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
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
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
Similar content being viewed by others
References
Lissauer, J. Chaotic motion in the solar system. Rev. Mod. Phys. 71, 835–845 (1999)
Kira, M. & Koch, S. W. Semiconductor Quantum Optics 1st edn (Cambridge Univ. Press, 2011)
Oganessian, Y. et al. Synthesis of nuclei of the superheavy element 114 in reactions induced by 48Ca. Nature 400, 242–245 (1999)
Kittel, C. Introduction to Solid State Physics 7th edn (Wiley, 2004)
Laughlin, R. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983)
Datta, S. Electronic Transport in Mesoscopic Systems 1st edn (Cambridge Univ. Press, 1997)
Papon, P., Leblond, J. & Meijer, P. The Physics of Phase Transitions: Concepts and Applications 2nd edn (Springer, 2006)
Endres, M. et al. Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334, 200–203 (2011)
Vershinin, M. et al. Local ordering in the pseudogap state of the high-TC superconductor Bi2Sr2CaCu2O8+δ . Science 303, 1995–1998 (2004)
Kanigel, A. et al. Evolution of the pseudogap from Fermi arcs to the nodal liquid. Nature Phys. 2, 447–451 (2006)
Daou, R. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010)
Frenkel, J. On the transformation of light into heat in solids. Phys. Rev. 37, 17–44 (1931)
Wannier, G. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937)
Kim, J. C., Wake, D. R. & Wolfe, J. P. Thermodynamics of biexcitons in a GaAs quantum well. Phys. Rev. B 50, 15099–15107 (1994)
Steele, A., McMullan, W. & Thewalt, M. Discovery of polyexcitons. Phys. Rev. Lett. 59, 2899–2902 (1987)
Turner, D. & Nelson, K. Coherent measurements of high-order electronic correlations in quantum wells. Nature 466, 1089–1092 (2010)
Jeffries, C. Electron–hole condensation in semiconductors. Science 189, 955–964 (1975)
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)
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)
Smith, R. P. et al. Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells. Phys. Rev. Lett. 104, 247401 (2010)
Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron–hole plasma. Nature 414, 286–289 (2001)
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)
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)
Cundiff, S. T. Optical two-dimensional Fourier transform spectroscopy of semiconductor nanostructures. J. Opt. Soc. Am. B 29, A69–A81 (2012)
Barker, J. A. & Henderson, D. What is “liquid”? Understanding the states of matter. Rev. Mod. Phys. 48, 587–671 (1976)
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)
Sastry, S. & Angell, C. Liquid–liquid phase transition in supercooled silicon. Nature Mater. 2, 739–743 (2003)
Mootz, M., Kira, M. & Koch, S. W. Pair-excitation energetics of highly correlated many-body states. New J. Phys. 15, 093040 (2013)
Hirschfelder, J. O. The energy of the triatomic hydrogen molecule and ion, V. J. Chem. Phys. 6, 795–806 (1938)
Thomson, J. On the structure of the atom. Phil. Mag. 7, 237–265 (1904)
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
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
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)
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nature12994
This article is cited by
-
Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states
Scientific Reports (2023)
-
Lightwave electronics in condensed matter
Nature Reviews Materials (2023)
-
Separating single- from multi-particle dynamics in nonlinear spectroscopy
Nature (2023)
-
Modelling of nanowall-based CdS/CdTe solar cells with embedded gold nanorods using TCAD simulation
Multiscale and Multidisciplinary Modeling, Experiments and Design (2023)
-
Attosecond clocking of correlations between Bloch electrons
Nature (2022)
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.