Inversion of exciton level splitting in quantum dots

The demonstration of degeneracy of exciton spin states is an important step toward the production of entangled photon pairs from the biexciton cascade. We measure the fine structure of exciton and biexciton states for a large number of single InAs quantum dots in a GaAs matrix; the energetic splitting of the horizontally and vertically polarized components of the exciton doublet is shown to decrease as the exciton confinement decreases, crucially passing through zero and changing sign. Thermal annealing is shown to reduce the exciton confinement, thereby increasing the number of dots with splitting close to zero.

Figure 1

Photoluminescence spectra from two single quantum dots (a) from an unannealed sample and (b) from a sample annealed for 5 min at 750 °C. Solid and dotted lines represent horizontally $\left(H\right)$ and vertically $\left(V\right)$ polarized detection for (a) and (b), respectively. Two groups of lines are observed corresponding to emission from exciton $\left(X\right)$ and biexciton $\left(XX\right)$ states as labeled. The inset to the figure shows a simple energy level diagram illustrating optical decay from the $XX$ state; the exciton level splitting $S$ is labeled.

Figure 2

Exciton level splitting $S$ (defined in the text, it is positive when the horizontally polarized component is at higher energy than the vertically) as a function of the exciton recombination energy for a large number of single quantum dots measured on annealed and unannealed samples. The dotted line shows a linear fit to the data and has a gradient of $-(1.3\pm 0.1)\times {10}^{-3}$. The histogram inset shows the measured error on the splitting.

Figure 3

Diamagnetic shifts of exciton ($X$, right axis) and biexciton ($XX$, left axis) states in single quantum dots as a function of the exciton recombination energy. Data for annealed and unannealed samples are shown.

Figure 4

Biexciton binding energy as a function of the exciton recombination energy for a large number of single quantum dots measured on annealed and unannealed samples.