Photon Statistics from Coupled Quantum Dots

We present an optical study of two closely stacked self-assembled $\mathrm{InAs}/\mathrm{GaAs}$ quantum dots. The energy spectrum and correlations between photons subsequently emitted from a single pair provide not only clear evidence of coupling between the quantum dots but also insight into the coupling mechanism. Our results are in agreement with recent theories predicting that tunneling is largely suppressed between nonidentical quantum dots and that the interaction is instead dominated by dipole-dipole coupling and phonon-assisted energy transfer processes.

Figure 1

(a) PL spectrum of a single layer of $\mathrm{InAs}/\mathrm{GaAs}$ QDs. Interference filters were used to select two emission lines from two QDs, with lateral separation of $2\mu \mathrm{m}$. (b) Photon autocorrelation for each line showing antibunching, $g^{(2)}(0)=0.31$ and 0.12 for QD1 and QD2, respectively. (c) Corresponding cross correlation showing $g^{(2)}(\tau )=1$ for all times, indicating that the lateral QDs are uncoupled.

Figure 2

(a) Schematic of the sample (top): two layers of $\mathrm{InAs}/\mathrm{GaAs}$ QDs are vertically stacked with a separation of 45 Å. Schematic band diagram (bottom) of the conduction band (CB) and valence band (VB) for two stacked QDs with different transition frequencies $\omega 1$ and $\omega 2$. The pump laser, with energy $\hslash {\omega }_{\mathrm{exc}}$, generates carriers in the GaAs matrix that relax into the wetting layers and from there into the QDs. (b) Typical power dependent PL spectra from an individual QD pair showing five dominant emission lines, labeled $X1–X5$.

Figure 3

PL for a pump power of 1.8 nW, of the $X1$ and $X2$ transitions versus temperature for a QD pair with $\Delta E_0=1.3\mathrm{meV}$. As the temperature is increased, the intensity from the energetically higher line, $X1$, is transferred to the $X2$ line.

Figure 4

Measured cross-correlation functions between the $X2–X1$, $X1–X5$, and $X2–X5$ lines (a)–(c) compared to the calculated functions between the $|01⟩$ and $|10⟩$, $|10⟩$ and $|11⟩$, and $|01⟩$ and $|11⟩$ states (g)–(i). All measurements show strong deviations from the uncoupled case $g^{(2)}(\tau )=1$ [see Fig. 1c], with minimum values at zero delay time of 0.16 (a), 0.32 (b), and 0.25 (c). Figures 4d, 4e, 4f show a level scheme of the states as used in the model, where $|00⟩$ corresponds to the ground state, $|01⟩$ and $|10⟩$ to the single exciton state, and $|11⟩$ to the interdot biexciton state. The calculated correlation functions (dots) were convolved with a Gaussian curve that reflects the $\sim 700\mathrm{ps}$ time resolution of the experimental system (lines).