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Nature Communications

Single-shot condensation of exciton polaritons and the hole burning effect

Eliezer Estrecho, Tingge Gao, Nataliya Bobrovska, M. D. Fraser, Mark Steger, Loren N. Pfeiffer, K. W. West, T. C. H. Liew, Michał Matuszewski, D. W. Snoke, Andrew G. Truscott, Elena A. Ostrovskaya

Published Jul 23, 2018• 62 citations
Publisher

Abstract

A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.

DOI
10.1038/s41467-018-05349-4

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A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.
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.
Development of spontaneous coherence is one of the hallmarks of bosonic condensation in a variety of physical systems, such as cold atoms, confined photons, and hybrid light-matter quasiparticles like exciton polaritons in semiconductors. While spatial coherence is well understood once a steady-state condensate has been established, its temporal evolution as the condensate forms is largely unexplored. Here, we explore the dynamical formation of a non-equilibrium, driven-dissipative exciton-polariton condensate through both time-resolved experiments and numerical modeling. Our study reveals that the spatial coherence is established through two distinct stages. The early-time stage is interaction-driven and features transient oscillations in spatial coherence. This stage is followed by a steady-state regime characterized by a spatially-uniform high degree of coherence that extends over the entire size of the system and persists over time. These stages of spatial coherence development occur in both free flowing and confined exciton-polariton systems that undergo a quench - rapid growth of the condensate starting from two different initial settings. Our study offers a deep insight into the process by which long-range spatial coherence is established in a non-equilibrium bosonic condensate.
Condensation of bosons causes spectacular phenomena such as superfluidity or superconductivity. Understanding the nature of the condensed particles is crucial for active control of such quantum phases. Fascinating possibilities emerge from condensates of light–matter-coupled excitations, such as exciton–polaritons, photons hybridized with hydrogen-like bound electron–hole pairs. So far, only the photon component has been resolved, while even the mere existence of excitons in the condensed regime has been challenged. Here we trace the matter component of polariton condensates by monitoring intra-excitonic terahertz transitions. We study how a reservoir of optically dark excitons forms and feeds the degenerate state. Unlike atomic gases, the atom-like transition in excitons is dramatically renormalized on macroscopic ground state population. Our results establish fundamental differences between polariton condensation and photon lasing and open possibilities for coherent control of condensates. Exciton–polaritons are bosonic quasi-particles resulting from strong coupling of excitons and photons but so far only their photon component had been resolved. Here, Menard et al. monitor the intra-excitonic transitions and study how a reservoir of optically dark excitons forms and feeds the degenerate state.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal-equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.