or ${T}_{2}^{*}$) of exciton are two controlling factors in the generation of SF from the BEC.

DOI
10.1103/physrevb.84.115206

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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 (\ensuremathτD{\ensuremath{\tau}}_{\mathrm{D}}\ensuremathτD​) 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 \ensuremathτD{\ensuremath{\tau}}_{\mathrm{D}}\ensuremathτD​ 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.
Superfluorescence (SF) originates from the spontaneous buildup of macroscopic coherence among initially incoherent emitters. Its formation is highly sensitive to dephasing and collective coupling in the system. Here, we observe room-temperature SF in CdS/CdSe/CdS spherical quantum wells. With increasing excitation fluence, the peak emission intensity shows a nearly quadratic increase, while the emission delay and pulse width decrease. Burnham-Chiao ringing is also observed, revealing the characteristic collective radiation dynamics of SF. Further experiments with stripe excitation show that shortening the excitation length L changes the dominant fast emission from amplified spontaneous emission to SF. More importantly, the threshold for SF under stripe excitation is only about 1/30 of that under spot excitation. This large reduction indicates that the propagating radiation field provided by spatially extended excitation favors the buildup of cooperative coherence. These findings provide direct experimental evidence for understanding ultrafast many-body coherence dynamics and offer a route to actively control collective emission at room temperature.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
The collective response of macroscopic quantum states under perturbation is widely used to study quantum correlations and cooperative properties, such as defect-induced quantum vortices in Bose–Einstein condensates and the non-destructive scattering of impurities in superfluids. Superfluorescence (SF), as a collective effect rooted in dipole–dipole cooperation through virtual photon exchange, leads to the macroscopic dipole moment (MDM) in high-density dipole ensembles. However, the perturbation response of the MDM in SF systems remains unknown. Echo-like behavior is observed in a cooperative exciton ensemble under a controllable perturbation, corresponding to an initial collapse followed by a revival of the MDM. Such a dynamic response could refer to a phase transition between the macroscopic coherence regime and the incoherent classical state on a time scale of 10 ps. The echo-like behavior is absent above 100 K due to the instability of MDM in a strongly dephased exciton ensemble. Experimentally, the MDM response to perturbations is shown to be controlled by the amplitude and injection time of the perturbations.
Superfluorescence (SF) is a many-body process in which a macroscopic polarization spontaneously builds up from an initially incoherent ensemble of excited dipoles and then cooperatively decays, producing a delayed pulse of coherent radiation. SF arising from electron-hole recombination has recently been observed in In0.2Ga0.8As/GaAs{\mathrm{In}}_{0.2}{\mathrm{Ga}}_{0.8}\mathrm{As}/\mathrm{GaAs}In0.2​Ga0.8​As/GaAs quantum wells [G. T. Noe et al., Nature Phys. 8, 219 (2012) and J.-H. Kim et al., Sci. Rep. 3, 3283 (2013)], but its observability conditions have not been fully established. Here, by performing magnetic field (B)(B)(B), temperature (T)(T)(T), and pump power (P)(P)(P) dependent studies of SF intensity, linewidth, and delay time through time-integrated and time-resolved magnetophotoluminescence spectroscopy, we have mapped out the $B\ensuremath{-}T\ensuremath{-}P$ region in which SF is observable. In general, SF can be observed only at sufficiently low temperatures, sufficiently high magnetic fields, and sufficiently high laser powers with characteristic threshold behavior. We provide theoretical insights into these behaviors based primarily on considerations on how the growth rate of macroscopic coherence depends on these parameters. These results provide fundamental new insight into electron-hole SF, highlighting the importance of Coulomb interactions among photogenerated carriers as well as various scattering processes that are absent in SF phenomena in atomic and molecular systems.
Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.