Phonon mediated off-resonant quantum dot–cavity coupling under resonant excitation of the quantum dot

We propose a model for phonon-mediated off-resonant quantum dot–cavity coupling and use it to successfully explain recently observed resonant quantum dot spectroscopic results. We explicitly incorporate the effect of phonons, which explains the role of temperature in the coupling mechanism and predicts an asymmetry in the coupling depending on whether the quantum dot is red or blue detuned with respect to the cavity. We show that the off-resonant coupling is enhanced by the cavity; in the absence of such enhancement, the coupling strength is greatly diminished at higher dot-cavity detunings. These results demonstrate that phonon-mediated processes effectively extend the detuning range in which off-resonant QD-cavity coupling may occur beyond that given by pure dephasing processes.

Figure 1

(a), (b) Energy levels of the coupled QD-cavity system where the QD is blue (a) and red (b) detuned from the cavity. A laser drives the quantum dot [transition between ground state $\left(1\right)$ and excited state $\left(2\right)$] resonantly. The excited state $\left(2\right)$ can decay via two paths: The first is by direct decay back to the ground state $\left(1\right)$ via the spontaneous emission; the second is by indirect decay via the emission [Fig. 1a] or absorption [Fig. 1b] of a phonon [transition $\left(2\right)$ to $\left(3\right)$] and subsequent emission of a photon at the cavity frequency [transition $\left(3\right)$ to $\left(1\right)$]. (c), (d) Emission $S\left(\omega \right)$ as a function of frequency $\omega$ for a resonantly driven QD, which is blue (c) and red (d) detuned from the cavity, where ${\omega }_l$ is the laser frequency. Three different cases are considered: without any dephasing, with pure dephasing, and with a cavity-enhanced phonon process. We observe the Mollow triplet at the QD frequency in all three cases. The insets of (c) and (d) show an enlarged view of the emission at the cavity frequency. For the simulation we assume $g/2\pi =\kappa /2\pi =20$ GHz, $\gamma /2\pi =1$ GHz, $\Omega /2\pi =6$ GHz, and QD-cavity detuning $\Delta =\pm 6\kappa$.

Figure 2

Theoretical resonance fluorescence $I$ collected from the cavity and QD linewidth for a blue-detuned QD ($\Delta >0$): (a) Normalized cavity fluorescence as a function of the Rabi frequency $\Omega$ of the laser for two models. Saturation of the cavity emission is observed. (b) Power broadened QD linewidth (read through the cavity, as in Ref.18) vs laser Rabi frequency $\Omega$ for QD-cavity detuning $\Delta /2\pi =6$ GHz. (c) Dependence of the saturated cavity emission $I_{sat}$ on the dot-cavity detuning $\Delta$. (d) Dependence of the intrinsic QD linewidth $\Delta {\omega }_0$ on dot-cavity detuning $\Delta$. $\Delta {\omega }_0/2\pi$ approaches $2(\gamma +{\gamma }_d)/2\pi$ or $2(\gamma +{\gamma }_r)/2\pi$ (both chosen to be 4 GHz) with large $\Delta$. (Parameters used for all the simulations are $\kappa /2\pi =g/2\pi =20$ GHz and $\gamma /2\pi =1$ GHz.)

Figure 3

(a) The difference in QD linewidths measured via collected emission through the off-resonant cavity for a blue ($\Delta {\omega }_{+}$) and a red ($\Delta {\omega }_{-}$) detuned QD for different values of the excitation laser Rabi frequency $\Omega$ as a function of the bath temperature $T$. (b) Ratio of the cavity intensity for an off-resonant QD blue $\left(I_{+}\right)$ and red $\left(I_{-}\right)$ detuned from the cavity as a function of the bath temperature $T$. For all the simulations, the absolute value of the QD-cavity detuning is kept at $10\kappa$.

Figure 4

Experimentally observed off-resonant cavity emission as a function of the detuning $\Delta$ between the resonantly driven QD and the cavity. Data are fitted with a model ${\Delta }^{-\alpha }$. Extracted values of $\alpha$ for the different curves are shown.

Figure 5

Resonance fluorescence $I$ collected from the cavity for a blue-detuned QD ($\Delta >0$). (a) ${\log }_e\left(I\right)$ as a function of the rates ${\gamma }_d$ and ${\gamma }_r$ (for two models, respectively). $\Delta /\kappa =10$. (b) ${\log }_e\left(I\right)$ as a function of the cavity linewidth $\kappa$, when the dot-cavity detuning $\Delta =10\kappa$. (c) QD linewidth as a function of the rates ${\gamma }_d$ and ${\gamma }_r$ for pure dephasing and the cavity-enhanced phonon process, respectively. In both cases, $\Omega /2\pi =1$ GHz and $\Delta =12\kappa$. The solid black line shows the theoretical estimates of the QD linewidth when the laser excitation power is very low and the QD is not significantly perturbed by the cavity. (Parameters used for all the simulations are $g/2\pi =\kappa /2\pi =20$ GHz and $\gamma /2\pi =1$ GHz.)