Two-Electron Linear Intersubband Light Absorption in a Biased Quantum Well

We point out a novel manifestation of many-body correlations in the linear optical response of electrons confined in a quantum well. Namely, we demonstrate that along with the conventional absorption peak at a frequency $\omega$ close to the intersubband energy $\Delta$, there exists an additional peak at frequency $\hslash \omega \approx 2\Delta$. This new peak is solely due to electron-electron interactions, and can be understood as excitation of two electrons by a single photon. The actual peak line shape is comprised of a sharp feature, due to excitation of pairs of intersubband plasmons, on top of a broader band due to absorption by two single-particle excitations. The two-plasmon contribution allows us to infer intersubband plasmon dispersion from linear absorption experiments.

Figure 1

(a) Two lowest size-quantization wave functions of a biased quantum well are shown schematically; for two-electron linear absorption, the incident photon energy must be close to $2\Delta$. (b) Two-electron intersubband absorption in the lowest order of the perturbation theory.

Figure 2

Diagrammatic representation of single-particle absorption (a) two-particle absorption and (b) two-electron dipole matrix element; (c) $V_A$ stands for $V_{1222}$ and $V_{1211}$ in first and second diagram, respectively.

Figure 3

Normalized two-electron absorption, $\Delta {\tilde{\alpha }}_2$, in $d=20\mathrm{nm}$ GaAs QW is shown for applied bias $U=30\mathrm{meV}$ and electron concentrations $N={10}^{11}{\mathrm{cm}}^{-2}$, $1.5\times {10}^{11}{\mathrm{cm}}^{-2}$, and $2.0\times {10}^{11}{\mathrm{cm}}^{-2}$. The right peak corresponds to two-plasmon absorption. Arrow indicates the position of single-electron absorption peak at $\Delta$. Inset: threshold behavior of two-electron absorption calculated from Eq. (15).