Bright and highly-polarized single-photon sources in visible based on droplet-epitaxial GaAs quantum dots in photonic crystal cavities

1. Introduction

An efficient source of single-photons is a crucial component for the quantum information processing [1], such as quantum communication [2], quantum computing [3] and quantum metrology [4]. Semiconductor self-assembled QDs are promising candidates for scalable single-photon emitters due to their near-unity quantum efficiency [5–7], wide spectra range [8] and compatibility with semiconductor foundries [9]. Tremendous progress has been made in the past decades in demonstrations of various single-photon sources and their applications via integrating the Stranski-Krastanov grown In(Ga)As QDs to different photonic nanostructures, such as micropillar [10], photonic crystals [11], nanobeam cavity [12], microlens [13] and nanowire waveguides [5]. However, such sources so far are operating at near infrared range (∼900 nm) which is not compatible with most of the atom-based quantum memories. In addition, the detection efficiency of photons near 900 nm is very limited with standard single-photon detectors [14].

Recently, GaAs/AlGaAs QDs fabricated by droplet epitaxy exhibit excellent optical characteristics at the wavelength of ∼780 nm due to the absence of lattice mismatch and material intermixing [15–17]. Encouragingly, by integrating such QDs with broadband circular Bragg grating [18,19] or optical antenna [20], high-performance entangled photon pairs as well as entanglement swapping [21] can be achieved, which opens up their potential applications in devices towards quantum repeater and quantum network [22]. In this work, we extend the wavelength of droplet epitaxial grown quantum dot (QD) to a visible wavelength range of ∼680 nm based on single GaAs QD decorating on the lobes of local droplet etching nanoholes. Furthermore, we embed this new type of single QD into visible photonic crystal cavity to achieve bright (>23.6%), pure (>96%) and highly-polarized (>82.7%) single-photon generations.

2. QDs growth and photonic crystal cavity fabrication

The QDs samples were grown by a solid source molecular beam epitaxy (MBE). The structure is consisted of a 500-nm-thick sacrificial Al_0.8Ga_0.2As layer, a 4-nm-thick GaAs layer, a 140-nm-thick Al_0.4Ga_0.6As layer and a 4-nm-thick GaAs capping layer from the bottom to the top. A layer of low-density (∼10⁻⁹–10⁻⁸ cm⁻²) AlGaAs quantum dots, which are embedded in the middle of the Al_0.4Ga_0.6As layer, are made by designing the lobes of the aluminum-droplet-etched nanoholes. Figure 1(a) shows the schematic diagram of the different steps of an aluminum (Al) droplet etching and AlGaAs QD formation process. In details, the droplets here are firstly formed by depositing 0.9 monolayer (ML) of Al at 0.4 ML/s without supplying arsenic (As) at 640 °C. In a post-growth annealing step of 300s duration, As diffusion from the substrate into the droplet material leads to nanohole formation beneath the Al droplets. AlGaAs QDs arise when As atoms diffuse to the edge of the Al droplet and form AlGaAs again with Al atoms and Ga atoms, as shown in the atomic force microscopy of a representative lobe of the nanohole in Fig. 1(b). Figure 1(c) and 1(d) provide the line-scan of the nanohole along the [1–10] crystal directions, which reveals an AlGaAs QD with a width of about 45 nm, a height of about 6.7 nm.

 

Fig. 1. (a) The schematic diagram of QD formation process. (b) and (c) The atomic force microscopy images of QDs. (d) The line-scan of the nanohole in (c) along the [1–10] crystal directions, which reveals an AlGaAs QD with a width of about 45 nm, a height of about 6.7 nm.

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The photonic crystal resonator studied here is a L3 defect PC cavity, i.e., a triangular lattice of airs holes with three holes missing in the ΓK direction. The cavity geometry was carefully engineering in order to increase the extraction efficiency, far field pattern as well as polarization characteristic. The optimized hole radius r is equal to 0.32a, while the shift s is set at 0.02a [23,24], with some holes around the cavity decreased to 0.25a [25] in radius. Electron-beam lithography (EBL) and inductively-coupled plasma reactive ion etching (ICP-RIE) were used to make hexagonal lattices of circular air holes (detailed in Appendix A, Fig. 5). The sacrificial layer was removed to form suspend membranes, which enables the vertical confinement of light via total internal reflection. Scanning electron microscopy (SEM) image of a typical L3 cavity with lattice constant a = 205 nm is presented in Fig. 2(a), which is superimposed with the normalized electric field intensity distribution |E| of the third-order cavity mode (M3) calculated by three-dimensional finite-difference time-domain (FDTD) method. We adopted the third-order mode M3 here because it exhibits convergent far-filed pattern for light collection with objective and broader operation bandwidth when comparing with the fundamental mode M1 (Fig. 2(c), FDTD results of the normalized electric field intensity distribution |E| of M1 and M3). As shown in Fig. 2(b), different resonant wavelengths of M3 from 670-720 nm can be achieved by slightly varying the lattice constant a from 200-215 nm.

 

Fig. 2. (a) Scanning electron microscopy (SEM) image of a typical L3 defect photonic crystal cavity, along with the normalized electric field intensity distribution |E| of M3 mode calculated by 3D-FDTD method. The periodicity of the air-hole a = 205 nm, radius r = 0.32a and shift s = 0.02a. (b) The spectra of cavity modes as a function of different periodicity in experiment. The red dash line shows the changing of M3 modes with the lattice constants. (c) The simulated electric field profiles of different cavity modes confined in the L3 defect cavity in (a). The color scale is normalized to max |E|.

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3. Optical measurements

The optical properties of the samples were characterized by a home-built micro-photoluminescence (micro-PL) system. Appendix B (Fig. 6) shows the schematic of our experiment setup. The sample was mounted in a closed-cycle cryostat at a temperature of ∼5K. A 400 nm continuous wave laser was used as an excitation source. The laser beam was focused onto a selected photonic crystal cavity with a spot diameter of ∼1 µm through a microscope objective with N.A. = 0.65. The reflected light and fluorescence from the sample were collimated by the same objective, and subsequently passed through a 450 nm long-pass filter (LPF) and a lens with focal distance of 200 millimeters before imported into a spectrometer. The cavity modes were adjusted by using a white light reflection in the cross-polarization configuration. To filter out the background light, the incident white light was sent through polarizer A with an angle of 45° from the cavity direction and then the reflected light went through polarizer B whose slow-axis is parallel to the fast-axis of polarizer A.

To characterize the collection efficiency, a mode-locked Ti: sapphire laser was utilized, which was tuned to a wavelength of 400 nm with pulse duration of ∼800 fs and a repetition rate of 79.3 MHz. A half-wave plate and a fixed polarizer were used to measure the polarization of the emitted photons from QDs. The signals went through a home-built band-pass filter (black dotted line frame in Appendix B) with a bandwidth of 0.18 nm (Appendix C, Fig. 7) and then were collected by a single-mode fiber. The second order correlation function g⁽²⁾(t) were performed for a single QD with a Hanbury-Brown-Twiss setup (red dotted line frame in Appendix B).

4. Results and analyses

We studied the optical properties of single QDs coupled to the M3 mode of L3 photonic crystal cavity. Thanks to the low density of QDs and the broad bandwidth of cavity modes, it is possible to optically access individual QDs without any additional sample processing. Figure 3(a) shows a saturated spectrum of an isolated dot (red line in Fig. 3(a)) under an excitation power of 30 µW. After passing through the home-built filter, a pure single-exciton line at 683.2 nm with a linewidth of 0.038 nm (Appendix C) is achieved, which is close to the spectral resolution of our setup. The blue circles and line in Fig. 3(a) present the measured M3 cavity mode with a low Q-factor of ∼170. The single-photon nature of the collected fluorescence at saturated power was identified from an intensity-correlation measurement shown in Fig. 3(b), revealing a nearly vanishing multiphoton probability at zero time delay [g⁽²⁾(0) = 0.04(2)]. The coupling of QDs with the cavity mode can be further confirmed by examining the polarization of exciton lines. As shown in Fig. 3(c), the emission line is strongly x-polarized with a polarization degree $\textrm{p} = |{{I_x} - {I_y}} |/|{{I_x} + {I_y}} |\, = \,82.7(1 )\textrm{ }\%$. Such a high degree of polarization state is very close to the simulated values of the x(y) oriented dipoles placed in the anti-node of the cavity mode (Fig. 3(d)). The deviation of the experiment from the simulations may be attributed to the non-ideal position of the QDs in cavity.

 

Fig. 3. (a) The PL spectrum of the QD emission (red line) and the measured cavity mode (blue dots) together with the Gauss-function fitting (blue line). (b) Intensity-correlation histogram obtained using a Hanbury Brown and Twiss type setup under 400 nm pulsed excitation. (c) A polar plot of the intensity of the exciton line as a function of polarization angle. (d) The polarization degree in simulation. Red (blue) line is simulated in x(y) dipole.

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To prove the brightness of this AlGaAs QD in L3 photonic crystal structure, we determine the extraction efficiency by measuring the photon counting rate from the avalanche photon diode (APD) under 400 nm pulsed excitation. The collection efficiency is defined as the probability of photons reaching per excitation pulse to the first lens. Figure 4(a) shows the detected fluorescent counts on a silicon single-photon detector as a function of normalized pulse laser power, achieving the total flux of 100000 counts/s. Taking into account the total transmission rates of optical set-ups (∼0.535%, see Table 1 in Appendix D), the collection efficiency (single-photon extraction efficiency) of the photonic crystal cavity at the first lens is 23.6(2) %. The simulated extraction efficiency is about 37% for an x-oriented dipole and about 26% for a y-oriented dipole (Fig. 4(b)). The relatively highly collection efficiency can be identified by the near Gaussian profile of the far-field pattern of x-oriented dipole in the cavity, as shown in Fig. 4(c). The y-oriented dipole in the cavity however exhibit less convergent far-field pattern and consequently lower collection efficiency. Considering the signal is coupled into a single mode fiber and the emission is x-polarized in our experiments, we believe that the measured QD in this cavity is more likely to be x-oriented. The deviation of the measured collection efficiency from the simulation may be due to non-ideal position of the QDs relative to the anti-node of the cavity mode.

 

Fig. 4. (a) Single-photon flux measured on APD, plotted as a function of laser excitation power (in saturation units). (b) The extraction efficiency at a collection angle of NA = 0.65 for x dipole (red line) and y dipole (blue line) as a function of wavelength in simulation. (c) The simulated far-field profiles of M3 mode with x dipole and y dipole.

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5. Conclusion and outlook

In conclusion, we demonstrate a bright single-photon source in visible based on droplet-epitaxial QDs embedded in L3 type photonic crystal nanocavities. By coupling the QDs to the M3 mode of the PC cavity, the extraction efficiency of 23.6%, the single-photon purity of 96%, and the polarization degree of 82.7% are obtained. Our work clearly demonstrated that the potential of droplet-epitaxial QDs as highly efficiently quantum light sources in visible for photonic quantum technologies.

Appendix A. Sample preparation

 

Fig. 5. The schematic of photonic crystal structures fabrication. The sample is first spin coated with a positive resist (ZEP520); The resist is exposed using a VISTEC EPBG5000 ES PLUS electron-beam lithography (EBL) system at 100 KV followed by the development process in dimethylbenzene for 70 seconds and IPA for 60 seconds; The mask pattern of the PC structure with the designed parameters is transferred into the sample via an inductively-coupled plasma reactive ion etching system (ICP-RIE, Oxford Instrument Plasmalab System 100 ICP 180); The resist is removed by ultrasonic cleaning in NMP (N-methyl-2-pyrrolidone) solution.

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Appendix B.

 

Fig. 6. Schematic of the experiment setup.

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Appendix C.

 

Fig. 7. The spectra of white light and QD’s fluorescence after passing through the home-built band pass filter setup. The full width at half maximum (FWHM) of 0.18 nm for white light and 0.038 nm for signal are achieved by Gauss fit and Lorentz fit, respectively.

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Appendix D. The experimental setup efficiency

Table 1. Experiment setup calibration. The transmission efficiency of the optical setups, measured by laser operated at 683 nm. The single-photon detector efficiency is achieved from the factory report of the APD.

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Funding

National Natural Science Foundation of China (11674402, 11704424, 11761131001, 11761141015, 11874437, 91750207); National Key Research and Development Program of China Stem Cell and Translational Research (2016YFA0301300, 2018YFA0306100); Guangzhou Science and Technology Program key projects (201805010004); Natural Science Foundation of Guangdong Province (2016A030310216, 2016A030312012, 2017A030310004, 2018B030311027).

Acknowledgments

We are grateful for financial support from the National Key R&D Program of China (2016YFA0301300, 2018YFA0306100), the National Natural Science Foundations of China (91750207, 11674402, 11761141015, 11761131001, 11874437, 11704424), Guangzhou Science and Technology project (201805010004), the Natural Science Foundations of Guangdong (2018B030311027, 2017A030310004, 2016A030310216, 2016A030312012), the national supercomputer center in Guangzhou.

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