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arXiv:cond-mat/9808157

Evidence for Stimulated Scattering of Excitons into Microcavity Polaritons

Tassone, F., Robin K. Huang, Y. Yamamoto

Published Aug 14, 1998• 0 citations
arXivHTMLPDF

Abstract

The wavefunction of a collection of identical quantum particles of integer spin (bosons) is even under exchange of the coordinates of any two of them. This symmetrization rule of quantum mechanics leads to stimulation of the scattering rate into final states whose population is larger than one. For massless photons, it is routinely observed in the laser. For massive bosons, most previous efforts concentrated in realizing the largely populated equilibrium Bose-Einstein condensate, and observing stimulated emission into it. Here we show that we do not need to produce such a condensate to observe final state stimulation. Instead, we take advantage of the highly non-equilibrium exciton reservoir and of the large polariton populations produced by external laser action on a semiconductor microcavity, and measure final state stimulation of the scattering rate of these excitons into the polaritons.

DOI
10.48550/arxiv.cond-mat/9808157

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The wavefunction of a collection of identical quantum particles of integer spin (bosons) is even under exchange of the coordinates of any two of them. This symmetrization rule of quantum mechanics leads to stimulation of the scattering rate into final states whose population is larger than one. For massless photons, it is routinely observed in the laser. For massive bosons, most previous efforts concentrated in realizing the largely populated equilibrium Bose-Einstein condensate, and observing stimulated emission into it. Here we show that we do not need to produce such a condensate to observe final state stimulation. Instead, we take advantage of the highly non-equilibrium exciton reservoir and of the large polariton populations produced by external laser action on a semiconductor microcavity, and measure final state stimulation of the scattering rate of these excitons into the polaritons.
Abstract When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g~\tilde{{{{{g}}}}}g~​ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
Summary form only given. Final state stimulation is the origin of amplification in optical lasers and atom lasers. Matter-wave amplification based on an incoherent gain medium has yet to be demonstrated, but is very attractive, particularly for the excitonic system, because electrically injected incoherent excitons can amplify probe excitons without requiring a coherent pump laser. In previous work, we have shown final state stimulation using the exciton-exciton scattering of polaritons in a GaAs based microcavity quantum well; the gain was negligibly small due to the small exciton-exciton scattering rate. However, the rate of exciton-exciton scattering at the exciton saturation density is 9 times larger in CdTe microcavity exciton-polaritons compared to those in GaAs.
A physical mechanism of the implementation of undamped Rabi oscillations in the system of exciton polaritons in a semiconductor microcavity in the presence of nonresonant pumping has been proposed. Various mechanisms of the stimulated scattering of excitons from the reservoir have been considered. It has been shown that undamped oscillations of the population of the photon component of the condensate can be caused by the feeding of a coherent Rabi oscillator owing to the pair scattering of excitons from the reservoir to the ground state. The effect should be observed in spite of a more intense relaxation of polaritons of the upper branch observed experimentally.
Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.
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.
Three-dimensional confinement of microcavity polaritons in a small post structure can be used to produce quasi-discrete polariton modes. For sufficiently small structures, the lowest confined polariton mode becomes well isolated from the other states. We consider the exciton–exciton scattering dynamics in the micropost system, and injection of moderate amount of excitons. We show that exciton–exciton scattering provides sufficient gain to produce stimulated emission of excitons into confined polaritons, well before collapse of the Rabi splitting. We also study the statistical properties of this matter laser, and beside usual Poisson statistics and linewidth reduction above threshold, we also find a linewidth increase very far above threshold, which is peculiar of this system, and shows strong similarities to properties of some proposed atomic laser systems.