Probing the ladder of dressed states and nonclassical light generation in quantum-dot–cavity QED

We investigate the photon-induced tunneling phenomena in a photonic crystal cavity containing a strongly coupled quantum dot and describe how this tunneling can be used to generate photon states consisting mainly of a particular Fock state. Additionally, we study experimentally the second-order autocorrelation $g^2\left(0\right)$ in the photon-induced tunneling regime as a function of the frequency and the power of the probe laser and observe signs of higher manifolds of the Jaynes-Cummings Hamiltonian in the frequency-dependent photon statistics of the transmitted light, as well as the strong power dependence of $g^2\left(0\right)$, distinguishing this effect clearly from bunching occurring in a thermal light source.

Figure 1

(a) Schematic of the coupled QD-cavity system driven by a Gaussian pulse (coherent state $|\alpha \rangle$). The transmitted light through the cavity is nonclassical ($|\psi \rangle$) due to the nonlinearity provided by the strongly coupled QD-cavity system. (b) The anharmonic Jaynes-Cummings ladder structure.

Figure 2

Numerically calculated photon statistics at the output of the QD-cavity system driven by Gaussian pulses with duration ${\tau }_p\sim 24$ ps. The simulation parameters are $g=2\pi \times 40$ GHz, $\kappa =2\pi \times 4$ GHz, and ${\mathcal{E}}_o=2\pi \times 9$ GHz; pure QD dephasing is neglected. (a) $P\left(n\right)$, probability of generating an $n$ photon state at the cQED system output as a function of laser-cavity detuning ${\Delta }_c$. (b) The ratios $r_1$ and $r_2$ (see text for details) as a function of ${\Delta }_c$. $r_m=\frac{P{\left(m\right)}^2}{P(m-1)P(m+1)}$, where $P\left(m\right)$ is the probability of having $m$ photons in the light. The dotted lines show the expected values of the ratios from a classical coherent state. (c) Second-order autocorrelation $g^{\left(2\right)}\left(0\right)$ as a function of ${\Delta }_c$. The red dashed line shows the expected $g^{\left(2\right)}\left(0\right)$ for a coherent state. (d) Second-order differential correlation $C^{\left(2\right)}\left(0\right)$ as a function of ${\Delta }_c$. (e) $C^{\left(2\right)}\left(0\right)$ as a function of the laser-cavity detuning ${\Delta }_c$ for different values of the peak laser field ${\mathcal{E}}_o/2\pi$ (in units of GHz). Every plot is normalized by the maximum $C^{\left(2\right)}\left(0\right)$, so that the peak value becomes 1 for all the plots. We observe that the peak in the $C^{\left(2\right)}\left(0\right)$ occurs at ${\Delta }_c=0.7g$ for weaker excitation (where the second-order manifold is excited resonantly via two photons). However, with increasing excitation power, the peak positions shifts toward ${\Delta }_c=0$ due to excitation of higher manifolds.

Figure 3

(a) The transmission spectrum of a strongly coupled QD-cavity system showing two polaritons. (b) Second-order coherence function at $t=0$, $g^{\left(2\right)}\left(0\right)$ as a function of the laser detuning from the empty cavity frequency. The system is excited with ${\tau }_p=24$ ps Gaussian pulses, with 80 MHz repetition frequency. The dashed gray (solid black) line results from a numerical simulation based on the system's experimental parameters and no (with) QD blinking. The average laser power for the measurement is $P_{\text{avg}}=0.2$ nW. For the simulations we use a QD dephasing rate ${\gamma }_d/2\pi =1$ GHz.

Figure 4

(a) Normalized differential correlation function $C^{\left(2\right)}\left(0\right)$ as a function of the laser detuning. The dashed red line shows the result of a numerical simulation based on the system's experimental parameters. (b) $g^{\left(2\right)}\left(0\right)$ in the tunneling regime (${\Delta }_c=0$) as a function of laser power $P_{\text{avg}}$ measured in front of the objective lens. The solid line shows the result of numerical simulation including the effects of QD blinking, while the inset plots the numerically simulated $g^{\left(2\right)}\left(0\right)$ in the absence of blinking. For the simulations we use a QD dephasing rate ${\gamma }_d/2\pi =1$ GHz.