Non-Markovian Model of Photon-Assisted Dephasing by Electron-Phonon Interactions in a Coupled Quantum-Dot–Cavity System

We investigate the influence of electron-phonon interactions on the dynamical properties of a quantum-dot–cavity QED system. We show that non-Markovian effects in the phonon reservoir lead to strong changes in the dynamics, arising from photon-assisted dephasing processes, not present in Markovian treatments. A pronounced consequence is the emergence of a phonon induced spectral asymmetry when detuning the cavity from the quantum-dot resonance. The asymmetry can only be explained when considering the polaritonic quasiparticle nature of the quantum-dot–cavity system. Furthermore, a temperature induced reduction of the light-matter coupling strength is found to be relevant in interpreting experimental data, especially in the strong coupling regime.

Figure 1

Evolution of the excited state population $s_{11}(t)$ for $\hslash g=140\mu \mathrm{eV}$, $\hslash \kappa =100\mu \mathrm{eV}$, $Q\approx {10}^4$, and $T=4\mathrm{K}$.

Figure 2

$t\to \infty$ limit of $\hslash {\gamma }_{12}(t)$ (blue [dark gray]) and $\hslash {\mathcal{G}}^{\gtrless }(t)$ (green [light gray] or red [medium gray]) for the parameters $\hslash g=140\mu \mathrm{eV}$ and $T=4\mathrm{K}$. $\mathrm{Im}[\hslash {\gamma }_{12}(\infty )]$ has the constant value $32.7\mu \mathrm{eV}$.

Figure 3

Real part of $\hslash {\gamma }_{12}(\infty )$ (solid) and $\hslash {\mathcal{G}}_R(\infty )$ (dashed) for $\hslash g=50$ (blue [dark gray]), 100 (red [medium gray]), 150 (green [light gray]) $\mu \mathrm{eV}$. The imaginary parts are independent of temperature and much smaller than the real part and therefore not shown.

Figure 4

Parameter space showing the presence of strong or weak coupling for the full model (solid line) and for ${\mathcal{G}}^{\gtrless }(t)=0$ (dashed line), with $\hslash \kappa =75$ (red [medium gray]), 125 (blue [dark gray]), 175 (green [light gray]), 225 (black), 275 (magenta [light-medium gray]) $\mu \mathrm{eV}$.