Quantum droplets of electrons and holes

Journal name:
Nature
Volume:
506,
Pages:
471–475
Date published:
DOI:
doi:10.1038/nature12994
Received
Accepted
Published online

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.

At a glance

Figures

  1. Quasiparticles in classical spectroscopy.
    Figure 1: Quasiparticles in classical spectroscopy.

    a, Schematic quasiparticles in direct-gap semiconductors. Open circles, holes; grey filled circles, electrons. See text for details. b, Measured absorption spectra as a function of the number of photons in the pump pulse, Npump, for pump–probe delay Δt = 2ps; the pump and probe have opposite circular polarization. The dark (white) colours denote the regions with strong (weak) absorption (see colour scale; peak absorption is normalized to one); the transparent yellow shaded areas with black lines on top show actual spectra corresponding to Npump = 2.8×106 (lower) and Npump = 9.5×106 (upper). The dashed lines indicate the shifts of the resonances, ω defines the photon energy, E1s,0 is the low-density exciton energy, and Ebind denotes the binding energy.

  2. Quantum droplet properties.
    Figure 2: Quantum droplet properties.

    a, Computed g(r) of a quantum droplet having radius R = 91nm, n = 4 and ρehρe = ρh = 2.5×1010cm−2. The cylinder represents the droplet shell, the correlated part (Δg(r)) is indicated by a yellow area, and the grey area corresponds to the plasma (ρeρh). b, Computed binding energy as a function of ρeh. Energy dispersion for each droplet is continued as a dashed line after the next higher quantum droplet becomes the lowest-energy state; the white line continues the 6-ring Ebind. The horizontal line indicates the biexciton binding energy. The shaded areas denote the ground-state bands. The filled circle defines the binding energy for the configuration presented in a.

  3. Detection of quantum droplets via quantum spectroscopy.
    Figure 3: Detection of quantum droplets via quantum spectroscopy.

    a, Contour plot of ΔαMB (on colour scale) as a function of Npump and Ebind. The dark (white) contours indicate the regions with large (small) increase in ΔαMB. The biexciton Ebind (horizontal line) matches the low-density binding in Fig. 1b. Grey shaded horizontal bands denote the computed energy ranges of 4-, 5-, 6- and 7-ring droplets. The yellow areas with black traces show ΔαMB at Npump = 1.0×106 (left, open circle), 2.6×106 (middle, red sphere) and 4.2×106 (right, blue sphere). b, Temporal evolution of ΔαMB for Npump = 3.8×106. Grey shaded horizontal bands denote the 4- and 5-ring bands. Inset, Fourier-transformed ΔαMB at Ebind = 3.3meV (horizontal yellow line in b). The vertical grey shaded rectangle determines the expected range for 4–5 ring splitting.

  4. Direct measurement of quantum-droplet signatures.
    Figure 4: Direct measurement of quantum-droplet signatures.

    Main figure, differential absorption trace recorded at 3meV binding energy as a function of pump–probe delay. The measured (red line) and low-pass filtered (black line) traces are shown. Inset, corresponding intensity spectra (red line) together with the experimental noise floor (blue horizontal line) and energy ranges (vertical cyan shaded rectangles) expected for transitions between the 4- and 5-ring droplet and the 4- and 6-ring droplet, identified in Fig. 2b. a.u., arbitrary units.

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Author information

Affiliations

  1. JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado 80309-0440, USA

    • A. E. Almand-Hunter,
    • H. Li &
    • S. T. Cundiff
  2. Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA

    • A. E. Almand-Hunter &
    • S. T. Cundiff
  3. Department of Physics, Philipps-University Marburg, Renthof 5, 35032 Marburg, Germany

    • M. Mootz,
    • M. Kira &
    • S. W. Koch

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.

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The authors declare no competing financial interests.

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