Direct observation of acoustic phonon mediated relaxation between coupled exciton states in a single quantum dot molecule

We probe acoustic phonon mediated relaxation between tunnel coupled exciton states in an individual quantum dot molecule in which the interdot quantum coupling and energy separation between exciton states is continuously tuned using static electric field. Time resolved and temperature dependent optical spectroscopy are used to probe interlevel relaxation around the point of maximum coupling. The radiative lifetimes of the coupled excitonic states can be tuned from $\sim 2\mathrm{ns}$ to $\sim 10\mathrm{ns}$ as the spatially direct and indirect character of the wave function is varied by detuning from resonance. Acoustic phonon mediated interlevel relaxation is shown to proceed over time scales comparable to the direct exciton radiative lifetime, indicative of a relaxation bottleneck for level spacings in the range $\mathrm{\Delta }E\sim 3-6\mathrm{meV}$.

Figure 1

(Color online) (a) PL spectra of a single QDM as a function of the electric field. (Inset) Schematic of the $n-i$ Schottky diodes studied. (b) Upper panel, experimental (symbols) and calculated (dashed lines) exciton energies for $X_A$ and $X_B$. Middle panel, energy splitting between $X_A$ and $X_B$ and fitting (see text). Lower panel, relative intensities $I_{A,B}∕(I_A+I_B)$ and the resonant field (dashed line).

Figure 2

(Color online) (a) Normalized PL decay curves for $X_A$ and $X_B$ measured at $F-F_{\mathrm{crit}}=2.6\mathrm{kV}∕\mathrm{cm}$, plotted in a semilog scale. Dashed and the solid lines are fits with a monoexponential function and a biexponential function, respectively. (b) The PL decay rates for $X_A$ $\left(D_a\right)$ (solid circles) and $X_B$ (solid squares) obtained by the monoexponential fittings. Total population decay rates for $X_B$ $\left(D_b\right)$ (open squares) based on the rate equation model discussed in the text are also shown.

Figure 3

(Color online) (a) Experimental (solid squares) and calculated (solid line) radiative recombination rates plotted as a function of $F$. (Inset) schematic processes for radiative recombinations of the exciton states $X_A$ and $X_B$, relaxation between them, and electron capture. (b) Phonon relaxation rate $\gamma ={\gamma }_0$ at $4.2\mathrm{K}$ from $X_A$ to $X_B$ obtained from the time-resolved PL and rate-equation model.

Figure 4

(Color online) (a) Experimental and (b) calculated relative intensities of $X_A$ and $X_B$ at $4.2\mathrm{K}$ and $45\mathrm{K}$.