# Quantum dot single-photon source

Last updated

A quantum dot single-photon source is based on a single quantum dot placed in an optical cavity. It is an on-demand single-photon source. A laser pulse can excite a pair of carriers known as an exciton in the quantum dot. The decay of a single exciton due to spontaneous emission leads to the emission of a single photon. Due to interactions between excitons, the emission when the quantum dot contains a single exciton is energetically distinct from that when the quantum dot contains more than one exciton. Therefore, a single exciton can be deterministically created by a laser pulse and the quantum dot becomes a nonclassical light source that emits photons one by one and thus shows photon antibunching. The emission of single photons can be proven by measuring the second order intensity correlation function. The spontaneous emission rate of the emitted photons can be enhanced by integrating the quantum dot in an optical cavity. Additionally, the cavity leads to emission in a well-defined optical mode increasing the efficiency of the photon source.

## History

With the growing interest in quantum information science since the beginning of the 21st century, research in different kinds of single-photon sources was growing. Early single-photon sources such as heralded photon sources [1] that were first reported in 1985 are based on non-deterministic processes. Quantum dot single-photon sources are on-demand. A single-photon source based on a quantum dot in a microdisk structure was reported in 2000. [2] Sources were subsequently embedded in different structures such as photonic crystals [3] or micropillars. [4] Adding DBRs allowed emission in a well-defined direction and increased emission efficiency. [5] Most quantum dot single-photon sources need to work at cryogenic temperatures, which is still a technical challenge. [5] The other challenge is to realize high-quality quantum dot single-photon sources at telecom wavelength for fiber telecommunication application. [6] The first report on Purcell-enhanced single-photon emission of a telecom-wavelength quantum dot in a two-dimensional photonic crystal cavity with a quality factor of 2,000 shows the enhancements of the emission rate and the intensity by five and six folds, respectively. [7]

## Theory of realizing a single-photon source

Exciting an electron in a semiconductor from the valence band to the conduction band creates an excited state, a so-called exciton. The spontaneous radiative decay of this exciton results in the emission of a photon. Since a quantum dot has discrete energy levels, it can be achieved that there is never more than one exciton in the quantum dot simultaneously. Therefore, the quantum dot is an emitter of single photons. A key challenge in making a good single-photon source is to make sure that the emission from the quantum dot is collected efficiently. To do that, the quantum dot is placed in an optical cavity. The cavity can, for instance, consist of two DBRs in a micropillar (Fig. 1). The cavity enhances the spontaneous emission in a well-defined optical mode (Purcell effect), facilitating efficient guiding of the emission into an optical fiber. Furthermore, the reduced exciton lifetime ${\displaystyle \Delta t}$ (see Fig. 2) reduces the significance of linewidth broadening due to noise.

The system can then be approximated by the Jaynes-Cummings model. In this model, the quantum dot only interacts with one single mode of the optical cavity. The frequency of the optical mode is well defined. This makes the photons indistinguishable if their polarization is aligned by a polarizer. The solution of the Jaynes-Cummings Hamiltonian is a vacuum Rabi oscillation. A vacuum Rabi oscillation of a photon interacting with an exciton is known as an exciton-polariton.

To eliminate the probability of the simultaneous emission of two photons it has to be made sure that there can only be one exciton in the cavity at one time. The discrete energy states in a quantum dot allow only one excitation. Additionally, the Rydberg blockade prevents the excitation of two excitons at the same space... [8] The electromagnetic interaction with the already existing exciton changes the energy for creating another exciton at the same space sightly. If the energy of the pump laser is tuned on resonance, the second exciton cannot be created. Still, there is a small probability of having two excitations in the quantum dot at the same time. Two excitons confined in a small volume are called biexcitons. They interact with each other and thus slightly change their energy. Photons resulting from the decay of biexcitons have a different energy than photons resulting from the decay of excitons. They can be filtered out by letting the outgoing beam pass an optical filter. [9] The quantum dots can be excited both electrically and optically. [5] For optical pumping, a pulsed laser can be used for excitation of the quantum dots. In order to have the highest probability of creating an exciton, the pump laser is tuned on resonance. [10] This resembles a ${\displaystyle \pi }$-pulse on the Bloch sphere. However, this way the emitted photons have the same frequency as the pump laser. A polarizer is needed to distinguish between them. [10] As the direction of polarization of the photons from the cavity is random, half of the emitted photons are blocked by this filter.

## Experimental realization

There are several ways to realize a quantum dot-cavity system that can act as a single-photon source. Typical cavity structures are micro-pillars, photonic crystal cavities, or tunable micro-cavities. Inside the cavity, different types of quantum dots can be used. The most widely used type are self-assembled InAs quantum dots grown in the Stranski-Krastanov growth mode, but other materials and growth methods such as local droplet etching [11] [12] have been used. A list of different experimental realizations is shown below:

• Micropillars: In this approach, quantum dots are grown between two distributed bragg reflectors (DBR mirrors). The DBRs are typically both grown by molecular beam epitaxy (MBE). For the mirrors two materials with different indices of refraction are grown in alternate order. Their lattice parameters should match to prevent strain. A possible combination is a combination of aluminum arsenide and gallium arsenide-layers. [10] [13] After the first DBR, material with smaller band gap is used to grow the quantum dot above the first DBR. The second layer of DBRs can now be grown on top of the layer with the quantum dots. The diameter of the pillar is only a few microns wide. To prevent the optical mode from exiting the cavity the micropillar must act as a waveguide. Semiconductors usually have relatively high indices of refraction about n≅3. [14] Therefore, their extraction cone is small. On a smooth surface the micropillar works as an almost perfect waveguide. However losses increase with roughness of the walls and decreasing diameter of the micropillar. [15] The edges thus must be as smooth as possible to minimize losses. This can be achieved by structuring the sample with Electron beam lithography and processing the pillars with reactive ion etching. [9]
• Tunable micro-cavities hosting quantum dots can be also used as single-photon source. [16] Different compared to micro-pillars, only a single DBR is grown below the quantum dots. The second part of the cavity is a curved top mirror that is physically detached from the semiconductor. The top-mirror can be moved with respect to the quantum dot position which allows tuning the cavity quantum dot coupling as needed. A further advantage over micro-pillars is that the charge-environment of the quantum dots can be stabilized by using diode structures. [17] A disadvantage of the micro-cavity system is that it requires additional mechanical components to tune the cavity which increases the overall system size.
• Microlens and solid immersion lens: To increase the brightness of a quantum dot single-photon source, also microlens structures have been used. [18] The concept is to reduce losses due to total internal reflection similar to what can be achieved with a solid immersion lens. [19]
• Other single-photon sources are nanobeam or photonic crystal waveguides [20] [21] [22] that contain quantum dots. For such structures, no DBRs are needed but can be used to improve the outcoupling efficiency. Compared to micropillars, this architecture has the advantage that on-chip routing of photons is possible. [23] On the other side, the structure sizes are much smaller requiring more advanced nano-fabrication techniques. The close proximity of quantum dots to the surface is a further challenge.

### Verification of emission of single photons

Single photon sources exhibit antibunching. As photons are emitted one at a time, the probability of seeing two photons at the same time for an ideal source is 0. To verify the antibunching of a light source, one can measure the autocorrelation function ${\displaystyle g^{(2)}(\tau )}$. A photon source is antibunched if ${\displaystyle g^{(2)}(0)}$${\displaystyle g^{(2)}(\tau )}$. [24] For an ideal single photon source, ${\displaystyle g^{(2)}(0)=0}$. Experimentally, ${\displaystyle g^{(2)}(\tau )}$ is measured using the Hanbury Brown and Twiss effect. Using resonant excitation schemes, experimental values for ${\displaystyle g^{(2)}(0)}$ are typically in the regime of just a few percent. [10] [13] Values down to ${\displaystyle g^{(2)}(0)=7.5\times 10^{-5}}$ have been reached without resonant excitation. [25]

### Indistinguishability of the emitted photons

For applications the photons emitted by a single photon source must be indistinguishable. The theoretical solution of the Jaynes-Cummings Hamiltonian is a well-defined mode in which only the polarization is random. After aligning the polarization of the photons, their indistinguishability can be measured. For that, the Hong-Ou-Mandel effect is used. Two photons of the source are prepared so that they enter a 50:50 beam splitter at the same time from the two different input channels. A detector is placed on both exits of the beam splitter. Coincidences between the two detectors are measured. If the photons are indistinguishable, no coincidences should occur. [26] Experimentally, almost perfect indistinguishability is found. [13] [10]

## Applications

Single-photon sources are of great importance in quantum communication science. They can be used for truly random number generators. [5] Single photons entering a beam splitter exhibit inherent quantum indeterminacy. Random numbers are used extensively in simulations using the Monte Carlo method.

Furthermore, single photon sources are essential in quantum cryptography. The BB84 [27] scheme is a provable secure quantum key distribution scheme. It works with a light source that perfectly emits only one photon at a time. Due to the no-cloning theorem, [28] no eavesdropping can happen without being noticed. The use of quantum randomness while writing the key prevents any patterns in the key that can be used to decipher the code.

Apart from that, single photon sources can be used to test some fundamental properties of quantum field theory. [1]

## Related Research Articles

Photoluminescence is light emission from any form of matter after the absorption of photons. It is one of many forms of luminescence and is initiated by photoexcitation, hence the prefix photo-. Following excitation various relaxation processes typically occur in which other photons are re-radiated. Time periods between absorption and emission may vary: ranging from short femtosecond-regime for emission involving free-carrier plasma in inorganic semiconductors up to milliseconds for Phosphorescence processes in molecular systems; and under special circumstances delay of emission may even span to minutes or hours.

Cathodoluminescence is an optical and electromagnetic phenomenon in which electrons impacting on a luminescent material such as a phosphor, cause the emission of photons which may have wavelengths in the visible spectrum. A familiar example is the generation of light by an electron beam scanning the phosphor-coated inner surface of the screen of a television that uses a cathode ray tube. Cathodoluminescence is the inverse of the photoelectric effect, in which electron emission is induced by irradiation with photons.

In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal lattice and serve as a charge carrier to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move in the solid; however, if some electrons transfer from the valence to the conduction band, then current can flow. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances with large band gaps are generally insulators, those with smaller band gaps are semiconductors, while conductors either have very small band gaps or none, because the valence and conduction bands overlap.

In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the avoided crossing principle. Polaritons describe the crossing of the dispersion of light with any interacting resonance. To this extent polaritons can also be thought as the new normal modes of a given material or structure arising from the strong coupling of the bare modes, which are the photon and the dipolar oscillation. The polariton is a bosonic quasiparticle, and should not be confused with the polaron, which is an electron plus an attached phonon cloud.

The term biophotonics denotes a combination of biology and photonics, with photonics being the science and technology of generation, manipulation, and detection of photons, quantum units of light. Photonics is related to electronics and photons. Photons play a central role in information technologies, such as fiber optics, the way electrons do in electronics.

Quantum dots (QDs) are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from larger particles due to quantum mechanics. They are a central topic in nanotechnology. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band. The excited electron can drop back into the valence band releasing its energy by the emission of light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the conductance band and the valence band.

An optical microcavity or microresonator is a structure formed by reflecting faces on the two sides of a spacer layer or optical medium, or by wrapping a waveguide in a circular fashion to form a ring. The former type is a standing wave cavity, and the latter is a traveling wave cavity. The name microcavity stems from the fact that it is often only a few micrometers thick, the spacer layer sometimes even in the nanometer range. As with common lasers this forms an optical cavity or optical resonator, allowing a standing wave to form inside the spacer layer, or a traveling wave that goes around in the ring.

Sound amplification by stimulated emission of radiation (SASER) refers to a device that emits acoustic radiation. It focuses sound waves in a way that they can serve as accurate and high-speed carriers of information in many kinds of applications—similar to uses of laser light.

The Hong–Ou–Mandel effect is a two-photon interference effect in quantum optics which was demonstrated in 1987 by three physicists from the University of Rochester: Chung Ki Hong (홍정기), Zheyu Ou (区泽宇) and Leonard Mandel. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the temporal overlap of the photons on the beam splitter is perfect, the two photons will always exit the beam splitter together in the same output mode. The photons have a 50:50 chance of exiting either output mode. If they become more distinguishable, the probability of them going to different detectors will increase. In this way the interferometer can accurately measure bandwidth, path lengths and timing. Since this effect relies on the existence of photons it can not be fully explained by classical optics.

A spaser or plasmonic laser is a type of laser which aims to confine light at a subwavelength scale far below Rayleigh's diffraction limit of light, by storing some of the light energy in electron oscillations called surface plasmon polaritons. The phenomenon was first described by David J. Bergman and Mark Stockman in 2003. The word spaser is an acronym for "surface plasmon amplification by stimulated emission of radiation". The first such devices were announced in 2009 by three groups: a 44-nanometer-diameter nanoparticle with a gold core surrounded by a dyed silica gain medium created by researchers from Purdue, Norfolk State and Cornell universities, a nanowire on a silver screen by a Berkeley group, and a semiconductor layer of 90 nm surrounded by silver pumped electrically by groups at the Eindhoven University of Technology and at Arizona State University. While the Purdue-Norfolk State-Cornell team demonstrated the confined plasmonic mode, the Berkeley team and the Eindhoven-Arizona State team demonstrated lasing in the so-called plasmonic gap mode.

Yoshihisa Yamamoto is an applied physicist and the director of Physics & Informatics Laboratories, NTT Research, Inc. He is also Professor (Emeritus) at Stanford University and National Institute of Informatics (Tokyo).

An optical transistor, also known as an optical switch or a light valve, is a device that switches or amplifies optical signals. Light occurring on an optical transistor’s input changes the intensity of light emitted from the transistor’s output while output power is supplied by an additional optical source. Since the input signal intensity may be weaker than that of the source, an optical transistor amplifies the optical signal. The device is the optical analog of the electronic transistor that forms the basis of modern electronic devices. Optical transistors provide a means to control light using only light and has applications in optical computing and fiber-optic communication networks. Such technology has the potential to exceed the speed of electronics, while conserving more power.

The Purcell effect is the enhancement of a quantum system's spontaneous emission rate by its environment. In the 1940s Edward Mills Purcell discovered the enhancement of spontaneous emission rates of atoms when they are incorporated into a resonant cavity.

Single-photon sources are light sources that emit light as single particles or photons. They are distinct from coherent light sources (lasers) and thermal light sources such as incandescent light bulbs. The Heisenberg uncertainty principle dictates that a state with an exact number of photons of a single frequency cannot be created. However, Fock states can be studied for a system where the electric field amplitude is distributed over a narrow bandwidth. In this context, a single-photon source gives rise to an effectively one-photon number state. Photons from an ideal single-photon source exhibit quantum mechanical characteristics. These characteristics include photon antibunching, so that the time between two successive photons is never less than some minimum value. This is normally demonstrated by using a beam splitter to direct about half of the incident photons toward one avalanche photodiode, and half toward a second. Pulses from one detector are used to provide a ‘counter start’ signal, to a fast electronic timer, and the other, delayed by a known number of nanoseconds, is used to provide a ‘counter stop’ signal. By repeatedly measuring the times between ‘start’ and ‘stop’ signals, one can form a histogram of time delay between two photons and the coincidence count- if bunching is not occurring, and photons are indeed well spaced, a clear notch around zero delay is visible.

The semiconductor luminescence equations (SLEs) describe luminescence of semiconductors resulting from spontaneous recombination of electronic excitations, producing a flux of spontaneously emitted light. This description established the first step toward semiconductor quantum optics because the SLEs simultaneously includes the quantized light–matter interaction and the Coulomb-interaction coupling among electronic excitations within a semiconductor. The SLEs are one of the most accurate methods to describe light emission in semiconductors and they are suited for a systematic modeling of semiconductor emission ranging from excitonic luminescence to lasers.

Quantum-optical spectroscopy is a quantum-optical generalization of laser spectroscopy where matter is excited and probed with a sequence of laser pulses.

A nanophotonic resonator or nanocavity is an optical cavity which is on the order of tens to hundreds of nanometers in size. Optical cavities are a major component of all lasers, they are responsible for providing amplification of a light source via positive feedback, a process known as amplified spontaneous emission or ASE. Nanophotonic resonators offer inherently higher light energy confinement than ordinary cavities, which means stronger light-material interactions, and therefore lower lasing threshold provided the quality factor of the resonator is high. Nanophotonic resonators can be made with photonic crystals, silicon, diamond, or metals such as gold.

JCMsuite is a finite element analysis software package for the simulation and analysis of electromagnetic waves, elasticity and heat conduction. It also allows a mutual coupling between its optical, heat conduction and continuum mechanics solvers. The software is mainly applied for the analysis and optimization of nanooptical and microoptical systems. Its applications in research and development projects include dimensional metrology systems, photolithographic systems, photonic crystal fibers, VCSELs, Quantum-Dot emitters, light trapping in solar cells, and plasmonic systems. The design tasks can be embedded into the high-level scripting languages MATLAB and Python, enabling a scripting of design setups in order to define parameter dependent problems or to run parameter scans.

The model usually designated as Lugiato–Lefever equation (LLE) was formulated in 1987 by Luigi Lugiato and René Lefever as a paradigm for spontaneous pattern formation in nonlinear optical systems. The patterns originate from the interaction of a coherent field, that is injected into a resonant optical cavity, with a Kerr medium that fills the cavity.

Pascale Senellart is a French physicist who is a Senior Researcher at the French National Centre for Scientific Research and Professor at the École Polytechnique. She has worked on quantum light sources and semiconductor physics. She was awarded the CNRS Silver Medal in 2014 and made Fellow of The Optical Society in 2018.

## References

1. Grangier, Philippe; Roger, Gerard; Aspect, Alain (1986). "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences". EPL (Europhysics Letters). 1 (4): 173. Bibcode:1986EL......1..173G. CiteSeerX  . doi:10.1209/0295-5075/1/4/004.
2. Michler, P.; Kiraz, A.; Becher, C.; Schoenfeld, W.V.; Petroff, P.M.; Zhang, Lidong; Hu, E.; Imamoglu, A. (2000). "A Quantum Dot Single-Photon Turnstile Device". Science. 290 (5500): 2282–2285. Bibcode:2000Sci...290.2282M. doi:10.1126/science.290.5500.2282. PMID   11125136.
3. Kress, A.; Hofbauer, F.; Reinelt, N.; Kaniber, M.; Krenner, H.J.; Meyer, R.; Böhm, G.; Finley, J.J. (2005). "Manipulation of the spontaneous emission dynamics of quantum dots in two-dimensional photonic crystals". Phys. Rev. B. 71 (24): 241304. arXiv:. Bibcode:2005PhRvB..71x1304K. doi:10.1103/PhysRevB.71.241304. S2CID   119442776.
4. Moreau, E.; Robert, I.; Gérard, J.M.; Abram, I.; Manin, L.; Thierry-Mieg, V. (2001). "Single-mode solid-state single-photon source based on isolated quantum dots in pillar microcavities". Appl. Phys. Lett. 79 (18): 2865–2867. Bibcode:2001ApPhL..79.2865M. doi:10.1063/1.1415346.
5. Eisaman, M. D.; Fan, J.; Migdall, A.; Polyakov, S. V. (2011-07-01). "Invited Review Article: Single-photon sources and detectors". Review of Scientific Instruments. 82 (7): 071101–071101–25. Bibcode:2011RScI...82g1101E. doi:. ISSN   0034-6748. PMID   21806165.
6. Senellart, P.; Solomon, G.; White, A. (2017). "High-performance semiconductor quantum-dot single-photon sources". Nature Nanotechnology. 12 (11): 1026–1039. Bibcode:2017NatNa..12.1026S. doi:10.1038/nnano.2017.218. PMID   29109549.
7. Birowosuto, M. D.; Sumikura, H.; Matsuo, S.; Taniyama, H.; Veldhoven, P.J.; Notzel, R.; Notomi, M. (2012). "Fast Purcell-enhanced single-photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling". Sci. Rep. 2: 321. arXiv:. Bibcode:2012NatSR...2E.321B. doi:10.1038/srep00321. PMC  . PMID   22432053.
8. T. Kazimierczuk; D. Fröhlich; S. Scheel; H. Stolz & M. Bayer (2014). "Giant Rydberg excitons in the copper oxide Cu2O". Nature. 514 (7522): 343–347. arXiv:. Bibcode:2014Natur.514..343K. doi:10.1038/nature13832. PMID   25318523. S2CID   4470179.
9. Gold, Peter (2015). "Quantenpunkt-Mikroresonatoren als Bausteine für die Quantenkommunikation".Cite journal requires |journal= (help)
10. Ding, Xing; He, Yu; Duan, Z-C; Gregersen, Niels; Chen, M-C; Unsleber, S; Maier, Sebastian; Schneider, Christian; Kamp, Martin; Höfling, Sven; Lu, Chao-Yang; Pan, Jian-Wei (2016). "On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar". Physical Review Letters. 116 (2): 020401. arXiv:. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID   26799002. S2CID   206266974.
11. Gurioli, Massimo; Wang, Zhiming; Rastelli, Armando; Kuroda, Takashi; Sanguinetti, Stefano (2019). "Droplet epitaxy of semiconductor nanostructures for quantum photonic devices". Nature Materials. 18 (8): 799–810. arXiv:. doi:10.1038/s41563-019-0355-y. ISSN   1476-1122.
12. Zhai, Liang; Löbl, Matthias C.; Nguyen, Giang N.; Ritzmann, Julian; Javadi, Alisa; Spinnler, Clemens; Wieck, Andreas D.; Ludwig, Arne; Warburton, Richard J. (2020). "Low-noise GaAs quantum dots for quantum photonics". Nature Communications. 11 (1). doi:10.1038/s41467-020-18625-z. ISSN   2041-1723. PMC  .
13. Somaschi, Niccolo; Giesz, Valérian; De Santis, Lorenzo; Loredo, JC; Almeida, Marcelo P; Hornecker, Gaston; Portalupi, Simone Luca; Grange, Thomas; Anton, Carlos; Demory, Justin (2016). "Near-optimal single-photon sources in the solid state". Nature Photonics. 10 (5): 340–345. arXiv:. Bibcode:2016NaPho..10..340S. doi:10.1038/nphoton.2016.23. S2CID   119281960.
14. Herve, P.; Vandamme, L. K. J. (1994). "General relation between refractive index and energy gap in semiconductors". Infrared Physics & Technology. 35 (4): 609–615. Bibcode:1994InPhT..35..609H. doi:10.1016/1350-4495(94)90026-4.
15. Reitzenstein, S. & Forchel, A. (2010). "Quantum dot micropillars". Journal of Physics D: Applied Physics. 43 (3): 033001. doi:10.1088/0022-3727/43/3/033001.
16. Tomm, Natasha; Javadi, Alisa; Antoniadis, Nadia Olympia; Najer, Daniel; Löbl, Matthias Christian; Korsch, Alexander Rolf; Schott, Rüdiger; Valentin, Sascha René; Wieck, Andreas Dirk; Ludwig, Arne; Warburton, Richard John (2021). "A bright and fast source of coherent single photons". Nature Nanotechnology. 16 (4): 399–403. arXiv:. doi:10.1038/s41565-020-00831-x. ISSN   1748-3387.
17. Najer, Daniel; Söllner, Immo; Sekatski, Pavel; Dolique, Vincent; Löbl, Matthias C.; Riedel, Daniel; Schott, Rüdiger; Starosielec, Sebastian; Valentin, Sascha R.; Wieck, Andreas D.; Sangouard, Nicolas; Ludwig, Arne; Warburton, Richard J. (2019). "A gated quantum dot strongly coupled to an optical microcavity". Nature. 575 (7784): 622–627. arXiv:. doi:10.1038/s41586-019-1709-y. ISSN   0028-0836.
18. Fischbach, Sarah; Schlehahn, Alexander; Thoma, Alexander; Srocka, Nicole; Gissibl, Timo; Ristok, Simon; Thiele, Simon; Kaganskiy, Arsenty; Strittmatter, André; Heindel, Tobias; Rodt, Sven; Herkommer, Alois; Giessen, Harald; Reitzenstein, Stephan (2017). "Single Quantum Dot with Microlens and 3D-Printed Micro-objective as Integrated Bright Single-Photon Source". ACS Photonics. 4 (6): 1327–1332. doi:10.1021/acsphotonics.7b00253. ISSN   2330-4022. PMC  .
19. Schöll, Eva; Hanschke, Lukas; Schweickert, Lucas; Zeuner, Katharina D.; Reindl, Marcus; Covre da Silva, Saimon Filipe; Lettner, Thomas; Trotta, Rinaldo; Finley, Jonathan J.; Müller, Kai; Rastelli, Armando; Zwiller, Val; Jöns, Klaus D. (2019). "Resonance Fluorescence of GaAs Quantum Dots with Near-Unity Photon Indistinguishability". Nano Letters. 19 (4): 2404–2410. doi:10.1021/acs.nanolett.8b05132. ISSN   1530-6984. PMC  .
20. Liu, Feng; Brash, Alistair J.; O’Hara, John; Martins, Luis M. P. P.; Phillips, Catherine L.; Coles, Rikki J.; Royall, Benjamin; Clarke, Edmund; Bentham, Christopher; Prtljaga, Nikola; Itskevich, Igor E.; Wilson, Luke R.; Skolnick, Maurice S.; Fox, A. Mark (2018). "High Purcell factor generation of indistinguishable on-chip single photons". Nature Nanotechnology. 13 (9): 835–840. doi:10.1038/s41565-018-0188-x. ISSN   1748-3387.
21. Uppu, Ravitej; Pedersen, Freja T.; Wang, Ying; Olesen, Cecilie T.; Papon, Camille; Zhou, Xiaoyan; Midolo, Leonardo; Scholz, Sven; Wieck, Andreas D.; Ludwig, Arne; Lodahl, Peter (2020). "Scalable integrated single-photon source". Science Advances. 6 (50): eabc8268. doi:10.1126/sciadv.abc8268. ISSN   2375-2548. PMC  .
22. Rengstl, U.; Schwartz, M.; Herzog, T.; Hargart, F.; Paul, M.; Portalupi, S. L.; Jetter, M.; Michler, P. (2015). "On-chip beamsplitter operation on single photons from quasi-resonantly excited quantum dots embedded in GaAs rib waveguides". Applied Physics Letters. 107 (2): 021101. doi:10.1063/1.4926729. ISSN   0003-6951.
23. Papon, Camille; Zhou, Xiaoyan; Thyrrestrup, Henri; Liu, Zhe; Stobbe, Søren; Schott, Rüdiger; Wieck, Andreas D.; Ludwig, Arne; Lodahl, Peter; Midolo, Leonardo (2019). "Nanomechanical single-photon routing". Optica. 6 (4): 524. arXiv:. doi:10.1364/OPTICA.6.000524. ISSN   2334-2536.
24. Paul, H (1982). "Photon antibunching". Reviews of Modern Physics. 54 (4): 1061–1102. Bibcode:1982RvMP...54.1061P. doi:10.1103/RevModPhys.54.1061.
25. Schweickert, Lucas; Jöns, Klaus D.; Zeuner, Katharina D.; Covre da Silva, Saimon Filipe; Huang, Huiying; Lettner, Thomas; Reindl, Marcus; Zichi, Julien; Trotta, Rinaldo; Rastelli, Armando; Zwiller, Val (2018). "On-demand generation of background-free single photons from a solid-state source". Applied Physics Letters. 112 (9): 093106. doi:10.1063/1.5020038. ISSN   0003-6951.
26. C. K. Hong; Z. Y. Ou & L. Mandel (1987). "Measurement of subpicosecond time intervals between two photons by interference". Phys. Rev. Lett. 59 (18): 2044–2046. Bibcode:1987PhRvL..59.2044H. doi:10.1103/PhysRevLett.59.2044. PMID   10035403.
27. C. H. Bennett and G. Brassard. "Quantum cryptography: Public key distribution and coin tossing". In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, volume 175, page 8. New York, 1984. http://researcher.watson.ibm.com/researcher/files/us-bennetc/BB84highest.pdf
28. Wootters, William; Zurek, Wojciech (1982). "A Single Quantum Cannot be Cloned". Nature . 299 (5886): 802–803. Bibcode:1982Natur.299..802W. doi:10.1038/299802a0. S2CID   4339227.