Competition between pure dephasing and photon losses in the dynamics of a dot-cavity system

We demonstrate that in quantum-dot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both dephasing mechanisms strongly affects the transition from the weak- to the strong-coupling regime as well as the shape of the spectral triplet that represents the quantum-dot occupation in Fourier space. The width of the central peak in the triplet is expected to decrease with rising temperature, while the widths and heights of the side peaks depend nonmonotonically on the dot-cavity coupling.

Figure 1

Real parts of the eigenvalues of the matrix $M$ in Eq. (1) as a function of the bare light-matter coupling $g$ calculated with $\kappa =0.1{\mathrm{ps}}^{-1}$ and $r=0.001{\mathrm{ps}}^{-1}$ assuming a constant pure dephasing rate $\gamma =0.01{\mathrm{ps}}^{-1}$ and $\tilde{g}=g$ (thin green lines) and using $\gamma$ and $\tilde{g}$ obtained from path-integral calculations for the microscopic model of a spherical GaAs dot with radius 3 nm at $T=10$ K (thick blue lines). The inset shows the imaginary part of ${\lambda }_{+}$ ($\mathrm{Im}\left[{\lambda }_0\right]=0$, $\mathrm{Im}\left[{\lambda }_{-}\right]=-\mathrm{Im}\left[{\lambda }_{+}\right]$).

Figure 2

Pure dephasing damping rate $\gamma \left(g\right)$ and renormalized light-matter coupling $\tilde{g}\left(g\right)/g$ obtained as a function of the bare light-matter coupling $g$ by fitting path-integral calculations for the microscopic model at three temperatures using Eqs. (4, 5, 6).

Figure 3

Real parts of the eigenvalues ${\lambda }_{\pm }$ of the matrix $M$ in Eq. (1) calculated at selected temperatures with parameters $\kappa =0.1{\mathrm{ps}}^{-1}$ and $r=0.001{\mathrm{ps}}^{-1}$ and using values for $\gamma (g,T)$ and $\tilde{g}(g,T)$ obtained from the microscopic path-integral calculations. The thin green line labeled “no shift” represents a calculation accounting for $\gamma (g,T)$ at $T=100$ K but without the renormalization of the light-matter coupling, i.e., $\tilde{g}=g$.

Figure 4

Real eigenvalue ${\lambda }_0$ of the matrix $M$ in Eq. (1) calculated for the same parameters and conditions as ${\lambda }_{\pm }$ shown in Fig. 3.

Figure 5

Solid lines: spectra $\mathrm{Re}\left[{\rho }_{11}\left(\omega \right)\right]$ calculated for different values of the dot-cavity coupling $g$ at $T=10$ K and $\kappa =0.1$, $r=0.001{\mathrm{ps}}^{-1}$. Dashed lines: $\mathrm{Re}\left[{\rho }_{11}\left(\omega \right)\right]$ calculated for $\kappa =r=0$ with otherwise identical parameters. The heights of all central peaks as well as of the side peaks for $g=0.1{\text{ps}}^{-1}$ and $\kappa =r=0$ (dashed black line) are clipped to improve the visibility of the other side peaks.

Figure 6

(a) Full width at half maximum (FWHM) of the central peak in the spectra $\mathrm{Re}\left[{\rho }_{11}\left(\omega \right)\right]$ as a function of the dot-cavity coupling $g$ calculated at $T=10$ K (blue dashed line with squares), $T=50$ K (purple dashed line with triangles), and $T=100$ K (red dashed line with circles). Triplet spectra at $T=10$ (thin blue line), $T=50$ K (purple line), and $T=100$ K (thick red line) calculated for (b) $g=0.075{\mathrm{ps}}^{-1}$ and (c) $g=0.15{\mathrm{ps}}^{-1}$. In all panels, $\kappa =0.1{\mathrm{ps}}^{-1}$ and $r=0.001{\mathrm{ps}}^{-1}$.