Resonant excitation of nanowire quantum dots

GaAs quantum dots in nanowires are one of the most promising candidates for scalable quantum photonics. They have excellent optical properties, can be frequency-tuned to atomic transitions, and offer a robust platform for fabrication of multi-qubit devices that promise to unlock the full technological potential of quantum dots. Coherent resonant excitation is necessary for virtually any practical application because it allows, for instance, for on-demand generation of single and entangled photons, photonic clusters states, and electron spin manipulation. However, emission from nanowire structures under this excitation scheme has never been demonstrated. Here we show, for the first time, biexciton–exciton cascaded emission via resonant two-photon excitation and resonance fluorescence from an epitaxially grown GaAs quantum dot in an AlGaAs nanowire. We also report that resonant excitation schemes, combined with above-bandgap excitation, can be used to clean and enhance the emission of nanowire quantum dots.


INTRODUCTION
GaAs 1,2 and InGaAs 3 quantum dots (QDs) are excellent single photons sources in terms of purity and near-unity indistinguishability. GaAs QDs, in particular, have shown the highest degree of photon polarization entanglement 4 . These QDs emit around 780 nm, near the D 2 lines of 87 Rb, a stable and reliable reference frequency to which each emitter can be tuned 5,6 and frequencylocked for quantum network operation 7 . These characteristics make them one of the best candidates for applications in quantum information networks 8,9 .
Resonant excitation of semiconductor QDs 10-13 allows for ondemand operation, by triggering the emission with precisely timed pumping pulses. Resonance fluorescence (RF) of the exciton has been shown to allow a high-precision linewidth scan of the emission line 14 and it is necessary to optically initialize 15 , manipulate 16 , and readout 17 the spin of the exciton. On the other hand, two-photon excitation (TPE) of the biexciton has been shown to be necessary to obtain a clean biexciton emission and a high degree of indistinguishability and entanglement from cascaded emission of GaAs QDs 4 .
In our previous work 18 , we have shown that GaAs QDs can be embedded in AlGaAs nanowires during bottom-up growth in a molecular beam epitaxy reactor, adding new possibilities to the system. For instance, any number of emitters can be precisely positioned within the same nanowire, making the nanowire QDs structure an ideal platform for advanced multi-qubit devices 19,20 that are not possible today with their bulk counterparts. Also, the precise size and position of each emitter can be controlled during growth, enabling tuning of the emission wavelength and fabrication of complex devices. The combined system of QDs in nanowires also provides additional functional advantages, challenging to obtain with QDs in bulk but achievable with nanowires, as for example high extraction efficiency 21,22 , maximal fiber mode coupling 23,24 , positioning in uniform arrays 25,26 , and scalable integration to photonic circuits 27,28 .
However, no coherent resonant excitation of nanowire QDs has been demonstrated to date. The emission of incoherently non-resonantly excited GaAs QDs has been observed to typically have no clean biexciton emission 4 and does not allow for the necessary on-demand operation of the emitters. On the other hand, resonant excitation based on cross-polarization schemes requires excellent filtering of the excitation laser. The rough surfaces and the multiple facets of the nanowire, visible for example in Fig. 1a, scramble the wavefront of the scattered laser, producing a nonuniform polarization which reduces the laser rejection and thus makes it more difficult to separate the scattered excitation from the RF signal. Lack of a clean excitation technique strongly limits the usability of nanowires QDs for practical quantum technology applications.
Here we demonstrate resonant TPE of the biexciton and resonant excitation of the exciton in a nanowire QD. We show that the biexciton, which is barely visible under above band-gap excitation, emerges bright with a clean spectrum under resonant TPE and generates a biexciton-exciton cascaded emission to the ground state.

RESULTS AND DISCUSSION
Optical characterization In Fig. 1a we show a scanning electron microscope image of a nanowire QD, highlighted in blue. The GaAs QD, being very small and embedded inside the AlGaAs, is not visible. Also in Fig. 1, we present the optical characterization of a nanowire QD under above bandgap excitation (Fig. 1b, c) and TPE (Fig. 1d, e), at a temperature of 1.5 K. Figure 1b shows the energy levels and the relevant transitions under above bandgap excitation, where we draw |0>, |X 0 >, and |XX 0 >, the ground state, neutral exciton and biexciton levels, and |0*> and |X*>, the state of a QD filled by a single charge and the charged exciton. Under such excitation every level is excited in a non-deterministic way, producing the typical spectrum in Fig. 1c. In most cases, we observe a bright line, the neutral exciton emission X 0 , and a group of one or more lines at 1-3 nm longer wavelength than the exciton. In the vast majority of cases, the neutral biexciton emission XX 0 is not or barely visible under this type of excitation, while the neutral exciton is always present. Figure 1e shows the schematic of the energy levels and emission under resonant TPE of the biexciton state |XX 0 >. In this case, the laser is tuned at half the energy difference between the ground state and the biexciton. This excites |XX 0 > resonantly via TPE producing the spectrum in Fig. 1d, showing identical intensity for the X 0 and XX 0 lines. For this experiment, the laser passes through a set of ultra-narrow notch filters each with full width at half maximum (FWHM) of 0.4 nm. The first filtering is done on the excitation path, to clean the laser from its tail to avoid it tampering with the detection of the X 0 or XX 0 lines. The second filtering is done on the emission path, suppressing the scattered laser by~7 orders of magnitude. What remains after filtering is visible in the spectrum as a narrow laser line (L) and a broad modulation coming from the remaining tail of the laser. This type of laser rejection allows performing TPE without the use of crosspolarization setups 29,30 thus, for instance, allowing for simultaneous measurements of different polarization projections, used in entanglement demonstrations. For this nanowire QD, the laser also excites a charged exciton X*. This transition is visible, most probably, due to phonon-assisted excitation 31 . This type of excitation, even if low in efficiency, is a process that requires only one photon and thus results in a bright X* line.
Remarkably, our GaAs nanowire QDs show similar optical characteristics to their bulk counterpart of symmetric GaAs QDs 4 , widely studied for their clear potential for quantum photonic applications.
Time-resolved measurements In Fig. 2a, we show the measured fast decay of the X 0 line measured under pulsed above-bandgap excitation. A monoexponential fit, convoluted with the instrument response function of our setup, reveals a radiative recombination lifetime of 409 ± 11 ps.
In Fig. 2b, c, we show the cross-correlation measurements of the neutral exciton with charged exciton or neutral biexciton. The antibunching visible in Fig. 2b proves the X 0 and X* lines are npj Quantum Information (2020) 93 Published in partnership with The University of New South Wales mutually exclusive and thus coming from the same QD, while its large temporal width, as compared to the exciton lifetime, reveals a few-ns-long charging and discharging mechanisms. Given the fast decay of the exciton, the X 0 −X 0 and XX 0 −XX 0 antibunching could not be clearly resolved, but the clear bunching in the X 0 −XX 0 cross-correlation, shown in Fig. 2c, proves cascaded emission. The full set of correlation measurements can be found in the Supplementary Fig. 1.
Excitation power dependencies In Fig. 3 we present the power dependencies of the excitonic lines for both above bandgap and TPE. Figure 3a shows the integrated intensities of X 0 and X* while varying the power of only the green above bandgap laser. As expected in this case, X 0 and X* grow with similar rates until they eventually saturate, in the same range of excitation power. Note that the XX 0 line is not visible under above bandgap excitation, as already observed in epitaxial GaAs QDs 4 , due to the presence of several multi-excitonic lines that suppress the XX 0 line. For this reason, TPE is used to directly address the biexciton state.
In Fig. 3b we show the integrated intensity of all three lines versus the power of the resonant two-photon red laser. In this case, we observe an equal rate for X 0 and XX 0 , as expected for cascaded emission at low excitation powers 29 . This behavior is due to the fact that the exciton state is populated only after the decay of the biexciton state and thus we expect one exciton photon for each biexciton photon. The power of the used excitation laser in the current experimental setup is not enough to reach the saturation condition of the excitonic lines.
Lastly, in Fig. 3c, we show the case of fixed-power TPE with additional application of above bandgap pumping. This slight addition is known to enhance the intensity of X 0 and XX 0 excited via the TPE process 4 . This mechanism is thought to be due to the stabilization of charges and filling of charge traps in the vicinity of the QD, that could otherwise bring the system in long-lived and non-emitting states 32 . This gating mechanism we observe for both TPE (Fig. 1d) and resonant fluorescence (Fig. 4c). In Fig. 3c, we show the effect of such an additional gating laser, which clearly reduces the intensity of X* line in favor of the X 0 and XX 0 lines. At high enough powers of the green laser, the X 0 line is also excited nonresonantly, showing higher intensity than the XX 0 line, just before saturation. We note that this dependence of an additional above-bandgap laser has been observed to change from emitter to emitter. Nonetheless, generally speaking, a very small amount of above bandgap excitation (not enough to directly excite the emitter) results in improved TPE and enhanced emission of X 0 and XX 0 .
Resonant fluorescence In Fig. 4 we show resonant fluorescence measurement of a nanowire QD. A schematic of the measurement configuration used for the experiment is shown in Fig. 4a. This setup, similar to the ones used in previous experimental demonstrations 14,33 on bulk emitters with flat outer surfaces, uses a cross-polarization scheme that allows to distinguish the scattered excitation laser from the QD emission. The excited QDs will, in most cases, emit a mixture of light horizontal (H) and vertical (V) linearly polarized or right-hand (R) and left-hand (L) circularly polarized, while the laser is strongly linearly polarized in only one direction and can, therefore, be efficiently filtered. After passing through the polarizing beam splitter, the laser focused by the lens shows the typical "flower" pattern (see Fig. 4b and Supplementary Note 2 for details) that comes from the focusing 34 . This flower pattern is a result of the non-perfect polarization filtering of a strongly focused beam but shows still virtually no remaining laser in the center, where most of the QD emission is present. This pattern is aligned with a single mode fiber that acts as a pinhole in our confocal system, resulting in a laser rejection of~6 orders of magnitude.
In Fig. 4c we show the integrated intensity of the exciton line of a nanowire QD while scanning the laser through the resonance at an excitation power much lower than the saturation condition. This scan allows us to infer the QD linewidth by a Gaussian fit (assuming inhomogeneous broadening), which shows a FWHM of 118.3 µeV, far from the lifetime-limited emission linewidth for this dot, due to nearby charge fluctuations 35,36 . During the scan, a minimal amount of above-bandgap laser is also applied, only to gate the emission. This helps because it makes it possible to perform a scan with and without QD emission, allowing to correct for the background coming from the remaining laser (see Supplementary Note 3 for details). This scheme was tested on several nanowire QDs, with results varying mostly on laser rejection and not on the underlying physics.
We note that the exciton linewidth did not vary substantially between the three different excitation techniques (FWHM 110 µeV for above bandgap excitation, 104 µeV for TPE, and 108 µeV for RF), while all of them result in a linewidth far from the lifetime limit. This, rather unexpected result, suggests that the limiting factor is intrinsic to the structure and the local environment around the QDs 35 , and not to the excitation process, even if we have shown in our previous work that some QDs show much narrower linewidths, down to 9.4 µeV 18 .

Conclusions
In summary, we have demonstrated resonant excitation of an exciton and biexciton in GaAs nanowire QDs. This was possible thanks to a combination of technological advancements of the nanowire platform (i.e., relatively high brightness and narrow linewidth) and careful optimization of the optical setup. Under two-photon continuous-wave resonant excitation, our nanowire QDs show a clean spectrum and biexciton-exciton cascaded emission. This result is obtained without polarization filtering, allowing for further polarization-resolving measurements, such as entanglement generation, and substantially reducing the setup complexity. A cross-polarization confocal microscope is developed to resonantly drive the exciton, demonstrating resonant fluorescence of a nanowire QD. This allows to directly and individually drive excitonic transitions in nanowire QDs, paving the way to advanced multi-qubit photonic devices where the quantum state of each QD in a nanowire can be individually addressed and manipulated.

Sample growth
We grow our nanowire QDs by Au-catalyzed vapor-liquid-solid (VLS) method in a molecular beam epitaxy reactor on a Si(111) substrate. After a 0.1 nm Au deposition at 550°C, the gold forms droplets of~20 nm in diameter. At a temperature of 510°C, a V/III flux (ratio of 3) is applied to grow Al 0.3 Ga 0.7 As nanowires with a diameter set by the gold catalyst. At any given point, the Al flux can be turned off to grow an insertion of GaAs (the QD) for a few seconds. Then, the AlGaAs nanowire growth is resumed. MBE growth of Au-catalyzed AlGaAs nanowires leads to the spontaneous formation of unintentional shell structure around the core. This shell forms via vapor-solid process typically with Al content twice larger than in the core 37 . Thus, AlGaAs overgrowth after the GaAs insertion leads to complete embedding of the QD. Further details and transmission electron microscopy images of the grown nanowire QDs can be found in the literature 38 .

Measurement setup
All optical measurements are performed at a temperature of 1.5 K in a closed-cycle He cryostat, developed by Cryovac. The above-bandgap excitation is done by using a continuous wave 532 nm laser to measure the spectrum or gate the TPE, and with a titanium sapphire (TiSa) picosecond laser, tuned to 730 nm, for the lifetime measurements. The TPE and correlation measurements are done by using a Toptica tunable diode laser (765-805 nm), filtered~7 orders of magnitude from the RF signal, with very narrow Optigrate notch filters. All excitation lasers are focused onto the sample with an objective with a numerical aperture of 0.85, which also collects the emission. The emission signal is then coupled free-space to either one or two 75 cm spectrometers with a 1800 g/mm holographic grating providing a resolution of~0.01 nm. The spectrometers were equipped with low-noise Peltier-cooled coupled charged devices to measure the photoluminescence spectrum, or with single-photon detectors to measure lifetime or correlations. For lifetime measurements we use a fast micro-photon devices (MPD) detector (~170 ps FWHM), while for correlation measurements we use two slower Excelitas detectors (~500 ps FWHM). Taking into consideration the measured lifetime, the setup efficiency and the typical number of photons measured at the spectrometers, we estimated an overall photon extraction efficiency on the order of 1%, for nanowire QDs without any intentional cavity design or tapering optimization. The RF measurement uses the same Toptica laser, but in a different setup: the excitation laser passes through a polarizer, a polarizing beam splitter, and a quarter-waveplate before reaching the sample. The quarter-waveplate is necessary to compensate for any degree of elliptical polarization the beam gathers in the setup because of non-perfect optics. The emission and laser reflection pass through the quarter-waveplate and the polarizing beam splitter and then they are coupled to a single mode fiber and sent to the spectrometer, as shown in Fig. 4a. Following a careful alignment and optimization of the rotating polarizer and waveplate, the scattered laser can be reduced by~6 orders of magnitude while keeping most of the photoluminescence signal.

DATA AVAILABILITY
Data available from the authors upon reasonable request. Correspondence and requests for materials should be addressed to Nika Akopian.