Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum droplets of electrons and holes

Abstract

Interacting many-body systems are characterized by stable configurations of objects—ranging from elementary particles to cosmological formations1,2,3—that also act as building blocks for more complicated structures. It is often possible to incorporate interactions in theoretical treatments of crystalline solids by introducing suitable quasiparticles that have an effective mass, spin or charge4,5 which in turn affects the material’s conductivity, optical response or phase transitions2,6,7. Additional quasiparticle interactions may also create strongly correlated configurations yielding new macroscopic phenomena, such as the emergence of a Mott insulator8, superconductivity or the pseudogap phase of high-temperature superconductors9,10,11. In semiconductors, a conduction-band electron attracts a valence-band hole (electronic vacancy) to create a bound pair, known as an exciton12,13, which is yet another quasiparticle. Two excitons may also bind together to give molecules, often referred to as biexcitons14, and even polyexcitons may exist15,16. In indirect-gap semiconductors such as germanium or silicon, a thermodynamic phase transition may produce electron–hole droplets whose diameter can approach the micrometre range17,18. In direct-gap semiconductors such as gallium arsenide, the exciton lifetime is too short for such a thermodynamic process. Instead, different quasiparticle configurations are stabilized dominantly by many-body interactions, not by thermalization. The resulting non-equilibrium quantum kinetics is so complicated that stable aggregates containing three or more Coulomb-correlated electron–hole pairs remain mostly unexplored. Here we study such complex aggregates and identify a new stable configuration of charged particles that we call a quantum droplet. This configuration exists in a plasma and exhibits quantization owing to its small size. It is charge neutral and contains a small number of particles with a pair-correlation function that is characteristic of a liquid. We present experimental and theoretical evidence for the existence of quantum droplets in an electron–hole plasma created in a gallium arsenide quantum well by ultrashort optical pulses.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Quasiparticles in classical spectroscopy.
Figure 2: Quantum droplet properties.
Figure 3: Detection of quantum droplets via quantum spectroscopy.
Figure 4: Direct measurement of quantum-droplet signatures.

References

  1. Lissauer, J. Chaotic motion in the solar system. Rev. Mod. Phys. 71, 835–845 (1999)

    Article  ADS  Google Scholar 

  2. Kira, M. & Koch, S. W. Semiconductor Quantum Optics 1st edn (Cambridge Univ. Press, 2011)

    Book  Google Scholar 

  3. Oganessian, Y. et al. Synthesis of nuclei of the superheavy element 114 in reactions induced by 48Ca. Nature 400, 242–245 (1999)

    Article  ADS  CAS  Google Scholar 

  4. Kittel, C. Introduction to Solid State Physics 7th edn (Wiley, 2004)

    MATH  Google Scholar 

  5. Laughlin, R. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983)

    Article  ADS  Google Scholar 

  6. Datta, S. Electronic Transport in Mesoscopic Systems 1st edn (Cambridge Univ. Press, 1997)

    Google Scholar 

  7. Papon, P., Leblond, J. & Meijer, P. The Physics of Phase Transitions: Concepts and Applications 2nd edn (Springer, 2006)

    Book  Google Scholar 

  8. Endres, M. et al. Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334, 200–203 (2011)

    Article  ADS  CAS  Google Scholar 

  9. Vershinin, M. et al. Local ordering in the pseudogap state of the high-TC superconductor Bi2Sr2CaCu2O8+δ . Science 303, 1995–1998 (2004)

    Article  ADS  CAS  Google Scholar 

  10. Kanigel, A. et al. Evolution of the pseudogap from Fermi arcs to the nodal liquid. Nature Phys. 2, 447–451 (2006)

    Article  ADS  CAS  Google Scholar 

  11. Daou, R. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010)

    Article  ADS  CAS  Google Scholar 

  12. Frenkel, J. On the transformation of light into heat in solids. Phys. Rev. 37, 17–44 (1931)

    Article  ADS  CAS  Google Scholar 

  13. Wannier, G. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937)

    Article  ADS  CAS  Google Scholar 

  14. Kim, J. C., Wake, D. R. & Wolfe, J. P. Thermodynamics of biexcitons in a GaAs quantum well. Phys. Rev. B 50, 15099–15107 (1994)

    Article  ADS  CAS  Google Scholar 

  15. Steele, A., McMullan, W. & Thewalt, M. Discovery of polyexcitons. Phys. Rev. Lett. 59, 2899–2902 (1987)

    Article  ADS  CAS  Google Scholar 

  16. Turner, D. & Nelson, K. Coherent measurements of high-order electronic correlations in quantum wells. Nature 466, 1089–1092 (2010)

    Article  ADS  CAS  Google Scholar 

  17. Jeffries, C. Electron–hole condensation in semiconductors. Science 189, 955–964 (1975)

    Article  ADS  CAS  Google Scholar 

  18. Suzuki, T. & Shimano, R. Time-resolved formation of excitons and electron–hole droplets in Si studied using terahertz spectroscopy. Phys. Rev. Lett. 103, 057401 (2009)

    Article  ADS  Google Scholar 

  19. Kaindl, R. A., Carnahan, M. A., Hagele, D., Lovenich, R. & Chemla, D. S. Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003)

    Article  ADS  CAS  Google Scholar 

  20. Smith, R. P. et al. Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells. Phys. Rev. Lett. 104, 247401 (2010)

    Article  ADS  CAS  Google Scholar 

  21. Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron–hole plasma. Nature 414, 286–289 (2001)

    Article  ADS  CAS  Google Scholar 

  22. Khitrova, G., Gibbs, H. M., Jahnke, F., Kira, M. & Koch, S. W. Nonlinear optics of normal-mode-coupling semiconductor microcavities. Rev. Mod. Phys. 71, 1591–1639 (1999)

    Article  ADS  Google Scholar 

  23. Kira, M., Koch, S. W., Smith, R. P., Hunter, A. E. & Cundiff, S. T. Quantum spectroscopy with Schrödinger-cat states. Nature Phys. 7, 799–804 (2011)

    Article  ADS  Google Scholar 

  24. Cundiff, S. T. Optical two-dimensional Fourier transform spectroscopy of semiconductor nanostructures. J. Opt. Soc. Am. B 29, A69–A81 (2012)

    Article  ADS  CAS  Google Scholar 

  25. Barker, J. A. & Henderson, D. What is “liquid”? Understanding the states of matter. Rev. Mod. Phys. 48, 587–671 (1976)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926–935 (1983)

    Article  ADS  CAS  Google Scholar 

  27. Sastry, S. & Angell, C. Liquid–liquid phase transition in supercooled silicon. Nature Mater. 2, 739–743 (2003)

    Article  ADS  CAS  Google Scholar 

  28. Mootz, M., Kira, M. & Koch, S. W. Pair-excitation energetics of highly correlated many-body states. New J. Phys. 15, 093040 (2013)

    Article  ADS  Google Scholar 

  29. Hirschfelder, J. O. The energy of the triatomic hydrogen molecule and ion, V. J. Chem. Phys. 6, 795–806 (1938)

    Article  ADS  CAS  Google Scholar 

  30. Thomson, J. On the structure of the atom. Phil. Mag. 7, 237–265 (1904)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank R. Mirin at NIST-Boulder for growing the quantum well samples. The work at Philipps-University Marburg was supported by the Deutsche Forschungsgemeinschaft under grant KI 917/2-1, and the work at JILA was supported by the NSF under grant 1125844 and by NIST. S.T.C. acknowledges support from the Alexander von Humboldt Foundation.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed substantially to this work. The experiments were performed by the JILA group whereas the Philipps-University Marburg group was predominantly responsible for the theory.

Corresponding author

Correspondence to M. Kira.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-12 and additional references. (PDF 1607 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Almand-Hunter, A., Li, H., Cundiff, S. et al. Quantum droplets of electrons and holes. Nature 506, 471–475 (2014). https://doi.org/10.1038/nature12994

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature12994

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing