Ultra-low density and high performance InAs quantum dot single photon emitters

We report the development of high quality InAs quantum dots with an ultra-low density of 2 × 10 7 cm − 2 on (001) GaAs substrates. A significant reduction in the emission wavelength inhomogeneity has been observed. A representative dot has been characterized under cryogenic temperatures, demonstrating a close-to-ideal antibunching of both the exciton and biexciton emissions with a fitted g (2) (0) = 0.008 and 0.059, respectively. © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0209866


I. INTRODUCTION
The advancement of photonic based quantum technologies is expected to usher in a transformative change in data processing and communication protocols, 1 where photonic qubits are generated and manipulated on demand in the established quantum networks. 2or such technologies to realize their full functionalities, high efficiency photon counters, linear and non-linear photonic circuits, and single photon and entangled photon pair sources are necessary. 3Significant improvements have been demonstrated for photon detection 4 and linear circuits. 5However, significant progress in the development of scalable photon sources is needed for integrated quantum photonics.
Several physical systems have been investigated for single photon generation, including trapped individual ions, 6 defects in semiconductors, 7 isolated molecules, 8 parametric downconversion of laser pulses in non-linear crystals, 9,10 and semiconductor quantum dots (QDs).Although each system has its own merits and there is no clear winner yet, semiconductor quantum dots (QDs), coined as "artificial atoms," are nearly ideal two-level systems that can be deterministically triggered via optical 11 or electrical pumping 12,13 to produce quality indistinguishable single photons and outperform all other platforms on single photon emission rate. 11,14The radiative cascade decay from a biexciton state (XX) to the ground state through an exciton (X) intermediate state within a QD can be utilized to generate one pair of polarization entangled photons. 15espite the challenges to extract the photon pair efficiently 16 and complications induced by the shape and atomistic anisotropy of QDs, 17 QDs remain a strong contender as the sources for polarization entangled photon pairs in memory-based quantum repeaters 18 and other applications in quantum information processing. 19,20Epitaxially grown QDs also offer compactness and tunable emission properties that can be optimized for specific applications when embedded in optical cavities or photonic crystal structures. 21,22Sitecontrolled nucleation of QDs is also possible for deterministic QD placement, 23 although the performance for the site-controlled QDs falls short compared to those grown on planar substrates. 24The solid-state structures promise simple integration of individual QDs with existing and future photonic integrated circuits for on-chip single photon and entangled photon pair emitters.
The main hurdle that prevents QDs from serving as a scalable quantum light source is the inhomogeneous broadening, inherent of the statistical nature of the Stranski-Krastanov (S-K) growth mode for QD formation.In this paper, we present the development ARTICLE pubs.aip.org/aip/apq of InAs quantum dots with ultra-low density grown by molecular beam epitaxy on a (001) GaAs substrate.The average dot density is 2 × 10 7 cm −2 , which is the lowest demonstrated to date for S-K growth, to the best of our knowledge.This allows for the characterization of each individual dot and enables deterministic integration of these quantum dots into cavities. 25A significant reduction in the inhomogeneous broadening has been observed as the QDs are "decoupled" during growth at such low densities.A representative InAs QD embedded in a distributed Bragg reflector (DBR) cavity has been characterized at cryogenic temperatures, demonstrating closeto-ideal photon antibunching for both X and XX with short photon lifetimes.

A. Materials growth and characterization
All samples were grown in a Veeco Gen II solid source MBE reactor.To simplify the process of investigating the optimal growth conditions for the ultra-low density QDs, InAs was deposited on (001) GaAs under various growth conditions.The QDs were then capped with GaAs after a growth interruption of 60 s for the QDs to take shape, and the samples were finished with uncapped surface QDs grown under the same conditions as the embedded dots.Regardless of the growth rate and the total amount of InAs deposited, the QDs exhibit the best morphology in terms of the shape and the uniformity at a growth temperature of 490 ○ C, measured using a pyrometer, and an arsenic overpressure of 1 × 10 −6 Torr.Thus, we believe that the absolute arsenic pressure, instead of the commonly believed V/III flux ratio, is the controlling factor for QD morphology.To obtain the lowest QD density at a given deposition rate, the indium flux was terminated immediately upon the observation of 2D-3D transition via reflective high energy electron diffraction (RHEED).The total amount of InAs required for QD nucleation was 2 ML at the given temperature and arsenic overpressure, conveniently independent of the deposition rate.A further reduction in the dot density is achieved by lowering the deposition rate.As shown in Fig. 1(a), the QD density is reduced drastically as the growth rate of InAs is decreased from 0.11 to 0.0055 ML/s, corresponding to the lowest indium flux that could be reliably measured in our MBE reactor.A surface QD density as low as 2 × 10 7 cm −2 is then achieved reproducibly, which is the lowest density reported in the literature to the best of our knowledge.Recent results are briefly summarized in Table I.Such a density enables optical microcavity fabrication with precisely just one QD located inside each cavity on average. 26,32,33he photoluminescence of the embedded QDs was examined via hyperspectral imaging at ∼4 K.The emission intensity response of each pixel was overlaid with the corresponding spectral response, which allows for the visualization and statistical analysis of the embedded QDs, shown in Figs.1(b) and 1(c).Figure 1(d) shows the emission wavelengths of more than 50 QDs, illustrating a very narrow inhomogeneous broadening with an emission wavelength range between 918 and 935 nm.We attributed this narrow inhomogeneous broadening to the reduced Oswald ripening effect during the 60 s growth interruption.The material exchange process has potentially been greatly suppressed as the distance between the dots increases with low QD density.This narrow emission wavelength distribution would improve the probability of locating two or more optically QDs.The areal density of the embedded QDs was independently measured to be 2 × 10 7 cm −2 from the hyperspectral images.The DBR cavity was then designed to center at 927 nm.The bottom mirror consists of 22 periods of GaAs/AlAs superlattice, grown at 530 ○ C, while the top mirror consists of 15 periods, grown at 580 ○ C. The GaAs cavity thickness is 260.5 nm, schematically shown in Fig. 2(a).signal at 927 nm when shining a white light onto the sample from top down at 4 K, indicating cavity resonance.The spectrum is unnormalized and skewed due to the non-flat intensity distribution for the impinging white light.The QDs are placed at the center of the GaAs cavity.Given a narrow temperature window for high quality QD nucleation (±1.5 ○ C), the above suggests that the growth temperature has been correctly adjusted accounting for pyrometer reading drift due to the oscillation of surface reflectivity as the DBR growth proceeds.

B. Single photon characterization
To characterize the single photon properties of the InAs QDs, the sample with QDs embedded in a DBR cavity was cooled to 1.6 K.The ultra-low dot density allows for each QD to be characterized individually with a laser spot size of ∼1 μm 2 .Figure 3(a) shows the emission spectrum of one isolated dot pumped at 880 nm with various pumping powers between 0 and 512 μW.The pumping power is measured before the objective lens and is not corrected for possible transmission loss through the AR coated objective and cryostat windows.The X and the XX emission lines were initially identified by fitting the peak intensities with respect to the pumping power.
The X line shown in the inset of Fig. 3(a) illustrates a linear dependence of emission intensity on the pumping power, while the XX line intensity depends on the pumping power in a quadratic manner. 34To verify the nature of the quasiparticles, cross correlation measurements between the X and the XX lines were conducted.To analyze the single-photon stream by means of time-resolved photon counting, photons from the X and XX lines are first sent to different superconductor nanowire single photon detectors (SNSPDs) after passing through a transmission-grating-monochromator with a holographic grating (1200 grooves/mm).Then, the timestamps for the photon arrival times are correlated as shown in Fig. 3(b), where a clear bunching effect can be observed, suggesting that the X and XX emissions are correlated via the cascading process.The XX emits at a lower energy due to the binding nature of the two electron-hole pairs. 17The third major peak was then identified as a charged trion from the zero fine structure splitting (FSS), displayed in the polarization series in Fig. 4(a). 35o quantify the multiphoton contribution to the individual photon streams from the isolated QD, the emissions for the X and XX line were then each separately sent through a fiber-based 50/50 beam splitter and into different channels onto SNSPDs.The excitation power was 135 μW CW equivalent, with a pulse width of   ARTICLE pubs.aip.org/aip/apq even further improved if resonant excitation was implemented for both X and XX photons. 36The lifetime of the photon emission events determines the upper limit on the operation rate of the source.Figure 3(e) shows the lifetime measurements of the X and XX emissions, where the lifetimes were extracted from mono-exponential fits to be 213 ps for X emission and 113 ps for XX emission.Since the XX state consists of two excitons, where the decay of either exciton is registered as the XX emission, the XX decay rate is anticipated to be roughly twice the decay rate of the X state. 37,38We expect negligible Purcell enhancement since all measurements were done on dots embedded in a planar DBR cavity where the mode volume extends across the wafer.We then attribute the short lifetimes to possible Ga intermixing.However, we cannot exclude a local perturbation of the cavity that might lead to Purcell enhancement.Such short lifetimes are not only beneficial for higher operation rate and better indistinguishability, 39 but also advantageous in mitigating the influence of the environment and other unwanted processes on the quantum system. 11,40FSS of the intermediate X state during cascade emission process from XX to the ground state is another important figure of merit, as the non-zero FSS would reveal the which-path information.This would destroy the polarization entanglement between the photon pairs generated by the cascade process.To characterize the FSS of the above isolated QD, the emission spectra were recorded as we rotated a half-wave plate (HWP) in the common collection and excitation path in 5 ○ increments in combination with a polarizing beam splitter.Since the polarization of the excitation laser is not relevant in above-band excitation, this measurement analyzes the emission only.As shown in Fig. 4(a), a clear oscillation of the emission wavelength has been observed for the X and the XX emissions, but not for the charged X emission. 41Figures 4(b) and 4(c) show the extracted wavelength of the peak intensity as a function of the HWP angle. 29The fitted FSS is ∼39 μeV, potentially resulting from QD shape anisotropy. 17,42Such a value is within the commonly reported range 43 and could be further lowered by annealing 44 or added external fields. 45,46

III. CONCLUSION AND OUTLOOK
In conclusion, we have reproducibly achieved an InAs QD density as low as 2 × 10 7 cm −2 within a resonant cavity by carefully controlling the InAs deposition rate and other related growth conditions, especially the surface temperature uncertainty introduced by the DBR mirrors.A close-to-ideal antibunching effect has been observed for the exciton and biexciton emissions, with a g (2) (0) of 0.008 and 0.059 and a lifetime of 213 and 113 ps, respectively.The sparse placement of the QDs also conveniently facilitated a narrow emission wavelength distribution, which is beneficial for locating two or more optically identical QDs for various quantum applications.This material platform can serve as the building foundation for realizing large scale high quality single photon sources.

2 ©
FIG. 1.(a) From left to right, atomic force microscopy images of the surface dots deposited at a rate of 0.11, 0.055, 0.011, and 0.0055 ML/s.The surface dot densities are 4 × 10 10 , 2 × 10 10 , 4 × 10 9 , and 2 × 10 7 cm −2 , respectively.(b) and (c) Hyper-spectrum imaging of the embedded dots at two different locations, with the emission spectrum of one dot at each location.(d) Emission wavelength distribution of more than 50 dots.

FIG. 2 .
FIG. 2. (a) Schematic of the DBR structure with embedded QDs.(b) The reflected white light signal indicates the cavity resonance to be located at 927 nm as indicated by the dashed line.

FIG. 3 .
FIG. 3. (a) Power series emission spectra of one representative dot pumped at 880 nm.The inset shows the intensity power dependence of two major peaks X and XX.(b) Cross correlation measurement between X and XX emissions.A clear bunching behavior is observed at zero-time delay.(c) Photon lifetime measurements with pulsed excitation for both the exciton and the biexciton emissions.(d) and (e) Autocorrelation measurement of the X (left) and the XX line (right) under 880 nm pulsed excitation showing antibunching at zero-time delay.

2- 3
FIG. 4. (a) Emission intensity map with respect to the position of the HWP in a cross-polarization filtering setup.(b) and (c) Extracted peak intensity for X and XX emissions as a function of HWP position, respectively.

TABLE I .
Summary of recent progress on QD density and respective optical performance grown by MBE.DE stands for droplet epitaxy.