Superradiant Emission from a Collective Excitation in a Semiconductor

We report an anomalous wide broadening of the emission spectra of an electronic excitation confined in a two-dimensional potential. We attribute these results to an extremely fast radiative decay rate associated with superradiant emission from the ensemble of confined electrons. Lifetimes extracted from the spectra are below 100 fs and, thus, 6 orders of magnitude faster than for single particle transitions at similar wavelength. Moreover, the spontaneous emission rate increases with the electronic density, as expected for superradiant emission. The data, all taken at 300 K, are in excellent agreement with our theoretical model, which takes into account dipole-dipole Coulomb interaction between electronic excitations. Our experimental results demonstrate that the interaction with infrared light, which is usually considered a weak perturbation, can be a very efficient relaxation mechanism for collective electronic excitations in solids.

Figure 1

Comparison between an atomic ensemble and a two-dimensional electronic system. (a) Different atoms are labeled by their position in the real space and have flat dispersion in the momentum space. Provided that they occupy a volume $\ll {\lambda }^3$, their spectrum of interaction with the light can be represented as a harmonic ladder. (b) In a two-dimensional electronic system with only two confined subbands there is also a collection of identical two-level emitters, which, however, can be recognized by their momentum in the plane, rather than their positions. Coulomb interaction renormalizes the transition energy by a blueshift, but the overall shape of the optical spectrum stays identical. (c) In the case of several occupied subbands the harmonic spectrum is preserved. Here, the energy spacing $E_{\mathrm{MSP}}$ is provided by the many-body interactions, rather than the confining potential. Further explanations are provided in the Supplemental Material [19].

Figure 2

Spontaneous emission times as a function of the doping level for superradiant emission from the multisubband plasmon (red line, our case) at $\theta =60°$ and a single two-level emitter (blue) with the same energy as the collective excitation. The dashed line indicates the typical nonradiative lifetime in intersubband systems. With our doping level ($\approx {10}^{13}{\mathrm{cm}}^{-2}$), the collective excitation has an emission lifetime that is 6 orders of magnitude shorter than that of a single emitter. Furthermore, the radiation lifetime becomes comparable with the nonradiative lifetime, a situation that is unprecedented for a solid state system at room temperature.

Figure 3

(a) Top: SEM images of a facet and a single device (false colors). Bottom: comparison between an absorption spectrum (blue, dashed line) with an emission spectrum (red, continuous line) for a 18.5 nm wide quantum well doped at $2.2\times {10}^{13}{\mathrm{cm}}^{-2}$. Both spectra are taken at 300 K and $\theta =45°$. Inset: a device cross-section illustrating the source ($S$) to drain ($D$) bias scheme. (b) Light vs current ($L\text{−}I$) characteristics for an emission angle $\theta =45°$ and different heat sink temperatures. Notice that the 173 K curve is barely visible above the noise level. Inset: $V\text{−}I$ characteristic of the same device at 338 K.

Figure 4

Top left: scheme of our experimental configuration for collecting plasmon emission. Top right: color maps of the normalized emission spectra of samples with three different dopings. Bottom panel: the dotted lines are the normalized spectra of the three samples for $\theta =55°$. The continuous lines indicate Lorentzian fits.

Figure 5

(a) Spectral linewidths extracted from the data in Fig. 4 as a function of $\theta$, for the three different doping levels. The inset reports the same curves plotted as a function of ${\sin }^2\theta /\cos \theta$ and the corresponding linear fits. Their slopes provide directly the rate factor $N_s{\beta }_s$ from Eq. (2). (b) Radiative lifetimes of plasmons as a function of $\theta$ obtained by subtracting the nonradiative contribution. (c) Superradiant coefficient ${\beta }_s$ obtained by dividing the slopes of the linear fits in (a) by the doping concentration of the samples $N_s$. The gray dashed line represents the value ${\beta }_s=2(\alpha /m^{*})(\pi \hslash /n)$.