Linear spectrum of a quantum dot coupled to a nanocavity

We develop a theoretical formalism to model the linear spectrum of a quantum dot embedded in a high-quality cavity, in the presence of an arbitrary mechanism modifying the homogeneous spectrum of the quantum dot. Within the simple assumption of Lorentzian broadening, we show how the known predictions of cavity quantum electrodynamics are recovered. We then apply our model to the case where the quantum dot interacts with an acoustic-phonon reservoir, producing phonon sidebands in the response of the bare dot. In this case, we show that the sidebands can sustain the spectral response of the cavitylike peak even at moderate dot-cavity detuning, thus, supporting recent experimental findings.

Figure 1

Imaginary part of the quantum dot susceptibility in presence of longitudinal acoustic-phonon coupling (full) and without phonons (dashed), computed at $T=10\text{K}$. As an illustration, we plot the cavity mode optical density at 1 meV positive detuning (dotted).

Figure 2

Plot of the emission spectrum of the QD-cavity system in the presence of phonons (solid line) for different detunings $D={\omega }_0-{\omega }_C$. a) $D=-1\text{meV}$, b) $D=0\text{meV}$, c) $D=1\text{meV}$, and d) $D=2\text{meV}$ $\left(k_{B}T=10\text{K}\right)$. Comparison with no phonons (dashed line) is also given.

Figure 3

(Color online) Emission spectrum of the QD-cavity system plotted for different values of $k_{B}T$ (arbitrary units), ${\omega }_c-{\omega }_0=1\text{meV}$.