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Contemporary Physics

Exciton–polariton condensation

Jonathan Keeling, Natalia G. Berloff

Published Feb 17, 2011• 98 citations
Publisher

Abstract

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.

DOI
10.1080/00107514.2010.550120

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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.
Exciton-polaritons, mixed light-matter quasiparticles in semiconductors, have recently shown evidence for Bose-Einstein condensation. Some of the properties of condensates of exciton-polaritons are reviewed in this article. We first discuss the spontaneous appearance of long-range order and the way this can be easily accessed in the case of polariton fluids. We show that the Penrose-Onsager criterion is valid even for such a very special case of condensate. We then describe the experiments that allow observation of topological defects in the fluid: quantized vortices, half vortices, and hyperbolic spin vortices. We demonstrate through the comparison with the gross Pitaevskii equation that the appearance and stability of such vortices are linked with the dissipative nature of the condensate together with the presence of disorder. We then briefly summarize the experiments on superfluid behavior of the polaritons at large-enough densities and expand somewhat more on the dynamical behavior of turbulence in the wake of an obstacle, with the appearance of vortex streets. We finally show that the Bogoliubov transformation has been revealed through four-wave mixing experiments.
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic phase transition between a photon and a polariton BEC takes place after a single high-power excitation pulse and we find both condensed states in thermal equilibrium with the excited states. At the crossover, photons and polaritons coexist, which results in a decrease in the long-range spatial coherence. Build-up and successive depinning of polarisation is observed at the threshold of both polariton and photon condensation.
Exciton-polariton Bose-Einstein condensates (BECs) are newly emerged quantum systems that are capable of showing macroscopic quantum phenomena with intrinsic open-dissipative nature. The spatial distribution of the polariton density, without any external potential, can be controlled by the geometric shape of the pumping laser, enabling the investigation of polariton dynamics with topologically non-trivial configurations. Meanwhile, exciton-polaritons have spin degrees of freedom inherited from excitons and photons, making it a candidate for the realization of quantum logic gates. In this thesis, we will investigate theoretically the nonlinear dynamics of exciton-polariton BECs involving both polaritons' spatial degrees of freedom and spin degrees of freedom, and interactions between them. This thesis is organised as follows: In Chapter 1, we will present an overall review of exiton-polariton systems and important properties of polariton BECs and then introduce the dynamical equations with various interactions that will serve as the main theoretical tool for subsequent chapters. Several polariton pumping and trapping techniques appearing in later chapters will also be introduced. In Chapter 2, we will investigate the superfluidity properties of a single-component polariton condensate under an incoherent annular pumping configuration. By studying the stability properties of polariton persistent currents, we find that the persistent currents can exhibit dynamical instability and energetic-like instability according to different parameter region. A stability phase diagram will be given and its relation with the Landau's criterion will be discussed. In Chapter 3, we will investigate the spin dynamics of a two-component polariton condensate under a homogeneous pumping configuration. Owing to the Josephson coupling, there exist multiple steady state solutions that allow of controlled spin state switching. A desynchronized region where there exists no stable steady solution is found. In the desynchronized region, a desynchronized state beating periodically over time can exist, which will serve as a building block of spin waves presented in the next chapter. In Chapter 4, by combining results from the previous two chapters we will investigate generally the nonlinear dynamics of polariton condensates under an annular pumping configuration. The spin-orbit interaction provided by the Josephson coupling supports azimuthon states that have simultaneous modulations in both amplitude and phase. The azimuthon states, when viewed in a different polarization basis, form rotating spin waves that can be referred to as the optical ferris wheel. In Chapter 5, results from previous chapters will be extended to micocavities that support the anisotropic TE-TM splitting interaction. Rotating singularities (small-scale vortices) are found as a result. Their properties and experimental observation techniques will be discussed. Chapter 2-5 provide a theoretical framework for the nonlinear dynamics of polariton condensates. They rely mostly on optical trapping techniques and are ready to be tested in experiments. In Chapter 6, polaritons trapped by an engineered periodic mesa potential will be discussed. We will investigate the band structure of polaritons under the influence of the periodic potential together with discussions on the phase-modulated interference pattern which corresponds to the polariton Talbot patterns observed in experiments.
Non-equilibrium polariton condensates entangle properties of lasers, atomic Bose- Einstein condensates (BEC) and semiconductor physics. They provide a great variety of physical phenomena while maintaining a simple theoretical description. Among those phenomena are nonlinear excitations such as solitons or spontaneous spin bifurcations. In this paper I first present a short overview on the theoretical basis of polaritons. Then starting from a scenario of excitation generation in equilibrium BEC I turn to corresponding phenomenona in polariton condensates such as dark soliton formation. Later the spin sensitive phenomena such as nonequilibrium bright solitons and half-bright solitons in semiconductor microcavities are discussed. Theoretically all the considered scenarios are described by partial differential equations (PDEs) and coupled systems thereof. The system of PDEs defines a so called condensate wave function, which completely describes the experimental relevant aspects of the physical system in a certain parameter regime where condensation occurs. The developed theories enables us particularly to make a variety of statements about excitations such as solitons and half-solitons in spinor systems forming within a non-equilibrium condensate. It turns out that by those means we can elucidate in particular the experimental implementation of a coherent superposition analog in a spin sensitive setting forming a macroscopic QUBIT within the semiconductor microcavity at temperatures in the Kelvin range.
In recent years, experiments by several groups have demonstrated spontaneous coherence in polariton systems, which can be viewed as a type of nonequilibrium Bose-Einstein condensation. In these systems, the polariton lifetime is longer than, but not much longer than, the polariton-polariton scattering time which leads to the thermalization. By contrast, over the past twenty years several groups have pursued experiments in a different system, which has very long exciton lifetime, up to 30 microseconds or more, essentially infinite compared to the thermalization time of the excitons. Thermal equilibrium of this type of exciton in a trap has been demonstrated experimentally. In this system, the interactions between the excitons are not short-range contact interactions, but instead are dipole-dipole interactions, with the force at long range going as 1/r31/r^{3}1/r3. Up to now there has not been a universally accepted demonstration of BEC in this type of system, and the way forward will require better understanding of the many-body effects of the excitons. I review what has been learned and accomplished in the past two decades in the search for an equilibrium BEC in this promising system.
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.