Influence of the Dark Exciton State on the Optical and Quantum Optical Properties of Single Quantum Dots

The dark exciton state strongly affects the optical and quantum optical properties of flat $\mathrm{InP}/\mathrm{GaInP}$ quantum dots. The exciton intensity drops sharply compared to the biexciton with rising pulsed laser excitation power while the opposite is true with temperature. Also, the decay rate is faster for the exciton than the biexciton and the dark-to-bright state spin flip is enhanced with temperature. Furthermore, long-lived dark state related memory effects are observed in second-order cross-correlation measurements between the exciton and biexciton and have been simulated using a rate-equation model.

Figure 1

PL spectra of QD $A$ and QD $B$ from sample $A$ under pulsed excitation at various PDs ($P_0=2\mathrm{W}/{\mathrm{cm}}^2$). $XX$ dominates even at very low PD as a result of the influence of the DS. Inset: Illustration of the splitting of the XS into a BS and a DS which occurs because excitons are composed of electrons ($J_z^e=\pm \frac{1}{2}$) and heavy holes ($J_z^{hh}=\pm \frac{3}{2}$) that can have total angular momenta $J_z^{\mathrm{exc}}=\pm 1$ ($\Uparrow \downarrow$) or $J_z^{\mathrm{exc}}=\pm 2$ ($\Uparrow \uparrow$).

Figure 2

Variation of the $X$ intensity relative to the overall ground state intensity (squares) for QD $A$ ($\mathrm{PD}=20\mathrm{W}/{\mathrm{cm}}^2$) and QD $C$ ($\mathrm{PD}=190\mathrm{W}/{\mathrm{cm}}^2$). The solid lines are Arrhenius fits obtained using a single activation energy, $E_A$. The error bars are larger for QD $A$ as a cold-finger cryostat was used. This geometry is less stable than the circular cryostat geometry that was used for QD $C$. Insets: Spectra from QD $A$ and QD $C$ recorded at different temperatures.

Figure 3

Time-resolved PL measurements of the QD $C$ $X$ (BS) and $XX$ at 4 K ($\mathrm{PD}=200\mathrm{W}/{\mathrm{cm}}^2$). The $X$ trace has been shifted vertically for clarity. The gray lines are exponential fits to the data.

Figure 4

(a) CCM between $X$ and $XX$ of QD $A$ ($\mathrm{PD}=14\mathrm{W}/{\mathrm{cm}}^2$). The distance between the peaks is equal to the time between two laser pulses. (b) CCM between the $X$ and $XX$ of QD $C$ ($\mathrm{PD}=150\mathrm{W}/{\mathrm{cm}}^2$). The dashed curved lines in (a) and (b) are guides to the eye. (c) As for (b), except that the temperature was raised to 30 K ($\mathrm{PD}=150\mathrm{W}/{\mathrm{cm}}^2$). (d) Level scheme on which the simulation in (e) and (f) is based (see main text). (e) Simulated $XX\mathrm{\text{−}}X$ CCM at different powers without considering ${\tau }_{\mathrm{bfl}}$. (f) As for (e) but at a fixed power of 0.5 and including ${\tau }_{\mathrm{bfl}}$ (5 ns and 600 ps).