# Quantum Light Source Based on Semiconductor Quantum Dots: A Review

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## Abstract

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## 1. Introduction

## 2. Ideal Single Photon Source

#### 2.1. Single-Photon Purity

^{(2)}(τ); the photon statistics of a quantum state of light are determined by recording g

^{(2)}(τ) defined as [26]:

^{(2)}(τ) indicates the probability of detecting a photon at each moment t and t + τ. The g

^{(2)}(0) = 1 − 1/N for the Fock state with photon number N. Only the superposition of the single-photon state and the vacuum state can get g

^{(2)}(0) = 0. All other states obtain this value as positive, so the closer this value is to 0, the better the single-photon nature is. At that time, g

^{(2)}(0) = 0, the probability of multiphoton is 0, and the anti-collective beam effect is presented. In addition, g

^{(2)}(0) = 1 for ordinary coherent light (laser) and g

^{(2)}(0) = 2 for thermal sources, g

^{(2)}(0) can be employed as a measure of the single-photon purity of a light source. Experimentally, the second-order correlation function of photons is generally measured by the Hanbury Brown and Twiss (HBT) interferometer [27] shown in Figure 1.

#### 2.2. Photon Indistinguishability

#### 2.3. Single-Photon Efficiency

_{1}= 3.59) and air (n

_{2}= 1), the angle of total reflection inward is small:

## 3. Self-Assembled Semiconductor Quantum Dots

#### 3.1. Growth of Self-Assembled Semiconductor Quantum Dots

#### 3.2. Band Structure of Self-Assembled Semiconductor Quantum Dots

_{z}= ±1/2 in the z-axis direction. In contrast, the ground state hole in the valence band shows p-wave symmetry. The angular momentum of the holes is 3/2. The holes in the z-axis direction are divided into heavy holes and light holes, with the spin component J

_{z}= ±3/2 in the z-axis direction for heavy holes and J

_{z}= ±1/2 in the z-axis direction for light holes; there is also a spin-orbit splitting energy band in the valence band, which has a spin of S

_{z}= 1/2 and a spin of J

_{z}= ±1/2 in the z-axis direction. Since the heavy hole levels are far apart, we consider only the effect of heavy holes when discussing the structure of the excitonic state of InAs/GaAs quantum dots. Optical excitation of semiconductor QD allows studying the energy level structure of QD, which also is the most common method to obtain single photons. Optically excited semiconductor QD can be divided into non-resonantly excited QDs (including band excitation and p-shell excitation) and resonantly excited QD (including pulsed resonant excitation-Raby oscillation and continuous resonant excitation-Mollow triplet state). Before the QD is excited, there are no additional charged particles inside the QD, and the excitation produces an electron-hole pair called neutral exciton $|\mathrm{X}\rangle $ (Excitons are formed due to the Coulomb interaction of electrons and holes with each other), in which the electrons and holes occupy the lowest energy levels of the conduction band and valence band, respectively. Since the optical selection law dictates that only transitions with total angular momentum M = ± 1 occur in photon absorption, if the spins of electrons and heavy holes are antiparallel, excitons with the angular momentum of ±1 on the z-axis ((S

_{z}= 1/2, J

_{z}= −3/2) or (S

_{z}= −1/2, J

_{z}= 3/2)) satisfy the transitions, it is called a bright exciton. If the spins of the electron and heavy hole are parallel and the angular momentum component of the exciton in the z-axis is ±2 ((S

_{z}= 1/2, J

_{z}=3/2) or (S

_{z}=−1/2, J

_{z}= −3/2)) is forbidden transitions, it is called a dark exciton [40]. QDs with a high degree of structural symmetry emit fluorescence spectral lines without dark excitons, only bright excitons. However, when the symmetry is broken by external factors (e.g., transverse magnetic field), a mixture of bright and dark excitons is generated, and the dark exciton component also appears in the fluorescence spectral line emitted by the QD.

## 4. Artificial-Microstructure Enhanced Single Photon Emission from Single Semiconductor Quantum Dot

_{0.65}Ga

_{0.35}As post. The disk area consists of 100 nm of GaAs, an InAs QD layer, and 100 nm of GaAs.) [42]; In 2002, Yuan Z. et al. achieved electrically driven single-photon emission for the first time at a temperature of 5 K [43]; In the same year, Santori C et al. tested the indistinguishability of photons emitted from a semiconductor QD in a microcavity through a HOM-type two-photon interference experiment, they find that consecutive photons are largely indistinguishable, with a mean wave-packet overlap as large as 0.81 [44]. In 2005, Badolato A. et al. observed clear signatures of cavity QED (such as the Purcell effect) in all fabricated structures by achieving a deterministic spatial and spectral overlap between a QD exciton line and a photonic crystal cavities mode. This approach immediately found application in cavity-assisted QD spin-flip Raman transition to generate indistinguishable single photons [45]. In 2006, Chang W. H. et al. realized an efficient single-photon source based on low-density InGaAs QDs embedded in linear-type photonic crystal cavities, and the devices feature the effects of a photonic band gap, yielding a single-mode spontaneous emission coupling efficiency as high as 92%, a high degree of single-photon purity of g

^{(2)}(0) = 0.01 and a linear polarization degree up to 95% [46].

^{(2)}(0) = 0.0028 ± 0.0012. The photon extraction of 65% and measured brightness of 0.154 ± 0.015 make this source 20 times brighter than any source of equal quality. There are still huge challenges regarding electrically pumped single-photon sources based on semiconductor quantum dots, such as complicated fabrication processes, low collection efficiency, and how to effectively overcome the effects of charge noise, etc. In 2017, Heindel T. et al. introduced an attractive type of integrated twin-photon source based on a QD deterministically integrated within a monolithic microlens, as shown in Figure 6c. Triggered generation of photon pairs with the same energy and polarization becomes possible by utilizing a biexciton–exciton radiative cascade, where the biexciton binding energy equals the fine structure splitting of the bright exciton. They observed strong temporal correlations of the photon twins in auto-correlation measurements, resulting in a pronounced symmetric bunching peak. Further, by comparing the measured cross- and auto-correlation traces, they are able to determine the efficiency of the twin-photon cascade and demonstrate a HOM-type two-photon interference of (234 ± 4) kHz. In addition, they employ a photon-number-resolving detector to directly verify twin-photon emission and to reconstruct the photon number distribution emitted by the quantum emitter [64]. In 2018, Rongling Su et al. successfully demonstrated the up-converted excitation on single QDs for efficient generations of single photons using a pillar microcavity. By tuning the excitation laser frequency into the high-energy sidebands of the DBR in the micropillar while keeping the QD spectrally resonant with the cavity mode, they achieved bright on-demand single-photon emissions with a collection efficiency of (77% ± 6%) and a g

^{(2)}(0) of 0.044 ± 0.003 that is six times better than the value under above-band excitations [65]. However, it is difficult to fabricate both Bragg resonators with many periodic thin layers using epitaxial methods and photonic crystals with periodic arrays of holes using electron beam lithography (EBL). In addition, surface plasmons in metallic structures have their intrinsic drawbacks, such as high optical losses, which can quench spontaneous emission, limiting their potential applications. The coupling of QDs to lossless all-dielectric photonic nanostructures based on high refractive index materials with optical response governed by multipolar Mie-type resonances has gained increasing popularity in recent years due to the simplicity in their fabrication is markedly easier. In 2017, Rutckaia V. et al. showed that Mie resonances govern the enhancement of the photoluminescent signal from embedded Ge(Si) QDs due to a good spatial overlap of the emitter position with the electric field of Mie modes. Based on the nanodisk mode engineering, they also show that the mode hybridization in a nanodisk trimer results in an up to 10-fold enhancement of the luminescent signal due to the excitation of resonant anti-symmetric magnetic and electric dipole modes [66]. In 2023, Kroychuk M K. et al. experimentally and numerically investigated the excitation of magnetic Mie-type resonance by linearly polarized light in a GaAs nanopillar oligomer with embedded InAs QD leads to quantum emitters absorption efficiency enhancement [67]. Moreover, they experimentally demonstrated more than ten times QDs photoluminescence (PL) enhancement and numerically reached forty times gain compared to unstructured film when the excitation wavelength is in the spectral vicinity of Mie-type resonance. We believe that QDs coupling with Mie-type resonant oligomers collective modes for nanoscale single-photon sources can be a promising candidate for next-generation quantum light sources for quantum information.

_{p}= 3.5) single-photon source realized by the fabrication of a hybrid III–V/dielectric circular Bragg grating (CBG) cavity directly bonded onto a piezoelectric actuator [68], as shown in Figure 6d. Such a kind of photonic system offers the potential for broadband high photon extraction efficiency and spontaneous emission rate enhancement. This device allows for reversible spectral tuning of the embedded quantum dot emitters and pure triggered single-photon generation with g

^{(2)}(0) = (1.5 ± 0.05) × 10

^{−3}, spontaneous emission lifetimes smaller than 200 ps. By applying 18 kV/cm electric filled to the piezo substrate, they achieved a tuning range larger than 0.78 meV for QD in resonance with the cavity mode. In 2023, Li X. et al. presented a bright semiconductor single-photon source heterogeneously integrated with an on-chip electrically injected microlaser. The CBG is located right on top of the micropillar laser, and an additional spacer is designed specifically to separate cavity modes in each distinct component, as schematically shown in Figure 6e [69]. Different from previous one-by-one transfer printing techniques implemented in hybrid QD photonic devices, multiple deterministically coupled QD-CBG single-photon sources were integrated with electrically injected micropillar lasers at one time via a potentially scalable transfer printing process assisted by the wide-field photoluminescence (PL) imaging technique. Optically pumped by electrically injected microlasers, pure single photons are generated with a high brightness of count rate of 3.8 M/s and an extraction efficiency of 25.44%. Such a high brightness is due to the enhancement by the cavity mode of the CBG, which is confirmed by a Purcell factor of 2.5.

^{(2)}(0) = 0.14 using InAs/GaAs bilayer QD coupled to a distributed Bragg reflector microcolumn cavity of 3 μm diameter. Cavity mode and Purcell enhancement have been observed clearly in microphotoluminescence spectra [70]. In 2018, Liu F. et al. obtained a single-photon source with a high single-photon purity of 97.4% and indistinguishability of >90% in a waveguide-coupled QD–photonic crystal microcavity system by embedding a QD into a photonic crystal microcavity. Enhanced single-photon emission from semiconductor QD is observed due to the Purcell effect of the photonic crystal microcavity when using π-pulsed resonant excitation, as shown in Figure 6f. The radiation lifetime of the waveguide-coupled photonic crystal cavity system was shortened to 22.7 ps; this leads to near-lifetime-limited single-photon emission that retains high indistinguishability (93.9%) on a timescale in which 20 photons may be emitted [71].

^{(2)}(0) = 0.01 in saturation) is achieved, and a good single-photon purity (g

^{(2)}(0) = 0.13) together with a high detector count rate of 191 kcps is demonstrated for a temperature of up to 77 K [72]. In 2022, Xu S. W. et al. demonstrated bright telecom O-band single-photon sources based on In(Ga)As/GaAs QD deterministically coupled to hybrid CBG resonators using a wide-field fluorescence imaging technique [73]. It is worth mentioning that to ensure spatial overlaps between the QDs and hybrid CBG cavity, they used a wide-field fluorescence imaging technique to extract the positions of QDs respective to the pre-fabricated alignment marks. The QD emissions are redshifted toward the telecom O-band using an ultra-low InAs growth rate and an InGaAs strain-reducing layer. The single-photon source under both continuous wave (CW) and pulsed operations are demonstrated, showing high brightness with count rates of 1.14 MHz and 0.34 MHz under saturation powers and single-photon purities of g

^{(2)}(0) = 0.11 ± 0.02(CW) and g

^{(2)}(0) = 0.087 ± 0.003 (pulsed) at low excitation powers. A Purcell factor of 4.2 with a collection efficiency of 11.2% ± 1% at the first lens is extracted, suggesting an efficient coupling between the QD and hybrid CBG cavity.

**Figure 6.**(

**a**) An illustration of a single QD embedded in a micropillar; (

**b**) Schematic of the electrically controlled single-photon sources: a micropillar coupled to a QD is connected to a surrounding circular frame by four one-dimensional wires [63]; ((

**b**) from Ref [63], reprint with the permission of Springer Nature Publishing). (

**c**) Illustration of our solid-state-based quantum light source constituted of a single QD deterministically integrated within a monolithic microlens [64]; ((

**c**) from Ref [64], licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)). (

**d**) An artistic sketch of CBG cavity strain-tunable single-photon source composed of a 125 nm GaAs membrane with In (Ga)As QDs, a 360 nm layer of SiO

_{2}, and a back reflecting gold mirror bonded to the piezo substrate [68]; ((

**d**) from Ref [68], reprint with the permission of ACS Publishing). (

**e**) Illustration of the bright semiconductor single-photon sources pumped by heterogeneously integrated micropillar lasers with electrical injections [69]; ((

**e**) from Ref [69], licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)). (

**f**) Waveguide-coupled QD-H1 photonic crystal cavities single-photon sources [71]. ((

**f**) from Ref [71], reprint with the permission of Springer Nature Publishing).

_{1}) and 897.04 nm (labeled as M

_{2}), with a splitting of 183 GHz, as shown in Figure 7b. Figure 7c shows the polarization of M

_{1}(M

_{2}) is parallel to the minor (major) axis, with a high degree of polarization of 99.7% (99.6%), which confirms the symmetry-broken, highly polarized nature of the elliptical micropillar cavity. The mode of the elliptical CBG cavities splits into a doublet (labeled as B1 and B2), and the splitting is 2.8 THz, which is 1.5 (1.3) times larger than the linewidth of B1 (B2), as shown in Figure 7e. Figure 7f shows with time-resolved resonance fluorescence measurements, the radiative lifetime for the QD coupled to the elliptical micropillar cavity and the elliptical CBG cavity are ~61.0(1)ps and ~69.1(1)ps, respectively, ~17.8 and ~15.7 times shorter than the average lifetime (~1.09 μs) of more than 20 QDs in the slab from the same area. They demonstrated a polarized single-photon efficiency of 0.60 ± 0.02 (0.56 ± 0.02), a single-photon purity of 0.975 ± 0.005 (0.991 ± 0.003), and indistinguishability of 0.975 ± 0.006 (0.951 ± 0.005) for the elliptical micropillar (elliptical CBG) cavity. This work provides promising solutions for truly optimal single-photon sources combining near-unity indistinguishability and near-unity system efficiency simultaneously.

_{2}, and the gold mirror surface at the bottom reflects the single photons radiated downward from the quantum dots into the metalens, thus improving the collection efficiency of the single-photon source radiation. Although the radiation from the QD single-photon source is random, it can always be decomposed into two opposite spin states with left-hand circular polarization and right-hand circular polarization. In order to separate these two spin state emissions along different directions, a geometric phase-based phase mutation can be used to design a metalens. Based on this design, the structure of the silicon-based metalens with bifocal point is obtained by using fluorescence imaging, precise positioning technique, and nano-processing techniques. The optical test results show that for the structure with θ

_{1}= −θ

_{2}= 0°, the half-height widths of the single-photon radiation in the horizontal and vertical directions are 5.47° and 5.99°, respectively, which are basically consistent with the simulated result of 5.8°; for the structure with θ

_{1}= −θ

_{2}= 20°, the half-height widths of the single-photon radiation in the horizontal and vertical directions are 4.84° and 3.17°, respectively. The polarization of left and right spin polarization is 88% and 78%, respectively. In the following year, the team proposed to place a single QD inside a micro-ring resonant cavity waveguide with second-order angular gratings embedded in the inner wall to enable efficient coupling of the QD with a micro-cavity mode with orbital angular momentum, as shown in Figure 8b [78]. When the two modes are modulated by the angular grating, the mode inside the micro-ring is scattered into free space in a spiral propagation, thus enabling the generation of orbital angular momentum photons. For a micro-ring resonant cavity with a fixed grating number q, where the angular quantum number p of the echo wall mode determines the topological charge number l of the outgoing orbital angular momentum, i.e., l = sign(p)(|p|-q) [79]. Therefore, the orbital angular momentum mode of the QD producing upward radiation in this micro-ring resonant cavity is a superposition state of order l. To maximize the coupling of the single photons emitted from the QD into the cavity mode, experimentally, they tuned the QD exciton lines to the center of the cavity mode by temperature tuning so that the peak position of the single photons resonates with the peak position of the cavity mode, thus achieving a spontaneous radiation rate enhancement of the quantum dot by the micro-ring resonant cavity by a factor of about 2. The single-photon purity of the single-photon source carrying orbital angular momentum emitted by characterizing the second-order correlation function with zero delays is close to 90%. The near-field and far-field mode distributions obtained from the single-photon emitted light after cavity mode modulation show that the outgoing photons carry a superposition of the orbital angular momentum states.

_{p}= 1.8 ± 0.4) for this topological quantum light source and demonstrate its emission of nonclassical light (the second-order correlation function of the in resonant QD gives a g

^{(2)}(0) = (0.365 ± 0.006)) on demand [87]. Figure 8c shows a sketch of the structure, where the cut through the structures highlights the difference in the cavity layer thickness and, therefore, a difference in the optical confinement potential.

**Figure 8.**(

**a**) Illustration of the designed structure for manipulating QD emission [77]. The structure consists of three layers: a top metasurface layer, a middle dielectric layer with a QD embedded, and a bottom gold reflector layer; ((

**a**) from Ref [77], licensed under a Creative Commons Attribution (CC BY) license). (

**b**) Schematic of the devices emitting single photons carrying OAM [78]. Single epitaxial QDs are located in each microring with an angular grating patterned along the inner wall; ((

**b**) from Ref [78], reprint with the permission of Springer Nature Publishing). (

**c**) Sketch of an etch-and-overgrowth zigzag chain with n = 11 coupled traps [87]. The defect mode is indicated at the left side of the chain; the detuning of the QD to the cavity plotted vs. the intensity of the QD emission shows a clear enhancement at zero detuning. ((

**c**) from Ref [87], reprint with the permission of ACS Publishing).

## 5. Artificial Microstructures Enhanced Entangled Photon Emission from Semiconductor Quantum Dots

^{6}s

^{−1}and measured lifetimes down to (14 ± 1)ps for the $|\mathrm{XX}\rangle $ transition and (23 ± 1) ps for the $|\mathrm{X}\rangle $ transition, corresponding to Purcell factors up to 11. In the same year, Ginés L et al. utilized a micropillar cavity (the QD is deterministically positioned in the center of the micropillar, the top 5 and bottom 18 pairs of λ/4 AlAs/GaAs DBR forming a cavity) with a low Q factor (280) and demonstrated that such the device with 69.4 (10)% efficiency that features broadband operation suitable for extraction of photon pairs, and the design of the device could be further optimized to allow for extraction efficiency of 85% [98]. The QD is excited collinearly with the axis of the micropillar. The inset represents the two-photon resonant excitation scheme: a laser coherently couples the ground $|g\rangle $ to the biexciton state $|\mathrm{XX}\rangle $ through two-photon resonant excitation, the QD system decays to the ground state via exciton state $|\mathrm{X}\rangle $, emitting the biexciton-exciton cascade, as shown in Figure 9c.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The possible output results and probability amplitudes of two photons incident through a 50:50 beam splitter.

**Figure 3.**(

**a**) Schematic diagram of the inward total reflection angle of GaAs material; (

**b**) Interaction of the two-energy system with the cavity.

**Figure 4.**(

**a**) Lattice mismatch on InAs/GaAs material; (

**b**) AFM images of self-organized grown InAs/GaAs QD, the bright spot-like structures are typical of QD with lateral diameters of 10~70 nm and heights of 1~10 nm. Inset: shows a three-dimensional scanning tunneling microscopy image of an uncovered InAs QD grown on GaAs (001) [37]. (

**b**) inset from Ref [37], reprint with the permission of AIP Publishing).

**Figure 5.**(

**a**) Energy level structure of InAs/GaAs QD; (

**b**) Schematic diagram of neutral exciton and charged exciton.

**Figure 7.**(

**a**) Illustration of the InGaAs QD elliptical micropillar single-photon sources [74]; (

**b**) Two fundamental modes of the elliptical micropillar, M

_{1}and M

_{2}; (

**c**) Polarization-resolved measurement of the two cavity modes, which are perpendicular to one another; (

**d**) Schematic structure of the elliptical CBG, which consists of a central elliptical disk; (

**e**) Two non-degenerate modes of broadband CBG cavity, B

_{1}and B

_{2}. The investigated quantum dot is resonant with B

_{2}; (

**f**) Radiative lifetime of the quantum dots coupled to the elliptical CBG cavity (red) and in the elliptical micropillar cavity (blue). ((

**a**–

**f**) from Ref [74], reprint with the permission of Springer Nature Publishing).

**Figure 9.**(

**a**) An illustration of a CBG cavity on a highly efficient broadband reflector with a single QD emitting entangled photon pairs. (

**b**) Sketch of the CBG cavity on a six-legged piezoelectric substrate mounted on a chip carrier [97]; ((

**b**) from Ref [97], licensed under a Creative Commons Attribution (CC BY) license). (

**c**) Schematic of the micropillar cavity entangled photon generation and the excitation method [98]. ((

**c**) from Ref [98], licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)).

Photonic Structure | Life Time (ns) | Wavelength (nm) | ${\mathit{g}}^{2}\left(0\right)$ | References |
---|---|---|---|---|

Micropillar | 0.65 | ~917 | 0.05 | [47] |

Micropillar | 0.015 | ~956 | 0.18 | [48] |

Photonic crystal cavities | 0.045 | ~944 | 0.05 | [49] |

Tapered nanowires | 2.4 | ~915 | <0.008 | [50] |

Photonic crystal cavities | ~1 | ~1550 | 0.43 ± 0.04 | [51] |

Tapered nanowires | 1.7 ± 0.1 | ~881 | 0.12 | [52] |

Photonic crystal cavities | 0.2 | ~1550 | 0.10 ± 0.02 | [53] |

Photonic crystal cavities | 0:87 ± 0:15 | ~910 | 0:27 ± 0:07 | [54] |

Nano-trumpet | 0.82 | ~907 | 0.31 | [55] |

Micropillar | 0.265–0.270 | ~932 | 0.05 | [56] |

Micropillar | ~0.39 | ~941 | 0.012(2) | [57] |

Photonic crystal cavities | 1.61 | ~905 | 0.04 ± 0.05 | [58] |

Adiabatic pillar | 0.14 ± 0.04 | ~945 | 0.10 ± 0.03 | [59] |

Microlens | ~1 | ~925 | <0.01 | [60] |

Circular Bragg grating(CBG) cavities | 0.52 | ~907 | 0.009 ± 0.005 | [61] |

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Li, R.; Liu, F.; Lu, Q.
Quantum Light Source Based on Semiconductor Quantum Dots: A Review. *Photonics* **2023**, *10*, 639.
https://doi.org/10.3390/photonics10060639

**AMA Style**

Li R, Liu F, Lu Q.
Quantum Light Source Based on Semiconductor Quantum Dots: A Review. *Photonics*. 2023; 10(6):639.
https://doi.org/10.3390/photonics10060639

**Chicago/Turabian Style**

Li, Rusong, Fengqi Liu, and Quanyong Lu.
2023. "Quantum Light Source Based on Semiconductor Quantum Dots: A Review" *Photonics* 10, no. 6: 639.
https://doi.org/10.3390/photonics10060639