Coulomb-assisted cavity feeding in nonresonant optical emission from a quantum dot

Recent experiments have demonstrated that for a quantum dot in an optical resonator, off-resonant cavity-mode emission can occur even for detunings of the order of 10 meV. We show that Coulomb-mediated Auger processes based on additional carriers in delocalized states can facilitate this far off-resonant emission. A theoretical approach is developed for the nonperturbative treatment of the Auger-assisted quantum-dot carrier recombination. Using this method we present numerical calculations of the far off-resonant cavity feeding rate and cavity mean photon number, confirming efficient coupling at higher densities of carriers in the delocalized states. In comparison to fast Auger-like intraband scattering processes, we find a reduced overall efficiency of Coulomb-mediated interband transitions due the required electron-hole correlations for the recombination processes.

Figure 1

Cavity feeding rate for a nonresonant QD coupled to the continuum of WL states at a temperature of 77 K obtained by using the SWA. We vary the WL carrier density $n_{\mathrm{WL}}$ from ${10}^8$ to ${10}^{12}$/cm${}^2$ and consider electron and hole envelopes that are equal (lines without dots) or differ by a factor of 2 (lines with dots). In all calculations we use ${\alpha }^h=0.15/$nm. For comparison the spontaneous emission rate is shown (dotted line) for typical parameters ($\kappa =0.1/$ps, $\Gamma =0.01/$ps, $P=0.1/$ps). Note that the rates are normalized to the square of the light-matter coupling strength.

Figure 2

Steady-state cavity mean photon number generated by an off-resonant QD mediated by the continuum of WL states for a carrier density of ${10}^{12}/$cm${}^2$ by using the SWA (solid) and the SPA (dashed dotted) for a temperature of 77 K. Additionally, results for nonequal envelopes (lines with dots) and pure JC coupling (dotted) are shown. Typical parameters are used ($g=0.1/$ps, $\kappa =0.1/$ps, $\Gamma =0.01/$ps, $P=0.1/$ps).

Figure 3

Influence of artificial renormalization/broadening of the SPA result, as a consequence of uncorrelated electrons and holes. Shown is the steady-state mean photon number for a carrier density of ${10}^{12}/$cm${}^2$, a temperature of 77 K, and nonequal envelopes ${\alpha }^e/{\alpha }^h=2$. Without broadening the dashed-dotted line corresponds to the result in Fig. 2.