Bose–Einstein condensation of polaritons

Bose–Einstein condensation of polaritons is a growing field in semiconductor optics research, which exhibits spontaneous coherence similar to a laser, but through a different mechanism. A continuous transition from polariton condensation to lasing can be made similar to that of the crossover from a Bose–Einstein condensate to a BCS state in the context of Fermi gases.[1][2] Polariton condensation is sometimes called “lasing without inversion”.[3][4]

Overview

Polaritons are bosonic quasiparticles which can be thought of as dressed photons. In an optical cavity, photons have an effective mass, and when the optical resonance in a cavity is brought near in energy to an electronic resonance (typically an exciton) in a medium inside the cavity, the photons become strongly interacting, and repel each other. They therefore act like atoms which can approach equilibrium due to their collisions with each other, and can undergo Bose-Einstein condensation (BEC) at high density or low temperature. The Bose condensate of polaritons then emits coherent light like a laser. Because the mechanism for the onset of coherence is the interactions between the polaritons, and not the optical gain that comes from inversion, the threshold density can be quite low.

History

The theory of polariton BEC was first proposed by Atac Imamoglu[5] and coauthors including Yoshihisa Yamamoto. These authors claimed observation of this effect in a subsequent paper,[6] but this was eventually shown to be standard lasing.[7][8] In later work in collaboration with the research group of Jacqueline Bloch, the structure was redesigned to include several quantum wells inside the cavity to prevent saturation of the exciton resonance, and in 2002 evidence for nonequilibrium condensation was reported[9] which included photon-photon correlations consistent with spontaneous coherence. Later experimental groups have used essentially the same design. In 2006, the group of Benoit Deveaud and coauthors reported the first widely accepted claim of nonequilibrium Bose–Einstein condensation of polaritons[10] based on measurement of the momentum distribution of the polaritons. Although the system was not in equilibrium, a clear peak in the ground state of the system was seen, a canonical prediction of BEC. Both of these experiments created a polariton gas in an uncontrolled free expansion. In 2007, the experimental group of David Snoke demonstrated nonequilibrium Bose–Einstein condensation of polaritons in a trap,[11] similar to the way atoms are confined in traps for Bose–Einstein condensation experiments. The observation of polariton condensation in a trap was significant because the polaritons were displaced from the laser excitation spot, so that the effect could not be attributed to a simple nonlinear effect of the laser light. Jaqueline Bloch and coworkers observed polariton condensation in 2009,[12] after which many other experimentalists reproduced the effect (for reviews see the bibliography). Evidence for polariton superfluidity was reported in by Alberto Amo and coworkers,[13] based on the suppressed scattering of the polaritons during their motion. This effect has been seen more recently at room temperature,[14] which is the first evidence of room temperature superfluidity, albeit in a highly nonequilibrium system.

Equilibrium polariton condensation

The first clear demonstration of Bose–Einstein condensation of polaritons in equilibrium[15] was reported by a collaboration of David Snoke, Keith Nelson, and coworkers, using high quality structures fabricated by Loren Pfeiffer and Ken West at Princeton. Prior to this result, polariton condensates were always observed out of equilibrium.[16][17] All of the above studies used optical pumping to create the condensate. Electrical injection, which enables a polariton laser which could be a practical device, was shown in 2013 by two groups.[18][19]

Nonequilibrium condensation

Polariton condensates are an example, and the most well studied example, of Bose-Einstein condensation of quasiparticles. Because most of the experimental work on polariton condensates used structures with very short polariton lifetime, a large body of theory has addressed the properties of nonequilibrium condensation and superfluidity. In particular, Jonathan Keeling[20] and Iacopo Carusotto and C. Ciuti [21] have shown that although a condensate with dissipation is not a “true” superfluid, it still has a critical velocity for onset of superfluid effects.

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See also
  • Bose-Einstein condensation of quasiparticles

References
  1. Universal Themes of Bose-Einstein Condensation, published by Cambridge University Press (2017). ISBN 978-1107085695, ISBN 1107085691 This book reviews much of the work on polariton condensation, and compares and contrasts these condensates to atomic condensates.
  2. Deng, Hui; Haug, Hartmut; Yamamoto, Yoshihisa (2010-05-12). "Exciton-polariton Bose-Einstein condensation". Reviews of Modern Physics. American Physical Society (APS). 82 (2): 1489–1537. doi:10.1103/revmodphys.82.1489. ISSN 0034-6861.
  3. Carusotto, Iacopo; Ciuti, Cristiano (2013-02-21). "Quantum fluids of light". Reviews of Modern Physics. American Physical Society (APS). 85 (1): 299–366. arXiv:1205.6500. doi:10.1103/revmodphys.85.299. ISSN 0034-6861.
  4. D. Snoke and J. Keeling, “Polariton condensates come of age,” Physics Today, in press.
  5. Imamog¯lu, A.; Ram, R. J.; Pau, S.; Yamamoto, Y. (1996-06-01). "Nonequilibrium condensates and lasers without inversion: Exciton-polariton lasers". Physical Review A. American Physical Society (APS). 53 (6): 4250–4253. doi:10.1103/physreva.53.4250. ISSN 1050-2947.
  6. Pau, Stanley; Cao, Hui; Jacobson, Joseph; Björk, Gunnar; Yamamoto, Yoshihisa; Imamoğlu, Atac (1996-09-01). "Observation of a laserlike transition in a microcavity exciton polariton system". Physical Review A. American Physical Society (APS). 54 (3): R1789–R1792. doi:10.1103/physreva.54.r1789. ISSN 1050-2947.
  7. Kira, M.; Jahnke, F.; Koch, S. W.; Berger, J. D.; Wick, D. V.; Nelson, T. R.; Khitrova, G.; Gibbs, H. M. (1997-12-22). "Quantum Theory of Nonlinear Semiconductor Microcavity Luminescence Explaining "Boser" Experiments". Physical Review Letters. American Physical Society (APS). 79 (25): 5170–5173. doi:10.1103/physrevlett.79.5170. ISSN 0031-9007.
  8. Cao, H.; Pau, S.; Jacobson, J. M.; Björk, G.; Yamamoto, Y.; Imamŏglu, A. (1997-06-01). "Transition from a microcavity exciton polariton to a photon laser". Physical Review A. American Physical Society (APS). 55 (6): 4632–4635. doi:10.1103/physreva.55.4632. ISSN 1050-2947.
  9. Deng, Hui; Weihs, Gregor; Santori, Charles; Bloch, Jacqueline; Yamamoto, Yoshihisa (2002-10-04). "Condensation of Semiconductor Microcavity Exciton Polaritons". Science. American Association for the Advancement of Science (AAAS). 298 (5591): 199–202. doi:10.1126/science.1074464. ISSN 0036-8075.
  10. Kasprzak, J.; Richard, M.; Kundermann, S.; Baas, A.; Jeambrun, P.; et al. (2006). "Bose–Einstein condensation of exciton polaritons". Nature. Springer Science and Business Media LLC. 443 (7110): 409–414. doi:10.1038/nature05131. ISSN 0028-0836.
  11. Balili, R.; Hartwell, V.; Snoke, D.; Pfeiffer, L.; West, K. (2007-05-18). "Bose-Einstein Condensation of Microcavity Polaritons in a Trap". Science. American Association for the Advancement of Science (AAAS). 316 (5827): 1007–1010. Bibcode:2007Sci...316.1007B. doi:10.1126/science.1140990. ISSN 0036-8075. PMID 17510360.
  12. Wertz, Esther; Ferrier, Lydie; Solnyshkov, Dmitry D.; Senellart, Pascale; Bajoni, Daniele; Miard, Audrey; Lemaître, Aristide; Malpuech, Guillaume; Bloch, Jacqueline (2009-08-03). "Spontaneous formation of a polariton condensate in a planar GaAs microcavity". Applied Physics Letters. AIP Publishing. 95 (5): 051108. doi:10.1063/1.3192408. ISSN 0003-6951.
  13. Amo, Alberto; Lefrère, Jérôme; Pigeon, Simon; Adrados, Claire; Ciuti, Cristiano; et al. (2009-09-20). "Superfluidity of polaritons in semiconductor microcavities". Nature Physics. Springer Science and Business Media LLC. 5 (11): 805–810. doi:10.1038/nphys1364. ISSN 1745-2473.
  14. Lerario, Giovanni; Fieramosca, Antonio; Barachati, Fábio; Ballarini, Dario; Daskalakis, Konstantinos S.; et al. (2017-06-05). "Room-temperature superfluidity in a polariton condensate". Nature Physics. Springer Science and Business Media LLC. 13 (9): 837–841. arXiv:1609.03153. doi:10.1038/nphys4147. ISSN 1745-2473.
  15. Sun, Yongbao; Wen, Patrick; Yoon, Yoseob; Liu, Gangqiang; Steger, Mark; et al. (2017-01-05). "Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium". Physical Review Letters. American Physical Society (APS). 118 (1): 016602. doi:10.1103/physrevlett.118.016602. ISSN 0031-9007.
  16. Byrnes, Tim; Kim, Na Young; Yamamoto, Yoshihisa (2014-10-31). "Exciton–polariton condensates". Nature Physics. Springer Science and Business Media LLC. 10 (11): 803–813. arXiv:1411.6822. doi:10.1038/nphys3143. ISSN 1745-2473.
  17. Sanvitto, Daniele; Kéna-Cohen, Stéphane (2016-07-18). "The road towards polaritonic devices". Nature Materials. Springer Science and Business Media LLC. 15 (10): 1061–1073. doi:10.1038/nmat4668. ISSN 1476-1122.
  18. Bhattacharya, Pallab; Xiao, Bo; Das, Ayan; Bhowmick, Sishir; Heo, Junseok (2013-05-15). "Solid State Electrically Injected Exciton-Polariton Laser". Physical Review Letters. American Physical Society (APS). 110 (20): 206403. Bibcode:2013PhRvL.110t6403B. doi:10.1103/physrevlett.110.206403. ISSN 0031-9007. PMID 25167434.
  19. Schneider, Christian; Rahimi-Iman, Arash; Kim, Na Young; Fischer, Julian; Savenko, Ivan G.; et al. (2013). "An electrically pumped polariton laser". Nature. Springer Science and Business Media LLC. 497 (7449): 348–352. Bibcode:2013Natur.497..348S. doi:10.1038/nature12036. ISSN 0028-0836.
  20. Keeling, Jonathan (2011-08-16). "Superfluid Density of an Open Dissipative Condensate". Physical Review Letters. American Physical Society (APS). 107 (8): 080402. arXiv:1106.0682. doi:10.1103/physrevlett.107.080402. ISSN 0031-9007.
  21. Carusotto, Iacopo; Ciuti, Cristiano (2004-10-13). "Probing Microcavity Polariton Superfluidity through Resonant Rayleigh Scattering". Physical Review Letters. American Physical Society (APS). 93 (16): 166401. arXiv:cond-mat/0404573. doi:10.1103/physrevlett.93.166401. ISSN 0031-9007.

Further reading
  • Universal Themes of Bose-Einstein Condensation, published by Cambridge University Press (2017). ISBN 978-1107085695, ISBN 1107085691
  • John Robert Schrieffer, Theory of Superconductivity, (1964), ISBN 0-7382-0120-0
  • Bose–Einstein Condensation, published by Cambridge University Press (1996). ISBN 978-0-521-58990-1; ISBN 0-521-58990-8
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