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Physical Review

Bose-Einstein Condensation of Excitons

John M. Blatt, Karl W. Böer, Werner Brandt

Published Jun 1, 1962• 430 citations
Publisher

Abstract

This note discusses the question as to whether quasi-particles, such as excitons, i.e., nonlocalized excited states of solids, can fulfill necessary conditions for a Bose-Einstein condensation, and whether such condensation can be observed. Although uncertainties of present data on excitons preclude precise numerical predictions, it is concluded that under certain experimentally attainable circumstances excitons fulfill the necessary conditions, i.e., condensation is possible. Ways of detecting the condensation are considered, and a specific experiment is proposed.

DOI
10.1103/physrev.126.1691

Related papers

Bose-Einstein Condensation of Excitons and Biexcitons

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Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.

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The case of excitons as candidates for Bose–Einstein condensation is discussed, and experimental results in CuCl and Cu 2 O are presented. In CuCl, spectral analysis of the luminescence from biexcitons as a function of their density reveals a gradual evolution from classical statistics towards a quantum degenerate regime. The appearance of a sharp emission line below a critical temperature and above a critical density is attributed to the presence of a laser-induced Bose–Einstein condensate of excitonic molecules. This interpretation is supported by pump-probe experiments which show that additional particles injected in the presence of a biexciton condensate are drawn into it. In Cu 2 O, free exciton luminescence spectral analysis of ortho- and paraexcitons reveals a gradual evolution from a classical to a Bose quantum degenerate regime with increasing particle densities. Orthoexciton densities close to the critical density for condensation are obtained at high incoherent excitation. Under similar pumping, paraexciton densities exceeding the critical value are inferred from luminescence intensity ratios. Anomalous transport properties of paraexcitons, such as ballistic propagation over macroscopic distances and formation of soliton-like excitonic packets are discussed as evidence for excitonic superfluidity. Introduction Excitons The lowest electronically excited state of a non-metallic crystal corresponds to the promotion of one electron from the top of the highest fully occupied valence band to the bottom of the next empty conduction band. A correct evaluation of the required energy must include the Coulomb correlation between the promoted electron and all other electrons left behind in the valence band.

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Exciton–polariton condensation

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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.

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Abstract The original Bose–Einstein condensation (BEC) was theoretically established in the 1920s, for the case of an ideal gas of boson particles (a consequence of the symmetry of the wave function). In the 1990s, it was realized in systems of atomic alkali gases. At the beginning of the 21st century, investigators considered its emergence in solid‐state matter, and a BEC‐like phenomenon was observed in the case of bosonic quasiparticles (elementary excitations in solids). Both types of BEC can occur in a condensation in conditions of thermodynamic equilibrium. A third type of what has been dubbed a BEC in non‐equilibrium conditions can occur in systems of bosonic quasiparticles (phonons, magnons, excitons); this phenomenon (which can be considered as cases of systems with complex behavior) follows after a certain threshold of intensity of an external pumping source is achieved. In this review, after brief comments on the two types of BEC in equilibrium, a description is presented on how a BEC‐like phenomenon arises in systems of quasiparticles that are driven away from thermodynamic equilibrium, and several examples are described. This description is given within a unique theoretical framework, and a comparison with experimental results is performed; in addition, the possible technological applications are outlined.

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EXCITONS AS A NEW QUANTUM SYSTEM

A. Mysyrowicz

In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.

Le Journal de Physique Colloques•Jul 1, 1980•11 citations
This note discusses the question as to whether quasi-particles, such as excitons, i.e., nonlocalized excited states of solids, can fulfill necessary conditions for a Bose-Einstein condensation, and whether such condensation can be observed. Although uncertainties of present data on excitons preclude precise numerical predictions, it is concluded that under certain experimentally attainable circumstances excitons fulfill the necessary conditions, i.e., condensation is possible. Ways of detecting the condensation are considered, and a specific experiment is proposed.
Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.
The case of excitons as candidates for Bose–Einstein condensation is discussed, and experimental results in CuCl and Cu 2 O are presented. In CuCl, spectral analysis of the luminescence from biexcitons as a function of their density reveals a gradual evolution from classical statistics towards a quantum degenerate regime. The appearance of a sharp emission line below a critical temperature and above a critical density is attributed to the presence of a laser-induced Bose–Einstein condensate of excitonic molecules. This interpretation is supported by pump-probe experiments which show that additional particles injected in the presence of a biexciton condensate are drawn into it. In Cu 2 O, free exciton luminescence spectral analysis of ortho- and paraexcitons reveals a gradual evolution from a classical to a Bose quantum degenerate regime with increasing particle densities. Orthoexciton densities close to the critical density for condensation are obtained at high incoherent excitation. Under similar pumping, paraexciton densities exceeding the critical value are inferred from luminescence intensity ratios. Anomalous transport properties of paraexcitons, such as ballistic propagation over macroscopic distances and formation of soliton-like excitonic packets are discussed as evidence for excitonic superfluidity. Introduction Excitons The lowest electronically excited state of a non-metallic crystal corresponds to the promotion of one electron from the top of the highest fully occupied valence band to the bottom of the next empty conduction band. A correct evaluation of the required energy must include the Coulomb correlation between the promoted electron and all other electrons left behind in the valence band.
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.
Abstract The original Bose–Einstein condensation (BEC) was theoretically established in the 1920s, for the case of an ideal gas of boson particles (a consequence of the symmetry of the wave function). In the 1990s, it was realized in systems of atomic alkali gases. At the beginning of the 21st century, investigators considered its emergence in solid‐state matter, and a BEC‐like phenomenon was observed in the case of bosonic quasiparticles (elementary excitations in solids). Both types of BEC can occur in a condensation in conditions of thermodynamic equilibrium. A third type of what has been dubbed a BEC in non‐equilibrium conditions can occur in systems of bosonic quasiparticles (phonons, magnons, excitons); this phenomenon (which can be considered as cases of systems with complex behavior) follows after a certain threshold of intensity of an external pumping source is achieved. In this review, after brief comments on the two types of BEC in equilibrium, a description is presented on how a BEC‐like phenomenon arises in systems of quasiparticles that are driven away from thermodynamic equilibrium, and several examples are described. This description is given within a unique theoretical framework, and a comparison with experimental results is performed; in addition, the possible technological applications are outlined.
In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.