Controlling coherence between waveguide-coupled quantum dots

Abstract

We present a novel waveguide design that incorporates a split-diode structure, allowing independent electrical control of transition energies of multiple emitters over a wide range with minimal loss in waveguide coupling efficiency. We use this design to systematically map out the transition from superradiant to independent emission from two quantum dots. We perform both lifetime as well as Hanbury Brown-Twiss measurements on the device, observing anti-dips in the photon coincidences indicating collective emission while at the same time observing a drop in lifetime around zero detuning, indicating superradiant behaviour. Performing both measurement types allows us to investigate detuning regions which show both superradiant rate enhancement and inter-emitter coherence, as well as regions in which correlations persist in the absence of rate enhancement.

Figures (3)

• Figure 1: Independent tuning of QDs and properties of superradiant emission (a) Energy level diagram of two resonant waveguide-coupled QDs. The states $|e_1, e_2\rangle$ and $|g_1, g_2\rangle$ describe both QDs in their excited and ground states, respectively. The spectral detuning and dephasing rate are labelled $\Delta$ and $\gamma_d$. (b) Energy level diagram of two independent quantum emitters. The state $|e_1, g_2\rangle$ ($|g_1, e_2\rangle$) signifies that $X^-_{QD1}$ ($X^-_{QD2}$) is excited, while the other QD is in the ground state. (c) Expected intensity decay for an ideal system of two superradiant emitters with identical decay rates $\gamma$ given the depicted excitation scheme. (d) Expected autocorrelation function $g^{(2)}(\tau)$ for a pair of superradiant emitters with identical decay rates $\gamma$ given the depicted excitation scheme. (e) SEM image of the waveguide device. The positions of the two QDs are marked by white spots. The red and blue colouring marks the area of the two diodes that control the two QDs. Yellow indicates the areas that are etched for electrical isolation. Inset – SEM of the isolation etch in the waveguide. (f) Emission spectrum of the $X^-$ transitions of the two QDs, measured from the outcoupler of the device, as a function of the voltage applied to QD2 (voltage applied to the red area in (e)).
• Figure 2: Enhancement of emitter decay rate. (a) Comparison of the decay curves of the system with the QDs detuned by (i) $0$ µ eV, (ii) 1.1 µ eV, (iii) 2.2 µ eV and (iv) 3.3 µ eV. Measurements are performed with (yellow) and without (black) optical gating of QD2. Coloured lines indicate where the intensity drops below the thresholds used in (b) and (c). (b) Detuning dependence of the decay rate with (lighter lines) and without (darker lines) gating of QD2. The results are plotted as the time taken for the emission intensity to drop below three threshold values: $I_0/2$ (blue), $I_0/e$ (green) and $I_0/10$ (red). (c) Theoretical prediction of the results in (b). The shaded regions signify uncertainties in the model due to errors in the $X^-_{QD1}$ lifetime estimation (see main text).
• Figure 3: Photon correlations. Autocorrelation function of emission collected from the end of the waveguide as a function of emitter-emitter detuning. The yellow lines are theoretical predictions of the measurements.