1. Semiconductor quantum dots



Similar to the single atomic system, group III–V quantum dot (QD) possesses discrete energy levels owing to the three-dimensional confinement of charge carriers. Type-I band misalignment (straddling configuration) between the dot and the host materials allows the capturing of both electrons and holes in the potential well to form localized exciton, trion, or biexciton state within the nanostructure. Radiative recombination of these charge-carriers leads to single-photon emissions featuring a narrow linewidth of a few GHz at cryogenic temperatures. By carefully controlling the charge and nuclear-spin environment, emissions with transform-limited linewidth are demonstrated for both exciton and trion state^[2]. Comparing to the conventional spontaneous parametric down-conversion (SPDC) quantum light source where single photons are generated probabilistically at a low count rate imposed by Poisson statistics, QDs produce single photons deterministically with high-purity (i.e., low multiphoton emission probability), high-brightness (i.e., short radiative lifetime and large collection efficiency), and high indistinguishability. Thanks to the rapid development of material growth and nanofabrication techniques, the figure-of-merits of these quantum emitters have been continuously improved since the first proof-of-concept demonstration of single-photon emission 20 years ago^{[3, 4]}. By embedding a single self-assembled InGaAs/GaAs QD in a nano-pillar photonic structure, the issue of low photon-extraction efficiency from high refractive-index materials is well solved, and a benchmark extraction efficiency of 66%^[5], corresponding to a detection rate of 13 MHz, has been achieved. Moreover, Purcell effect, produced by spectrally and spatially coupling a QD to the photonic mode of a high-quality cavity, significantly speeds up the spontaneous decay process, which is not only beneficial for boosting the brightness of the light source, but also favored in terms of indistinguishability of the scattered photons. With the help of this marvelous effect, the near-optimal single-photon emission has been demonstrated with a purity of 0.0028, indistinguishability of 0.996, and 20 times more brightness than other sources of equal quality^[6]. It worth mentioning that the emission wavelength of this epitaxial semiconductor structure is electrically tunable^[7], and single-photon emissions under electrical injection have been realized^{[8, 9]}.



QDs are also the promising platforms for generating polarization-entangled photon pairs based on the radiative cascades from a biexciton state. Resonant two-photon pumping can deterministically create a biexciton in the QD, enabling on-demand generation of entanglement photon pairs at a high-yield rate^[10]. The entanglement fidelity of the photon pairs is limited by the fine structure splitting of exciton state, originating from the exchange interaction between electron and hole confined in an asymmetric potential. If the splitting is larger than the emission linewidth, which path information can leak out by the color of the photons, and the entanglement collapses. One way of protecting entanglement fidelity is to recover the circular symmetry of the confinement potential. Nano-hole filling QD achieves this goal by prepatterning symmetric holes via droplet etching before infilling with dot material^[11], which improves entanglement fidelity to 94%^[12]. By employing active strain-tuning techniques, for example, PMN-PT/silicon micro-electromechanical system^[13], the shape of the dot can be further manipulated with fine adjustment, leading to the near-optimal entanglement fidelity of 99%^[14] that matches the performance of the best probabilistic entangled photon sources. Moreover, by adjusting the bidirectional strain applied on a QD, its emission wavelength can be tuned by several meV without compromising the fine structure splitting^[13]. This capability partially alleviates the plague of inhomogeneous distribution of emission energy of semiconductor QDs. To boost the photon extraction efficiency of entangled photon pairs, a broadband antenna is needed due to the extra binding energy of bi-exciton state. Recently, this has been realized by fabricating a circular-ring grating on top of a QD membrane^[15] or utilizing a solid emersion lens to couple out the evanescent light waves^[16], where extraction efficiency of more than 60% for both cascaded photons has been demonstrated.



Since the emission wavelength of QD is determined by the physical size of the confinement potential well, which is extremely hard to control during epitaxial growth or nanohole engineering, a broad inhomogeneous distribution of photon energy is expected from an ensemble of QDs, which can be troublesome for applications requiring single photons to be indistinguishable. Besides, the shallow carrier confinement in As-based QDs limits their operation temperature to cryogenic one, rendering them cumbersome and economically unfriendly for applications in the field of quantum information processing (QIP).





2. Color centers in diamond



Up to date, more than 500 different optical-active impurities has been identified in diamond^[17], coined as color centers, with emission wavelengths covering a wide range of spectrum from ultraviolet to near-infrared. Although negatively charged nitrogen-vacancy (NV) center is the first emitter in diamond investigated as the single-photon source (SPS), its relatively poor optical properties hinder its potentials to be used as the building block for QIP. The strong electron-phonon coupling in NV centers significantly broadens the associated emission energy resulting in a weak zero-phonon line (ZPL) at 637 nm and a strong but broad phonon sideband (PSBs) extending up to 800 nm at room temperature. Even at 4 K, only 3% of the fluorescence is concentrated in the ZPL with a lifetime-limited linewidth of 13 MHz^[18]; meanwhile, the optical emission from NV centers also suffers from spectral diffusion^[19] and fluorescence intermittency^[20]. These deficiencies have fueled the investigation for alternative emitters that combine bright, homogeneous, and coherent optical transitions together, such as group-IV split-vacancy centers in diamond including Silicon-vacancy (SiV) center and Germanium-vacancy (GeV) center. Unlike the C_3v point group exhibited by NV center^[21], the molecular structure of split-vacancy centers possesses D_3d symmetry, where the Si or Ge atom takes the interstitial position between two adjacent vacancies in diamond^[22]. The inversion-symmetry guarantees vanishing of the permanent electric-dipole moment, rendering the system insensitive to the first-order Stark shift caused by the local electric-field fluctuations in the environment. These systems thus acquire intrinsic immunities to the spectral diffusion, allowing the observation of lifetime-limited linewidth^[23] without employing photonic structures, which is a key to realize two-photon interference from two distinct SiV centers^[24]. Moreover, these color centers are optically bright (up to 6 Mcps^[27]), and scatters more than 60% of photons into ZPL line^{[25, 26]}. The nearly complete linear polarization of the ZPL fluorescence at room temperature^{[25, 28]} is also favorable for information encoding in quantum cryptography applications. Meanwhile, SiV centers have been successfully integrated into various nano-photonic structures, including nanopillar^[29], waveguide^[30], and 2-dimensional photonic crystal cavities^{[31, 32]}, to further boost the performance or construct quantum photonic circuits. One main trade-off of using diamond as a host material is the sacrifice of technological maturity, which is a critical factor to consider regarding the large-scale applications, such as quantum network and distributed quantum computers.





3. Defects in other wide-bandgap materials



In comparison, the other two types of wide-bandgap materials, GaN and SiC, are backed by strong and mature industrial technologies. SiC has been used as abrasive since 1893, and was made as the first light-emitting diode (LED) with electroluminescence in 1907. Shortly thereafter, SiC-based LED was commercialized and manufactured until the 1980s, when the first GaN-based blue LED was born and developed^[33]. Since then, GaN has become the second most important semiconductor worldwide in terms of business share, just behind silicon. Both materials are widely used in various applications including high-voltage power transportation, solid-state microdisplays, and high-frequency electronics, providing the needed technological supports for scaling up the devices based on these two materials.



Recently, the discoveries of room-temperature optically-active emitters in standard GaN thin films with emission wavelengths covering 1.1–1.4 μm range^[34] sheds lights on searching for ambient on-demand quantum light source that is applicable for long-distance quantum communication. However, the nature of these emitters is still not clear, but arguing over two hypothetical mechanisms: cubic inclusions within a GaN hexagonal matrix (i.e. stacking fault defects)^[34–36]; point defects or impurities with a modulated density induced by local extended defect density^[37]. Elucidation of the nature of the emitters is necessary for the effective harness of these advantages for large-scale and deterministic fabrications.



Meanwhile, SiC-based SPS also captures a significant amount of attention, especially, silicon-vacancies V_Si defects and di-vacancy V_SiV_C defects, which are optically addressable on single defect level and behave as single-photon emitters^{[38, 39]}. These SPSs exhibit excellent photon statistics, and have a typical lifetime of about 1.2 ns. Together with descent internal quantum efficiency (~ 0.7), these defects demonstrate saturation count rates of up to 2 Mcps^[40], amongst the brightest defect-based SPS. However, the wide spectral distribution of emission energies challenges the integration of these emitters into photonic circuitry and cavities^[41].





4. Defects in two-dimensional materials



There are mainly two types of optical-active scattering centers prevailing in 2D host materials: bound exciton states confined within zero-dimensional potential wells generated by local strain and/or a crystallographic defect; single point defects and/or impurities. The first type dominates in layered WSe₂^[42–46], MoSe₂^{[47, 48]}, WS₂^[49], and GaSe^[50] materials with emission energies covering from 600 to 780 nm, but only viable at cryogenic temperatures due to the shallow confinement potentials^[51]. The second type is often found in layered hexagonal boron nitride (hBN)^{[52, 53]}, a wide bandgap 2D material with transition energy of ~ 6 eV^[54]. A variety of SPSs has been reported in hBN with ZPL energies covering a wide range of spectrum from ultraviolet (UV) to near-infrared (NIR). Emitters scattering NIR light (1.6–2.2 eV) are promising SPSs since they are exceptionally bright (> 4 Mcps^[55] in the absence of cavity or immersion lens) with low PSB concentration and strong linear polarization. They are also operable at room temperature^[52], and show excellent chemical, thermal, and photo stability^[56]. Furthermore, Fourier-transform limited linewidths have been observed from some of these quantum emitters^[57], which is reported to be sustainable up to room temperature when using resonant excitation^[58]. These remarkable optical properties justify the efforts to unveil the nature of these quantum emitters, a prerequisite to deploying for large-scale quantum applications. Prior theoretical studies suggest multiple possible structures^[59–62], including V_NN_B^[52], V_NC_B, and V_BO₂ configurations. However, experiments are inconclusive due to the broad ZPL window allowed by numerous defects. It worth pointing out that these emitters indeed suffer from spectral diffusion, blinking, and bleaching, implying pronounced interactions with the local environment^[51].





5. Carbon nanotubes



Although carbon nanotubes (CNTs) exhibit one-dimensional freedom that conflicts with the major requirement of 3D confinement of charge carriers to establish single-photon emission, recent developments in low-level covalent functionalization chemistry of CNTs provide routes to fulfill this requirement^[63], for instance, functionalization of the nanotube sidewall with oxygen groups via ozonation chemistry^[64], or using diazonium-based reactions to introduce aryl sp3 defects within the continuous sp2 structure of the nanotube^[65]. Both routes generate exciton localization at these synthetic defect sites with potential-well depths of more than 100 meV^[66], enabling single-photon emission at telecom wavelengths up to room temperature^{[67, 68]} with a typical apparent quantum yield of 10%–30%^{[64, 65]}. Along with the capabilities of electric injection^{[69, 70]}, CNTs arises as an appealing SPS with comparable performance as other systems. Furthermore, as individual nanometric emitting objects, CNTs offer unique advantages in terms of miniaturization^[70], but it simultaneously brings about enormous challenges in terms of device fabrication and electronic-environment isolation. While proof-of-concept devices are envisaged and realized recently^[71], the issues of scalability and fabrication yield remain problematic. The incompatibility of carbon nanotubes with materials necessary to fabricate photonic devices (e.g. Si, SiO₂, Si₃N₄) also introduces detrimental impacts on quantum yields of the CNTs detrimental impacts on quantum yields of the CNTs^[72].