Exciton–polariton condensation
TL;DR: In this article, the authors review the properties of microcavity exciton-polariton condensates and discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical conjectures.
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 sugg...
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01 Jan 1958
TL;DR: In this article, it was shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions).
Abstract: It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.
1,238 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
TL;DR: The results demonstrate the complex decay routes in such hybrid systems and that, contrary to expectations, the lower polariton is intrinsically long-lived.
Abstract: We present a comprehensive experimental study of the photophysical properties of a molecule-cavity system under strong coupling conditions, using steady-state and femtosecond time-resolved emission and absorption techniques to selectively excite the lower and upper polaritons as well as the reservoir of uncoupled molecules. Our results demonstrate the complex decay routes in such hybrid systems and that, contrary to expectations, the lower polariton is intrinsically long-lived.
197 citations
TL;DR: In this article, the authors consider the modelling of polariton graphs using the complex Ginzburg-Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.
Abstract: We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold or to study large scale synchronisation phenomena and dynamical phase transitions when operating above the threshold. We consider the modelling of polariton graphs using the complex Ginzburg-Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.
55 citations
TL;DR: In this paper, a polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates capable of minimising discrete and continuous spin Hamiltonians is proposed.
Abstract: Gain-dissipative systems of various physical origin have recently shown the ability to act as analogue minimisers of hard combinatorial optimisation problems. Whether or not these proposals will lead to any advantage in performance over the classical computations depends on the ability to establish controllable couplings for sufficiently dense short- and long-range interactions between the spins. Here, we propose a polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates capable of minimising discrete and continuous spin Hamiltonians. We elucidate the performance of the proposed computing platform for two types of couplings: relative and absolute. The interactions between the network nodes might be controlled by redirecting the emission between the condensates or by sending the phase information between nodes using resonant excitation. We discuss the conditions under which the proposed machine leads to a pure polariton simulator with pre-programmed couplings or results in a hybrid classical polariton simulator. We argue that the proposed architecture for the remote coupling control offers an improvement over geometrically coupled condensates in both accuracy and stability as well as increases versatility, range and connectivity of spin Hamiltonians that can be simulated with polariton networks.
45 citations
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40,330 citations
"Exciton–polariton condensation" refers background in this paper
...Experiments on extended 1D waveguides appear to suggest a process of relaxation is important, in allowing multimode condensation of modes that have no overlap with the pump spot, but which might couple via intermediate macroscopically occupied states [76,90]....
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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
"Exciton–polariton condensation" refers background or methods in this paper
...As such, increased temporal coherence should be seen by a line narrowing above threshold, which is indeed seen in experiments [60,64]....
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...Such an effect, due to the phase noise induced by interactions between particles, had been anticipated [65,66], but the broadening observed in experiments [60,64] was later found to be due to an extraneous source of noise....
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...Bottom: spatial coherence of CdTe, from [60], showing maps of fringe visibility as a function of displacement between source points on the sample....
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...Adapted from [60], results are for a CdTe microcavity, held at a cryostat temperature of 5 K....
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...In [60,64], a multi-mode pump laser was used, meaning that the intensity of injected polaritons fluctuated in time....
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TL;DR: The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splitting when the quantum wells and the optical cavity are in resonance.
Abstract: The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splitting when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons, and the electromagnetic field of the microcavity. An exciton oscillator strength of 4\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ is deduced for 76-\AA{} quantum wells.
2,006 citations
"Exciton–polariton condensation" refers background in this paper
...[28,29] can be clearly seen experimentally, since the transmission and reflection of the microcavity as a...
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