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Spontaneous coherence in a cold exciton gas

Naturevolume 483, pages584–588 (2012)Cite this article

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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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Figure 1:Emission, interference and coherence patterns of indirect excitons.
Figure 2:Coherence of indirect excitons in regions of an LBS and the external ring.
Figure 3:First-order coherence function and distribution in momentum space.
Figure 4:Patterns of the coherence length of excitons,ξ(x,y).
Figure 5:Fork-like defects in exciton interference patterns.

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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).

Author information

Authors and Affiliations

  1. Department of Physics, University of California at San Diego, La Jolla, 92093-0319, California, USA

    A. A. High, J. R. Leonard, A. T. Hammack, M. M. Fogler & L. V. Butov

  2. School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK,

    A. V. Kavokin

  3. Spin Optics Laboratory, State University of Saint Petersburg, 1, Ulianovskaya, 198504, Russia,

    A. V. Kavokin

  4. Materials Department, University of California at Santa Barbara, Santa Barbara, 93106-5050, California, USA

    K. L. Campman & A. C. Gossard

Authors
  1. A. A. High
  2. J. R. Leonard
  3. A. T. Hammack
  4. M. M. Fogler
  5. L. V. Butov
  6. A. V. Kavokin
  7. K. L. Campman
  8. A. C. Gossard

Contributions

All authors contributed to the work presented in this paper.

Corresponding author

Correspondence toA. A. High.

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Competing interests

The authors declare no competing financial interests.

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Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-5 and additional references. (PDF 1132 kb)

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High, A., Leonard, J., Hammack, A.et al. Spontaneous coherence in a cold exciton gas.Nature483, 584–588 (2012). https://doi.org/10.1038/nature10903

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Comments

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  1. D. C. Dai

    The spontaneous macroscopic quantum coherence of excitons in a usual direct-gap semiconductor crystal bulk at 5 Kelvin has been successfully demonstrated on ultrafast timescale a few months ago (DOI:10.1103/PhysRevB.84.115206), unfortunately this paper does not mention this, on the contrary, it insists saying that " Owing to recombination, excitons have a finite lifetime that is too short to allow cooling to low temperatures in usual semiconductors."
    does this style scientifically strict and fit a paper on Nature?

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Editorial Summary

Exciton condensate demonstrated

Like atoms, excitons — bound pairs of electrons and electron holes — can form a Bose–Einstein-condensate-like state with superfluidic properties below a critical temperature. In practice, this is difficult to achieve in a normal semiconductor owing to the short lifetime of excitons; they cannot be cooled down fast enough. This problem can be circumvented by making use of indirect excitons, which have much longer lifetimes because the electrons and holes are confined in separate quantum-well layers to prevent them from recombining too quickly. Previously, it has been shown that a cold exciton gas can be formed in this system; now, Highet al. observe spontaneous coherence in such a gas, characteristic of a condensate.

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