Dark-State Luminescence of Macroatoms at the Near Field

We theoretically analyze the optical near-field response of a semiconductor macroatom induced by local monolayer fluctuations in the thickness of a semiconductor quantum well, where the large active volume results in a strong enhancement of the light-matter coupling. We find that in the near-field regime bright and dark excitonic states become mixed, opening new channels for the coupling to the electromagnetic field. As a consequence, ultranarrow luminescence lines appear in the simulated two-photon experiments, corresponding to very long lived excitonic states, which undergo Stark shift and Rabi splitting at relatively small field intensities.

Figure 1

(a) Schematic sketch of the confinement potential for excitons and biexcitons, which is induced by local monolayer fluctuations in the thickness of a semiconductor quantum well, and the probing SNOM tip. (b) Photoexcitation scenario assumed in our calculations. A biexciton state is excited by SNOM within a two-photon process. Because of the biexciton binding $\delta E_b\sim 4\mathrm{meV}$, the luminescence of the biexciton-to-exciton transition is redshifted and the exciton-to-ground-state transition blueshifted with respect to ${\omega }_0$. The insets report the square modulus of the center-of-mass part of the exciton and biexciton wave functions [14, 19] (left columns) and the spatial near-field maps (right columns) for a terrace of dimension $100\mathrm{nm}\times 70\mathrm{nm}$ (dashed line) and for a Bethe-Bouwkamp near-field probe with a full width of half maximum of approximately 25 nm. In the optical far field only $X_0$ and $B_0$ are allowed, whereas $X_1$ and $B_1$ are forbidden because of symmetry.

Figure 2

Near-field luminescence spectra for two selected tip positions (a) A and (b) B, as indicated in Fig. 1b, and different temperatures. At position A the usual far-field selection rules apply, and the spectrum consists of two peaks associated with the $B_0\to X_0$ and $X_0\to 0$ transitions. At position B an additional ultranarrow peak appears, which is due to the radiative decay of the dark biexciton state $B_1$. Panel (c) shows the power dependence of the optical spectra at tip position B which have been normalized with respect to the respective maxima. The power and temperature dependence of the dark-state transition $B_1$ is magnified in panels (d)–(f). Photon energy zero is given by ${\omega }_0$. In our calculations we use the 12 exciton and 6 biexciton states of lowest energy.