Resonance Fluorescence of GaAs Quantum Dots with Near-Unity Photon Indistinguishability

Photonic quantum technologies call for scalable quantum light sources that can be integrated, while providing the end user with single and entangled photons on demand. One promising candidate is strain free GaAs/AlGaAs quantum dots obtained by aluminum droplet etching. Such quantum dots exhibit ultra low multi-photon probability and an unprecedented degree of photon pair entanglement. However, different to commonly studied InGaAs/GaAs quantum dots obtained by the Stranski–Krastanow mode, photons with a near-unity indistinguishability from these quantum emitters have proven to be elusive so far. Here, we show on-demand generation of near-unity indistinguishable photons from these quantum emitters by exploring pulsed resonance fluorescence. Given the short intrinsic lifetime of excitons and trions confined in the GaAs quantum dots, we show single photon indistinguishability with a raw visibility of , without the need for Purcell enhancement. Our results represent a milestone in the advance of GaAs quantum dots by demonstrating the final missing property standing in the way of using these emitters as a key component in quantum communication applications, e.g., as quantum light sources for quantum repeater architectures.


Time-correlated single-photon counting fit function including convolution with internal response function
We recorded the internal response function of our full setup by time-correlated photon counting of a short laser pulse resonant to the quantum dot transition, attenuated to count rates similar to the quantum dot, and its electrical trigger signal. The internal response function is used for a convolution with our fitting function: Here, Θ (t − t 0 ) is the Heaviside step function, which is multiplied with our main decay and an additional slow decay. t 0 and t 1 act as offsets in time, τ main and τ slow are decay times and f defines the frequency of the modulation. The main decay corresponds to the excited state life time and is modulated by a sine squared for fitting the exciton time-correlated single-photon counting data. We attribute the second slow decay with a decay time constant of τ slow = (550 ± 20) ps to spin flip-flop processes which give rise to an on-and-off blinking of the exciton transition. This second decay, with an amplitude 1000 times weaker than the main decay of the exciton, is not present for the trion and biexciton transitions (not shown), which makes it very likely that it indeed stems from spin flip-flop processes. We use the same fitting function, without the second slow decay and without the modulation to fit our trion time-correlated single-photon counting data.

Polarization resolved photoluminescence spectroscopy
To confirm the fine structure splitting of the exciton state, which we extracted from the oscillation in the time-correlated single-photon counting measurement, we recorded additional polarization resolved photoluminescence spectra under non-resonant excitation. For this we replaced the quarter-with a half waveplate before the polarizing beam splitter and recorded the quantum dot spectrum for different linear polarization angles and fitted the exciton transition with a Gaussian function. The corresponding measurement is depicted in Fig. S1 where we plot the exciton emission energy as a function of half waveplate angles. The data is

Analysis of two-photon interference measurements
We would like to point out that the quality of a fit to two-photon interference measurement data benefits strongly from high time resolution. In particular, it is crucial to be able to resolve possible quantum beats 3 and the dip (volcano shape) at time delay zero 4 in the measurement, otherwise the visibility will be overestimated when fitting the data. In Fig. S2 a), we show the raw data of the two-photon interference measurement of QD4, demonstrating that we can resolve quantum beats. Fig. S2 b) is a zoom in of the raw data around zero time delay, which shows the volcano shape resolved by our measurement. The reason for the above-mentioned overestimation is that the central peak will look like a single broader peak if the dip is not resolved. The error occurs when the data is fitted: The decay of all the quintuplet peaks are defined by the lifetime of the systems which is usually a shared fitting parameter of the quintuplet peaks.
Independently of the peak function used (ideally one should use the same fitting function as used for time-correlated single-photon counting, i.e. in the ideal case an exponential decay) the central peak width will be underestimated thanks to the larger statistics in the side peaks and the low maximum correlation events at time delay zero. To prove our point we artificially reduce our time resolution by binning the correlation data to time bins of 256 ps. The binned data is plotted in Fig. S2 c) to f). In all cases, the central peak of the quintuplet in the binned data does not show a sign of quantum beats and is not volcano shaped, due to the too low time resolution. For a comparison we now fit the quintuplet with commonly used fit functions, i.e., Lorentzian functions (Fig. S2 c)), Gaussians (Fig. S2 d)), Voigts (Fig. S2 e)) and exponential decays (Fig. S2 f)) and extract a two-photon interference visibility of V raw = 1 − 2×A 2 A 1 +A 3 from the fitted peak areas. The resulting visibilities, as well as the corrected visibilites are summarized in Table S1. This demonstrates that the visibility extracted from the binned data with reduced time resolution, independently of used fit function, is always overestimating the visibility compared to the raw data. Table S1: Overview of Hong-Ou-Mandel visibilities for the same data with bins summed up (raw) and fitted with different functions corrected and uncorrected with the maximally achievable visibility in our setup. Results for three different quantum dots are shown.  This time window is determined as follows: Since neighboring peaks are slightly overlapping, the time delays, for which the overlapping areas are the same, have to be determined.
Therefore, all peaks in the quintuplet are fitted with an exponential decay. The decay time is fixed in the fit and given by the lifetime of the transition which is extracted from a separate measurement using the fitting method explained above. Figure S3 a) shows a schematic histogram with a lifetime of 300 ps. The lifetime is chosen to be slightly higher compared to the typically measured lifetimes in order to make the overlap more visible. Figure S3 b) shows the overlap of two neighboring peaks in more detail. The intersections of two neighboring fits mark the wanted time delay (orange line in Fig. S3 b)). Here the overlapping areas (dark red and blue) of two peaks are the same, as shown in the graph. We want to point out that this intersection is not in the middle of the two peaks (which would be at 3 ns in the shown case) and varies even more for intersections between the center peak and side peaks due to the much lower number of coincidence events in the center peak. This method leads to individual time windows for each transition, given by the lifetime and peak height. The determined time windows are summarized in Table S2 for all transitions.  Figure S3: a) Schematic histogram with exponential decays and a lifetime of 300 ps. b) Zoom-in of the area marked with a black rectangle in a). The overlapping areas (dark blue and red) of the peaks are the same, when cutting at the time delay where the peaks intersect.