Abstract

Bose–Einstein condensates (BECs), the “fifth state of matter,” have in fact been discovered by chance both in liquid helium and in superconductors. Since these early encounters, BECs have been sought for, both in atom vapors and in solids. Here we report on the case of exciton polaritons. We discuss the experimental observation of macroscopically occupied polariton states and their possible attribution to a BEC. We also discuss the possible relation between a polariton condensate, a polariton laser, and a vertical surface-emitting laser (VCSEL). Vortices, superfluidity, Bogoliubov dispersion, half-vortices, and Josephson oscillations are then briefly summarized merrily for sake of discussion of the distinction between a polariton BEC and a VCSEL.

© 2012 Optical Society of America

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2011 (3)

M. Aßmann, J.-S. Tempel, F. Veit, M. Bayer, A. Rahimi-Iman, A. Löffler, S. Höfling, S. Reitzenstein, L. Worschech, and A. Forchel, “From polariton condensates to highly photonic quantum degenerate states of bosonic matter,” Proc. Natl. Acad. Sci. USA 108, 1804–1809 (2011).
[CrossRef]

S. Azzini, D. Gerace, M. Galli, I. Sagnes, R. Braive, A. Lemaître, J. Bloch, and D. Bajoni, “Ultra-low threshold polariton lasing in photonic crystal cavities,” Appl. Phys. Lett. 99, 111106 (2011).
[CrossRef]

V. Kohnle, Y. Léger, M. Wouters, M. Richard, M. T. Portela-Oberli, and B. Deveaud-Plédran, “From single particle to superfluid excitations in a dissipative polariton gas,” Phys. Rev. Lett. 106, 255302 (2011).
[CrossRef]

2010 (4)

D. Sanvitto, S. Pigeon, A. Amo, D. Ballarini, M. De Giorgi, I. Carusotto, R. Hivet, F. Pisanello, V. G. Sala, P. S. S. Guimaraes, R. Houdré, E. Giacobino, C. Ciuti, A. Bramati, and G. Gigli, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

K. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent oscillations in an exciton-polariton Josephson junction,” Phys. Rev. Lett. 105, 120403 (2010).
[CrossRef]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6, 860–864 (2010).
[CrossRef]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6, 860–864 (2010).
[CrossRef]

2009 (8)

E. Wertz, L. Ferrier, D. D. Solnyshkov, P. Senellart, D. Bajoni, A. Miard, A. Lemaître, G. Malpuech, and J. Bloch, “Spontaneous formation of a polariton condensate in a planar GaAs microcavity,” Appl. Phys. Lett. 95, 051108 (2009).
[CrossRef]

N. G. Vy, H. T. Cao, D. B. Tran Thoai, and H. Haug, “Time dependence of the ground-state population statistics of condensed microcavity polaritons,” Phys. Rev. B80, 195306 (2009).

D. Sarchi, M. Wouters, and V. Savona, “Polariton parametric photoluminescence in spatially inhomogeneous systems,” Phys. Rev., B79, 165315 (2009).

B. Nelsen, R. Balili, D. W. Snoke, L. Pfeiffer, and K. West, “Lasing and polariton condensation: two distinct transitions in GaAs microcavities with stress traps,” J. Appl. Phys. 105, 122414 (2009).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussi, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[CrossRef]

D. Semkat, W.-D. Kraeft, G. Manzke, D. Krempe, and K. Henneberger, “Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation,” Phys. Rev. B81, 155201 (2009).

K. Lagoudakis, T. Ostatnick, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef]

A. Amo, J. Lefrére, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nature 457, 291–295 (2009).
[CrossRef]

2008 (9)

K. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton–polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

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Solid State Commun. (2)

S. A. Moskalenko, “Reversible optico-hydrodynamic phenomena in a nonideal. exciton gas,” Solid State Commun. 4, 199–204 (1962).

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[CrossRef]

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Z. Phys. D (1)

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[CrossRef]

Other (5)

S. A. Moskalenko and D. W. Snoke, eds. Bose-Einstein Condensation of Excitons and Biexcitons and Coherent Nonlinear Optics with Excitons (Cambridge University, 2000).

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L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, 2003).

M. Richard,“Quasi-condensation de polaritons sous excitation incoherente dans les microcavities II-VI a base de CdTe,” PhD thesis (Université Joseph Fourier—Genoble 1, 2004).

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Figures (4)

Fig. 1.
Fig. 1.

In-plane dispersion of polaritons for different detunings between the photon mode and the exciton resonance. Left, negative detuning, the photon mode is 10 meV below the exciton resonance; middle, zero detuning; right, the photon mode is 10 meV above the exciton resonance (reproduced from [46] with the agreement of the author).

Fig. 2.
Fig. 2.

Spatial ordering of the polariton condensate. Below the threshold (0.3 Pth), the coherence is limited to the de Broglie wavelength of the polaritons. Above the threshold (1.9 Pth), significant correlations, disturbed by disorder, are observed up to the limits of the excitation spot.

Fig. 3.
Fig. 3.

(a) Results of theoretical simulation showing the amplitude of the condensate in the presence of disorder. Black arrows measure the polariton flow that is obtained from the phase of the condensate shown in (b) as k=φ (reproduced from [56] with the agreement of the author).

Fig. 4.
Fig. 4.

Interference fringes observed with the polarization resolved interferometer. On the left of the image appears the sigma 1 polarization and on the right, the sigma–. Dislocations forks are clearly observed (red and blue circles) in the left part of the image, but do not have a counterpart on the right side. These correspond to half-vortices.

Equations (1)

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Tc=2π2m(n2.612L3).

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