Abstract
If 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 of a number of fundamental phenomena in physics, including superconductivity, superfluidity and Bose–Einstein condensation1,2. Spontaneous coherence is the key characteristic of condensation in momentum space3. Excitons—bound pairs of electrons and holes—form a model system to explore the quantum physics of cold bosons in solids4,5. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy owing to their long lifetimes6. Here we report measurements of spontaneous coherence in a gas of indirect excitons. We found that spontaneous coherence of excitons emerges in the region of the macroscopically ordered exciton state7 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. A pattern of extended spontaneous coherence is correlated with a pattern of spontaneous polarization, revealing the properties of a multicomponent coherent state. We also observed phase singularities in the coherent exciton gas. All these phenomena emerge when the exciton gas is cooled below a few kelvin.
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References
Cornell, E. A. & Wieman, C. E. Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments. Rev. Mod. Phys. 74, 875–893 (2002)
Ketterle, W. When atoms behave as waves: Bose-Einstein condensation and the atom laser. Rev. Mod. Phys. 74, 1131–1151 (2002)
Penrose, O. & Onsager, L. Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576–584 (1956)
Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521–528 (1968)
Keldysh, L. V. & Kopaev Possible instability of the semimetallic state toward Coulomb interaction. Sov. Phys. Solid State 6, 2219–2224 (1965)
Butov, L. V. et al. Stimulated scattering of indirect excitons in coupled quantum wells: signature of a degenerate Bose-gas of excitons. Phys. Rev. Lett. 86, 5608–5611 (2001)
Butov, L. V., Gossard, A. C. & Chemla, D. S. Macroscopically ordered state in an exciton system. Nature 418, 751–754 (2002)
Chen, X. M. & Quinn, J. J. Excitonic charge-density-wave instability of spatially separated electron-hole layers in strong magnetic fields. Phys. Rev. Lett. 67, 895–898 (1991)
Wu, C., Shem, I. M. & Exciton condensation with spontaneous time-reversal symmetry breaking Preprint at http://arXiv.org/abs/0809.3532v1 (2008)
Tikhodeev, S. G., Kopelevich, G. A. & Gippius, N. A. Exciton transport in Cu2O: phonon wind versus superfluidity. Phys. Status Solidi B 206, 45–53 (1998)
Jang, J. I. & Wolfe, J. P. Auger recombination and biexcitons in Cu2O: a case for dark exciton matter. Phys. Rev. B 74, 045211 (2006)
Keldysh, L. V. The electron-hole liquid in semiconductors. Contemp. Phys. 27, 395–428 (1986)
Lozovik & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Sov. Phys. JETP 44, 389–397 (1976)
Fukuzawa, T., Kano, S. S., Gustafson, T. K. & Ogawa, T. Possibility of coherent-light emission from Bose condensed states of SEHPs. Surf. Sci. 228, 482–485 (1990)
Maialle, M. Z., de Andrada e Silva, E. A. & Sham, L. J. Exciton spin dynamics in quantum wells. Phys. Rev. B 47, 15776–15788 (1993)
Butov, L. V. & Filin, A. I. Anomalous transport and luminescence of indirect excitons in AlAs/GaAs coupled quantum wells as evidence for exciton condensation. Phys. Rev. B 58, 1980–2000 (1998)
Spielman, I. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet. Phys. Rev. Lett. 84, 5808–5811 (2000)
Eisenstein, J. P. & MacDonald, A. H. Bose-Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004)
Butov, L. V., Zrenner, A., Abstreiter, G., Böhm, G. & Weimann, G. Condensation of indirect excitons in coupled AlAs/GaAs quantum wells. Phys. Rev. Lett. 73, 304–307 (1994)
Tutuc, E., Shayegan, M. & Huse, D. A. Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing. Phys. Rev. Lett. 93, 036802 (2004)
Tiemann, L. et al. Exciton condensate at a total filling factor of one in Corbino two-dimensional electron bilayers. Phys. Rev. B 77, 033306 (2008)
Karmakar, B., Pellegrini, V., Pinczuk, A., Pfeiffer, L. N. & West, K. W. First-order quantum phase transition of excitons in quantum hall bilayers. Phys. Rev. Lett. 102, 036802 (2009)
Sen., Yang, Hammack, A. T., Fogler, M. M., Butov, L. V. & Gossard, A. C. Coherence length of cold exciton gases in coupled quantum wells. Phys. Rev. Lett. 97, 187402 (2006)
Fogler, M. M. Sen, Yang, Hammack, A. T., Butov, L. V. & Gossard, A. C. Effect of spatial resolution on the estimates of the coherence length of excitons in quantum wells. Phys. Rev. B 78, 035411 (2008)
Read, D., Liew, T. C. H., Rubo, Y. G. & Kavokin, A. V. Stochastic polarization formation in exciton-polariton Bose-Einstein condensates. Phys. Rev. B 80, 195309 (2009)
Butov, L. V. et al. Formation mechanism and low temperature instability of exciton rings. Phys. Rev. Lett. 92, 117404 (2004)
Rapaport, R. et al. Charge separation of dense two dimensional electron-hole gases: mechanism for exciton ring pattern formation. Phys. Rev. Lett. 92, 117405 (2004)
Scheuer, J. & Orenstein, M. Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities. Science 285, 230–233 (1999)
Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)
Lagoudakis, K. G. et al. Quantized vortices in an exciton–polariton condensate. Nature Phys. 4, 706–710 (2008)
Acknowledgements
We thank L. Levitov, T. Ostatnický, L. Sham, B. Simons and C. Wu for discussions. This work was supported by the DOE Office of Basic Energy Sciences (DE-FG02-07ER46449). The development of spectroscopy in a dilution refrigerator was supported by ARO and NSF. M.M.F. was supported by the UCOP. A.V.K. was supported by the Royal Society (UK).
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High, A., Leonard, J., Hammack, A. et al. Spontaneous coherence in a cold exciton gas. Nature 483, 584–588 (2012). https://doi.org/10.1038/nature10903
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DOI: https://doi.org/10.1038/nature10903
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