Bose-Einstein Condensation of Microcavity Polaritons in a Trap
18 May 2007-Science (American Association for the Advancement of Science)-Vol. 316, Iss: 5827, pp 1007-1010
TL;DR: Polaritons are created in a harmonic potential trap analogous to atoms in optical traps and observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission.
Abstract: We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.
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TL;DR: In this paper, a review of recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems is presented, from the superfluid flow around a defect at low speeds to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles.
Abstract: This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.
1,469 citations
TL;DR: In this article, the authors reviewed recent experiments and corresponding theoretical pictures based on the Gross-Pitaevskii equations and the Boltzmann kinetic simulations for a finite-size BEC of polaritons.
Abstract: In the past decade, a two-dimensional matter-light system called the microcavity exciton-polariton has emerged as a new promising candidate of Bose-Einstein condensation BEC in solids. Many pieces of important evidence of polariton BEC have been established recently in GaAs and CdTe microcavities at the liquid helium temperature, opening a door to rich many-body physics inaccessible in experiments before. Technological progress also made polariton BEC at room temperatures promising. In parallel with experimental progresses, theoretical frameworks and numerical simulations are developed, and our understanding of the system has greatly advanced. In this article, recent experiments and corresponding theoretical pictures based on the Gross-Pitaevskii equations and the Boltzmann kinetic simulations for a finite-size BEC of polaritons are reviewed.
1,110 citations
TL;DR: In this article, the existence of superfluidity in polaritons is investigated in terms of the Landau criterion and manifests itself as the suppression of scattering from defects when the flow velocity is slower than the speed of sound in the fluid.
Abstract: Similar to atoms in cold gases, exciton–polaritons in semiconductor microcavities can undergo Bose–Einstein condensation. A striking consequence of the appearance of macroscopic coherence in these systems is superfluidity. Now, clear evidence for such behaviour has been found in an exciton–polariton condensate. Superfluidity, the ability of a quantum fluid to flow without friction, is one of the most spectacular phenomena occurring in degenerate gases of interacting bosons. Since its first discovery in liquid helium-4 (refs 1, 2), superfluidity has been observed in quite different systems, and recent experiments with ultracold trapped atoms have explored the subtle links between superfluidity and Bose–Einstein condensation3,4,5. In solid-state systems, it has been anticipated that exciton–polaritons in semiconductor microcavities should behave as an unusual quantum fluid6,7,8, with unique properties stemming from its intrinsically non-equilibrium nature. This has stimulated the quest for an experimental demonstration of superfluidity effects in polariton systems9,10,11,12,13. Here, we report clear evidence for superfluid motion of polaritons. Superfluidity is investigated in terms of the Landau criterion and manifests itself as the suppression of scattering from defects when the flow velocity is slower than the speed of sound in the fluid. Moreover, a Cerenkov-like wake pattern is observed when the flow velocity exceeds the speed of sound. The experimental findings are in quantitative agreement with predictions based on a generalized Gross–Pitaevskii theory12,13, and establish microcavity polaritons as a system for exploring the rich physics of non-equilibrium quantum fluids.
820 citations
TL;DR: The observation of a Bose–Einstein condensate of photons is reported, formally equivalent to a two-dimensional gas of trapped, massive bosons, in a dye-filled optical microcavity which acts as a ‘white-wall’ box.
Abstract: Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. Martin Weitz and colleagues have now realized such conditions experimentally, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources. Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. These authors experimentally realise such conditions, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources. Bose–Einstein condensation (BEC)—the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density—has been observed in several physical systems1,2,3,4,5,6,7,8,9, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied10; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons11 or photon–photon scattering in a nonlinear resonator configuration12,13. Number-conserving thermalization was experimentally observed14 for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a ‘white-wall’ box. Here we report the observation of a Bose–Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose–Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases9 and new coherent ultraviolet sources15.
666 citations
TL;DR: A review of the physical properties of exciton-polariton condensates can be found in this article, where the authors examine topics such as the difference between polariton BEC, a polariton laser and a photon laser.
Abstract: Recently a new type of system exhibiting spontaneous coherence has emerged—the exciton–polariton condensate. Exciton–polaritons (or polaritons for short) are bosonic quasiparticles that exist inside semiconductor microcavities, consisting of a superposition of an exciton and a cavity photon. Above a threshold density the polaritons macroscopically occupy the same quantum state, forming a condensate. The polaritons have a lifetime that is typically comparable to or shorter than thermalization times, giving them an inherently non-equilibrium nature. Nevertheless, they exhibit many of the features that would be expected of equilibrium Bose–Einstein condensates (BECs). The non-equilibrium nature of the system raises fundamental questions as to what it means for a system to be a BEC, and introduces new physics beyond that seen in other macroscopically coherent systems. In this review we focus on several physical phenomena exhibited by exciton–polariton condensates. In particular, we examine topics such as the difference between a polariton BEC, a polariton laser and a photon laser, as well as physical phenomena such as superfluidity, vortex formation, and Berezinskii–Kosterlitz–Thouless and Bardeen–Cooper–Schrieffer physics. We also discuss the physics and applications of engineered polariton structures. Exciton–polaritons, resulting from the light–matter coupling between an exciton and a photon in a cavity, form Bose–Einstein-like condensates above a critical density. Various aspects of the physics of exciton–polariton condensates are now reviewed.
568 citations
References
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TL;DR: The Bose-Einstein condensation (BEC) phenomenon was first introduced by Bose as discussed by the authors, who derived the Planck law for black-body radiation by treating the photons as a gas of identical particles.
Abstract: In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for "bosons" – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
3,298 citations
TL;DR: A comprehensive set of experiments giving compelling evidence for BEC of polaritons of bosonic quasi-particles are detailed, which indicate the spontaneous onset of a macroscopic quantum phase.
Abstract: Phase transitions to quantum condensed phases—such as Bose–Einstein condensation (BEC), superfluidity, and superconductivity—have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 109 times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase. Bose–Einstein condensation (BEC), a form of matter first postulated in 1924, has famously been demonstrated in dilute atomic gases at ultra-low temperatures. Much effort is now being devoted to exploring solid-state systems in which BEC can occur. In theory semiconductor microcavities, where photons are confined and coupled to electronic excitations leading to the creation of polaritons, could allow BEC at standard cryogenic temperatures. Kasprzak et al. now present experiments in which polaritons are excited in such a microcavity. Above a critical polariton density, spontaneous onset of a macroscopic quantum phase occurs, indicating a solid-state BEC. BEC should also be possible at higher temperatures if coupling of light with solid excitations is sufficiently strong. Demokritov et al. have achieved just that, BEC at room temperature in a gas of magnons, which are a type of magnetic excitation. This paper presents a comprehensive set of experiments in which polaritons are excited in a semiconductor microcavity. Above a critical density of polaritons, massive occupation of the ground state at 19 K is observed and various pieces of experimental evidence point to a spontaneous onset of a macroscopic quantum phase.
2,527 citations
TL;DR: A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function.
Abstract: A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.
759 citations
TL;DR: A series of experimental studies of a polariton laser are presented, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure, finding its properties are similar to those of a normal photon laser.
Abstract: Nearly one decade after the first observation of Bose–Einstein condensation in atom vapors and realization of matter-wave (atom) lasers, similar concepts have been demonstrated recently for polaritons: half-matter, half-light quasiparticles in semiconductor microcavities. The half-light nature of polaritons makes polariton lasers promising as a new source of coherent and nonclassical light with extremely low threshold energy. The half-matter nature makes polariton lasers a unique test bed for many-body theories and cavity quantum electrodynamics. In this article, we present a series of experimental studies of a polariton laser, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure. The polaritons have an effective mass that is twice the cavity photon effective mass, yet seven orders of magnitude less than the hydrogen atom mass; hence, they can potentially condense at temperatures seven orders of magnitude higher than those required for atom Bose–Einstein condensations. Accompanying the phase transition, a polariton laser emits coherent light but at a threshold carrier density two orders of magnitude lower than that needed for a normal photon laser in a same structure. It also is shown that, beyond threshold, the polariton population splits to a thermal equilibrium Bose–Einstein distribution at in-plane wave number k∥ > 0 and a nonequilibrium condensate at k∥ > 0, with a chemical potential approaching to zero. The spatial distributions and polarization characteristics of polaritons also are discussed as unique signatures of a polariton laser.
380 citations
TL;DR: A massive redistribution of the polariton occupancy to two specific wave vectors, zero and approximately 3.9x10(4) cm(-1), is observed under conditions of continuous wave excitation of a semiconductor microcavity.
Abstract: A massive redistribution of the polariton occupancy to two specific wave vectors is observed under conditions of continuous wave excitation of a semiconductor microcavity.
The “condensation” of the polaritons to the two specific states arises from stimulated scattering at final
state occupancies of order unity. The stimulation phenomena, arising due to the bosonic character of
the polariton quasiparticles, occur for conditions of resonant excitation of the lower polariton branch.
High energy nonresonant excitation, as in most previous work, instead leads to conventional lasing in
the vertical cavity structure.
363 citations