Condensation of Semiconductor Microcavity Exciton Polaritons

Deng, Hui; Weihs, Gregor; Santori, Charles; Bloch, J.; Yamamoto, Yoshihisa

doi:10.1126/science.1074464

Cited by 806 publications

(778 citation statements)

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“…1 Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460, Marcoussis, France, 2 LASMEA, Clermont Université, Université Blaise Pascal, CNRS, 24 av des Landais, Aubiere, 63177, France, 3 Departamento de Fisica de Materiales, Universidad Autonoma de Madrid, Madrid 28049, Spain, 4 Institut des NanoSciences de Paris, CNRS UMR 7588, Université P. et M. Curie, Campus Boucicaut, 140 Rue de Lourmel, 75015 Paris, France, 5 Physics and Astronomy School, University of Southampton, Highfield, Southampton SO17 1BJ, UK. *e-mail: jacqueline.bloch@lpn.cnrs.fr.…”

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Spontaneous formation and optical manipulation of extended polariton condensates

et al. 2010

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Cavity exciton-polaritons 1,2 (polaritons) are bosonic quasiparticles offering a unique solid-state system for investigating interacting condensates 3-10 . Up to now, disorder-induced localization and short lifetimes 4,6,11 have prevented the establishment of long-range off-diagonal order 12 needed for any quantum manipulation of the condensate wavefunction. In this work, using a wire microcavity with polariton lifetimes much longer than in previous samples, we show that polariton condensates can propagate over macroscopic distances outside the excitation area, while preserving their spontaneous spatial coherence. An extended condensate wavefunction builds up with a degree of spatial coherence larger than 50% over distances 50 times the polariton de Broglie wavelength. The expansion of the condensate is shown to be governed by the repulsive potential induced by photogenerated excitons within the excitation area. The control of this local potential offers a new and versatile method to manipulate extended polariton condensates. As an illustration, we demonstrate synchronization of extended condensates by controlled tunnel coupling 13,14 and localization of condensates in a trap with optically controlled dimensions.Modern semiconductor technology allows the realization of nanostructures where both electronic and photonic states undergo quantum confinement. In particular in semiconductor microcavities, excitons confined in quantum wells and photons confined in a Fabry-Perot resonator can enter the light-matter strong coupling regime. This gives rise to the formation of cavity polaritons, mixed exciton-photon states that obey bosonic statistics 2 . The polariton dispersion presents a sharp energy minimum close to the states with zero in-plane wave vector (k = 0) with an effective mass m * three orders of magnitude smaller than that of the bare quantum well exciton. Recently, polariton Bose-Einstein condensation 3-10 (BEC) and related effects such as vortices 15,16 or superfluid 17-19 behaviour have been reported at unprecedented high temperatures. As a result of their finite lifetime, cavity polaritons are a model system to investigate dynamical BEC (refs 20,21), also referred to as a polariton laser effect, with a technological control of the resonator geometry and the polariton lifetime. In previously reported polariton laser systems, the cavity lifetime and the photonic disorder prevented the build-up of extended condensates needed for the realization of polariton circuits 22,23 . The measured coherence length ranged at best from 10 to 20 µm (refs 4,6,11,24), a few times the polariton thermal de Broglie wavelength.Here, we report on the spontaneous formation of extended polariton condensates with a spatial coherence extending over 50 times the thermal de Broglie wavelength. These condensates, made of a quantum degenerated light-matter state, are strongly out of equilibrium, thus deeply differing from atomic BEC. Spatial control of such extended condensates is demonstrated, opening the way to a new range of physic...

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Spontaneous formation and optical manipulation of extended polariton condensates

et al. 2010

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“…emergence of spontaneous coherence. Designing semiconductor structures with required characteristics and controlling the parameters of the exciton system gives an opportunity to study various types of exciton condensates.A condensate of exciton-polaritons was recently realized in semiconductor microcavities [9][10][11][12][13]. This condensate is characterized by a strong coupling of excitons to the optical field and a short lifetime of the polaritons.…”

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Spontaneous coherence in a cold exciton gas

High¹,

Leonard²,

Hammack³

et al. 2012

Nature

282

306

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Excitons, bound pairs of electrons and holes, form a model system to explore the quantum physics of cold bosons in solids. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy due to their long lifetimes. Here, we report on the measurement of spontaneous coherence in a gas of indirect excitons. We found that extended spontaneous coherence of excitons emerges in the region of the macroscopically ordered exciton state and in the region of vortices of linear polarization. The coherence length in these regions is much larger than in a classical gas, indicating a coherent state with a much narrower than classical exciton distribution in momentum space, characteristic of a condensate. We also observed phase singularities in the coherent exciton gas. Extended spontaneous coherence and phase singularities emerge when the exciton gas is cooled below a few Kelvin. Spontaneous coherence of excitonsIf bosonic particles are cooled down below the temperature of quantum degeneracy they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis for a number of fundamental phenomena in physics, including superconductivity, superfluidity, and Bose-Einstein condensation (BEC) [1][2][3][4][5]. Spontaneous coherence is the key characteristic of condensation in momentum space [6].Excitons are hydrogen-like bosons at low densities [7] and Cooper-pair-like bosons at high densities [8]. The bosonic nature of excitons allows for condensation in momentum space, i.e. emergence of spontaneous coherence. Designing semiconductor structures with required characteristics and controlling the parameters of the exciton system gives an opportunity to study various types of exciton condensates.A condensate of exciton-polaritons was recently realized in semiconductor microcavities [9][10][11][12][13]. This condensate is characterized by a strong coupling of excitons to the optical field and a short lifetime of the polaritons. Unlike BEC, equilibrium is not required for the polariton condensation and coherence in the polariton condensate forms due to a coherent optical field similar to coherence in lasers [14].There are intriguing theoretical predictions for a range of coherent states in cold exciton systems, including BEC [7], BCS-like condensation [8], charge-density-wave formation [15], and condensation with spontaneous timereversal symmetry breaking [16]. In these condensates, spontaneous coherence of exciton matter waves emerges below the temperature of quantum degeneracy.Since excitons are much lighter than atoms, quantum degeneracy can be achieved in excitonic systems at temperatures orders of magnitude higher than the microKelvin temperatures needed in atomic vapors [1, 2]. Exciton gases need be cooled down to a few Kelvin to enter the quantum regime. Although the temperature of the semiconductor crystal lattice T lat can be lowered well below 1 K in He-refrigerators, lower...

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“…Obviously, atoms aren't the only option for a Email address: ruoshui789@gmail.com (Jian-Jun Zhang) BEC. In recent years, with the development of techniques, the phenomenon of BEC was observed in several physical system [1][2][3][4][5][6][7][8][9], including exciton polaritions, solid-state quasiparticles and so on. We know that photons are the simplest of bosons, so that it would seem that they could in principle undergo this kind of condensation.…”

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Quantum entanglement and phase transition in a two-dimensional photon–photon pair model

Zhang

Yuan

Zhang

et al. 2013

Physica B: Condensed Matter

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We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.

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Condensation of Semiconductor Microcavity Exciton Polaritons

Cited by 806 publications

References 28 publications

Spontaneous formation and optical manipulation of extended polariton condensates

Spontaneous formation and optical manipulation of extended polariton condensates

Spontaneous coherence in a cold exciton gas

Quantum entanglement and phase transition in a two-dimensional photon–photon pair model

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