Interplay of coupling and superradiant emission in the optical response of a double quantum dot

We study theoretically the optical response of a double quantum dot structure to an ultrafast optical excitation. We show that the interplay of a specific type of coupling between the dots and their collective interaction with the radiative environment leads to very characteristic features in the time-resolved luminescence as well as in the absorption spectrum of the system. For a sufficiently strong coupling, these effects survive even if the transition energy mismatch between the two dots exceeds by far the emission linewidth.

Figure 1

(Color online) Graphical representation of the energy levels (basis states) and couplings in the double quantum dot system.

Figure 2

(Color online) [(a),(c)] The optical polarization as a function of time after an ultrafast excitation for uncoupled dots $\left(V=V_{\text{B}}=0\right)$ in the linear-response limit $\left(\alpha \to 0\right)$. [(b),(d)] The corresponding spectrum. (a) and (b) show the results for QDs interacting with a common reservoir in the Dicke limit, while (c) and (d) refer to dots radiating into independent reservoirs. Here, $\Gamma =0.01{\text{ps}}^{-1}$ and the values of $\Delta /\hslash$ are as shown in the figure (in ${\text{ps}}^{-1}$). Line definitions in (b) and (d) are the same as in (a) and (c). Dotted lines in (a) and (c) show the envelope $\pm \text{exp}\left(-\Gamma t/2\right)$. The vertical scale in (b) and (d) is the same.

Figure 3

(Color online) The transition from the “different dots” regime to the “identical dots” regime as manifested by the form of the absorption spectrum of a DQD system. Here, $\Gamma =0.01{\text{ps}}^{-1}$ and the values of $\Delta /\hslash$ are shown in the figures. Red solid lines: the actual system; blue dashed lines: the hypothetical system made of two dots interacting with separate reservoirs.

Figure 4

(Color online) (a) The optical polarization as a function of time after an ultrafast excitation for dots coupled by the static dipole moments only $\left(V=0,V_{\text{B}}\ne 0\right)$ for ${\text{tan}}^2\left(\alpha /2\right)=0.2$, $\Gamma =0.01{\text{ps}}^{-1}$, $\Delta /\hslash =0.01{\text{ps}}^{-1}$, and $V_{\text{B}}/\hslash =-0.3{\text{ps}}^{-1}$. Blue dashed line: real part; red solid line: imaginary part. (b) The Fourier transform of the polarization signal. Red solid line: parameters as in (a). Green dashed line: $\Delta /\hslash =0.001{\text{ps}}^{-1}$.

Figure 5

(Color online) Left panels: envelope of the optical beats for two coupled QDs emitting to a common reservoir and to separate reservoirs. For each value of $\Delta /\hslash$ (shown in the plot), the coupling $V$ is adjusted so that $\Omega =3{\text{ps}}^{-1}$ in each case. Right panels: the corresponding absorption spectra. Plots (a) and (b) show the properties of a DQD emitting to a common reservoir, while plots (c) and (d) correspond to two dots emitting to separate reservoirs. Dotted lines in (a) and (c) show exponential decay curves with the rates $\Gamma /2$ and $\Gamma$, while in (b) and (d) they show Lorentzians of equal weight and width $\Gamma /2$.