Explanation of Photon Correlations in the Far-Off-Resonance Optical Emission from a Quantum-Dot–Cavity System

In a coupled quantum-dot–nanocavity system, the photoluminescence from an off-resonance cavity mode exhibits strong quantum correlations with the quantum-dot transitions, even though its autocorrelation function is classical. Using new pump-power dependent photon-correlation measurements, we demonstrate that this seemingly contradictory observation that has so far defied an explanation stems from cascaded cavity photon emission in transitions between excited multiexciton states. The mesoscopic nature of quantum-dot confinement ensures the presence of a quasicontinuum of excitonic transitions, part of which overlaps with the cavity resonance.

Figure 1

QD background emission and level structure. (a) Typical QD PL spectrum on a semilogarithmic scale. Besides the well-known discrete QD lines, the weak background responsible for cavity feeding is visible. (b) Calculated energy-level diagram ($n\le 3$) of a neutral QD assuming a truncated parabolic in-plane confinement potential (energy separations between manifolds not to scale). (c) Calculated transition rates between states of different manifolds. States from $n\ge 2$ manifolds can decay into a large number of final states, thus forming a quasicontinuum of allowed transitions that can feed the CM.

Figure 2

Off-resonant cavity emission as a function of pump power. (a) Pump-power dependence of CM, $X^0$, $X^{1-}$, and $X{X}^0$ emission. The data were obtained by integrating PL intensities for different excitation powers in $\approx 0.3\mathrm{nm}$ wide windows around the different QD lines indicated in Fig. 1a. The CM exhibits complex dynamics due to cavity feeding from higher-lying multiexcitonic states. (b) Comparison of CM emission with the emission from the different QD shells. The CM dynamics is clearly dominated by the QD $s$ shell for powers below 500 nW, while at higher powers the $p$ shell takes over.

Figure 3

Experimental correlation histograms. (a)–(c) Cross correlations between the CM and the $X^0$ for different pump powers. $\tau >0$ refers to $X^0$ emission upon detection of a cavity photon. The bunching feature for $\tau >0$ disappears when increasing the pump power, as expected from our model. The time scale for the antibunching feature for negative delays reflects the repump time of the system. (d)–(e) CM autocorrelations for two different pump powers. Below saturation, clear bunching at $\tau =0$ is visible which disappears above saturation, in agreement with the model.

Figure 4

Simulation of cavity-feeding dynamics. (a) Monte Carlo random walk of excitation and photon-emission events (gray lines). The green horizontal lines correspond to the energy levels presented in Fig. 1b. Transitions resonant with the CM, $X^0$, and $X{X}^0$ lines are depicted in red, blue, and black, respectively. (b) Extracted CM-$X^0$ cross-correlation histogram reproducing the characteristic features observed in the experiment [compare Fig. 3c]. (c) Extracted CM autocorrelation curve, exhibiting strong bunching at zero time delay in accordance with the experimental result of Fig. 3e.