Observation of Excitonic $N$-Body Bound States: Polyexcitons in Diamond

We have found a series of resonances associated with the bound state (polyexcitons, ${\mathrm{PE}}^N\mathrm{s}$) of $N$ excitons up to $N=6$ in the emission spectra of diamond under two-photon excitation at around 10 K. Time-resolved spectra show a stepwise formation of ${\mathrm{PE}}^N\mathrm{s}$ with smaller to larger $N$, as well as a successive decay from larger to smaller $N$. At higher excitation levels, the transformation of ${\mathrm{PE}}^N\mathrm{s}$ into a condensed phase of electron-hole droplets occurs. The binding energies of the ${\mathrm{PE}}^N\mathrm{s}$, normalized to the exciton Rydberg energy, agree well with those of silicon, suggesting the universality of the phenomena.

Figure 1

(a) Time-integrated photoluminescence spectra at $T_{\mathrm{ex}}\sim 14\mathrm{K}$ at various excitation intensities. The average density of the electron-hole pairs is indicated in units of $n^{\prime }=3.1\times {10}^{14}{\mathrm{cm}}^{-3}$. (b) Schematic diagram of the radiative decay of an exciton following the transition from the ${\mathrm{PE}}^N$ state to the ${\mathrm{PE}}^{N-1}$ state. (c) Excitation-density dependence of the peak intensity of the $X^N$ ($N=2–6$) line normalized to that of the ${\mathrm{EX}}_{(\mathrm{TO})}$ emission.

Figure 2

Time-resolved photoluminescence image at $T_{\mathrm{ex}}=13\mathrm{K}$ and $n=1.6\times {10}^{15}{\mathrm{cm}}^{-3}$ ($=5.2n^{\prime }$), measured using a streak camera system. The ordinate shows the time delay after photoexcitation, and the abscissa is the photon energy. The temporal resolution is 0.12 ns. The trace at the bottom is the photoluminescence spectrum integrated over time.

Figure 3

Temporal profiles of the emission intensities of the exciton (Ex) and the ${\mathrm{PE}}^N$ (a) within the first 1.5 ns and (b) up to 20 ns at $T_{\mathrm{ex}}=13\mathrm{K}$ and $n=1.6\times {10}^{15}{\mathrm{cm}}^{-3}$ ($=5.2n^{\prime }$).

Figure 4

Temporal evolution of the PE emission and EHD-like broadband emission spectra at $T_{\mathrm{ex}}=13\mathrm{K}$ and $n=2.5\times {10}^{16}{\mathrm{cm}}^{-3}$($=81n^{\prime }$) showing (a) the formation and (b) the decay dynamics. The delay times are shown on the left-hand side of each panel. The spectra have been averaged over the temporal resolution of the measurements, which is 0.06 ns and 0.12 ns for (a) and (b), respectively. The solid circles indicate discrete emission peaks of ${\mathrm{PE}}^N\mathrm{s}$.