Radiative cascades from charged semiconductor quantum dots

We measured two-photon radiative cascades due to sequential recombination of quantum-dot confined electron-hole pairs in the presence of an additional spectator charge carrier. We use temporally resolved polarization sensitive intensity correlation measurements to fully characterize these radiative cascades. We identified direct, all optical cascades involving spin-blockaded intermediate states, and indirect cascades, in which nonradiative relaxation precedes the second radiative recombination. Our measurements provide spin dephasing rates of confined single carriers.

Figure 1

(Color online) (a) Schematic description of the energy levels of a singly positively charged QD. Vertical (curly) arrows indicate radiative (nonradiative) transitions between these levels. State occupation and spin wave functions are described to the left of each level where $\uparrow (\Downarrow )$ represents an electron (hole) with spin up (down). A short blue (dark gray) [long red (light gray)] arrow represents a carrier in its first (second) level. $S\left(T\right)$ stands for two holes’ singlet (triplet) state and 0 (3) for $S_z=0\left(S_z=\pm 3\right)$ total holes’ spin projection on the QD growth direction. Only one out of two (Kramers’) degenerate states is described. (b) Measured polarized PL spectra on which the actual transitions are identified. Red (blue) line represents the spectrum polarized along the major $\left(H\right)$ [minor $\left(V\right)$] axis of the QD. Excitonic (biexcitonic) transitions are marked by dash (dash-dot) lines. Transitions which are not discussed here are marked by gray letters. (c) Measured degree of linear polarization spectrum, along the in-plane symmetry axes of the QD. Positive (negative) value represents polarization along the $H\left(V\right)$ direction.

Figure 2

(Color online) Measured time-resolved, polarization sensitive intensity correlation functions, for the four radiative cascades described in Fig. 1. Zero time indicates the detection of the first photon, negative times indicate reverse order of detections. The direct cascades involving $T_3$, $T_0$, and $S^{\ast }$ as intermediate levels are presented in (a)–(c), respectively. The indirect cascade in which $S^{\ast }$ is the intermediate state after the first photon and the ground $X^{+1}\left(S\right)$ is the second emitting state presented in (d). The states involved in the first (second) photon emission are illustrated to the left (right) side of each panel. All symbols are as in Fig. 1. Blue (red) line stands for measured relative cross- (co-) circularly polarized photons. The bar presents the acquisition rate in coincidences per time bin (80 ps) per hour.

Figure 3

(Color online) Measured time-resolved, polarization sensitive intensity correlation measurements, between the radiative cascades. (a) [(c)] Correlations between the $S^{\ast }$ biexciton and the $T_0$, $\left[T_3\right]$ exciton. (b) [(d)] Correlations between the $T_0$, $\left[T_3\right]$ biexciton and the ground $X^{+1}\left(S\right)$ exciton. (e) [(f)] Correlation between the $T_3\left[T_0\right]$ biexciton and the $T_0\left[T_3\right]$ exciton. The meanings of all symbols are as in Fig. 2.