Phonon effects on the radiative recombination of excitons in double quantum dots

We study theoretically the radiative recombination of excitons in double quantum dots in the presence of carrier-phonon coupling. We show that the phonon-induced pure dephasing effects and transitions between the exciton states strongly modify the spontaneous emission process and make it sensitive to temperature, which may lead to nonmonotonic temperature dependence of the time-resolved luminescence. We show also that, under specific resonance conditions, the biexcitonic interband polarization can be coherently transferred to the excitonic one, leading to an extended lifetime of the total coherent polarization, which is reflected in the nonlinear optical spectrum of the system. We study the stability of this effect against phonon-induced decoherence.

Figure 1

The phonon spectral density for a few values of the interdot distance $D$.

Figure 2

The decay of the exciton occupation for three different initial states as shown for $D=6$ nm, $\theta =-\pi /6$, $T=4$ K. (a) Without carrier-phonon interaction; (b) with phonons, for $2\mathcal{E}=1.77$ meV; (c) with phonons, for $2\mathcal{E}=3.55$ meV.

Figure 3

The decay of the exciton occupation for the initial state $\left(\right|1\rangle +|2\rangle )/\sqrt{2}$ for $D=6$ nm. (a) Dominated by relaxation ($\theta =-\pi /3$) with strong carrier-phonon coupling ($2\mathcal{E}=1.77$ meV); (b) as previously, but with much weaker phonon effects ($2\mathcal{E}=7.1$ meV); (c) dominated by pure dephasing ($\theta =0$, $2\mathcal{E}=0$).

Figure 4

The decay time of the DQD photoluminescence. (a) A single DQD with $\Delta =0.5$ meV and $V=-0.2$ meV (red solid line), $-1$ meV (black dotted line), $-3$ meV (blue dashed line), and $-8$ meV (green dashed-dotted line). (b) An ensemble of DQDs with constant values of the coupling $V$ as in (a), with the average energy mismatch $\overline{\Delta }=0$, and with the standard deviation of $\Delta$ equal to $\sigma =0.5$ meV. (c) An ensemble of DQDs for $\overline{\Delta }=0$ and for three values of the standard deviation of $\Delta$: $\sigma =1$ meV (red solid line), 3 meV (blue dashed line), and 10 meV (green dashed-dotted line).

Figure 5

The evolution of single-exciton, biexciton, and total optical coherence for a DQD with $2\mathcal{E}=3$ meV in the absence of interaction with phonons. (a)–(c) Uncoupled dots with $E_{\mathrm{B}}=-3$, $-3.01$, and $-3.1$ meV, respectively. (d)–(f) Coupled dots with $\theta =-\pi /3$ and with the same values of $E_{\mathrm{B}}$ as in (d)–(f), respectively. In all the panels, the red solid line shows the total polarization, the green dashed line represents the biexciton polarization, and the blue dotted line shows the single-exciton polarization. The evolution of the average exciton occupation (scaled down by a factor of 3 to fit to the polarization amplitudes) is shown with gray dashed-dotted lines for comparison.

Figure 6

The evolution of single-exciton, biexciton, and total optical coherence for a DQD with $2\mathcal{E}=3$ meV with the carrier-phonon coupling taken into account. The value of $E_{\mathrm{B}}$ is taken at resonance. (a)–(c) Uncoupled dots at $T=0$, 10, and 20 K, respectively. (d)–(f) Coupled dots with $\theta =-\pi /3$ at the same three temperatures. Line coding as in Fig. 5.

Figure 7

The pump-probe absorption spectra (see text) at $T=4$ K (a), 10 K (b), and 20 K (c). Each plot shows three lines corresponding to exact resonance (red solid lines) and to a detuning of $0.05$ and $-0.05$ meV from the resonance (blue dotted and green dashed lines, respectively). Here, $2\mathcal{E}=3$ meV, $\theta =-\pi /3$.