Quantum dot single-photon source

<h2 id="history">History</h2>
With the growing interest in <a href="/facts/Quantum_information_science/JDuxpHp8">quantum information science</a> 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<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a> 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.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a> Sources were subsequently embedded in different structures such as photonic crystals<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> or micropillars.<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> Adding <a href="/facts/Distributed_bragg_reflector/UfJMWTLm">distributed bragg reflectors</a> (DBRs) allowed emission in a well-defined direction and increased emission efficiency.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> Most quantum dot single-photon sources need to work at <a href="/facts/Cryogenic_temperature/cw7dHAkp">cryogenic temperatures</a>, which is still a technical challenge.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> The other challenge is to realize high-quality quantum dot single-photon sources at telecom wavelength for fiber telecommunication application.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> 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.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a>

<h2 id="theory-of-realizing-a-single-photon-source">Theory of realizing a single-photon source</h2>

Exciting an electron in a <a href="/facts/Semiconductor/zFf3mGTE">semiconductor</a> from the <a href="/facts/Valence_band/2NUALlHJ">valence band</a> to the <a href="/facts/Conduction_band/2NUALlHJ">conduction band</a> creates an excited state, a so-called <a href="/facts/Exciton/aFIBtIqQ">exciton</a>. 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 <a href="/facts/Optical_cavity/BITPG3ga">optical cavity</a>. 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 (<a href="/facts/Purcell_effect/9rgFKAnB">Purcell effect</a>), facilitating efficient guiding of the emission into an optical fiber. Furthermore, the reduced exciton lifetime 
 
 
 
 Δ
 t
 
 
 {\displaystyle \Delta t}
 
 (see Fig. 2) reduces the significance of <a href="/facts/Spectral_line/HuI4Bj5f">linewidth broadening</a> due to noise.

The system can then be approximated by the <a href="/facts/Jaynes-Cummings_model/X0h03xKk">Jaynes-Cummings model</a>. 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 <a href="/facts/Polarization_(waves)/fP33m0eD">polarization</a> is aligned by a <a href="/facts/Polarizer/kPDwyboP">polarizer</a>. The solution of the Jaynes-Cummings Hamiltonian is a <a href="/facts/Vacuum_Rabi_oscillation/zrTVarBx">vacuum Rabi oscillation</a>. A vacuum Rabi oscillation of a photon interacting with an exciton is known as an <a href="/facts/Exciton-polaritons/qkpq8YFe">exciton-polariton</a>.
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...<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The <a href="/facts/Electromagnetic_interaction/oAkmALHT">electromagnetic interaction</a> with the already existing exciton changes the energy for creating another exciton at the same space slightly. 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 <a href="/facts/Biexciton/uzSw1QrU">biexcitons</a>. 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 <a href="/facts/Optical_filter/WdCmGqaq">optical filter</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> 
The quantum dots can be excited both electrically and optically.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> For optical pumping, a pulsed <a href="/facts/Laser/jk6PTvvT">laser</a> 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.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> This resembles a 
 
 
 
 π
 
 
 {\displaystyle \pi }
 
-pulse on the <a href="/facts/Bloch_sphere/CvgaFMNf">Bloch sphere</a>. However, this way the emitted photons have the same frequency as the pump laser. A polarizer is needed to distinguish between them.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> As the direction of polarization of the photons from the cavity is random, half of the emitted photons are blocked by this filter.

<h2 id="experimental-realization">Experimental realization</h2>
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, <a href="/facts/Photonic_crystal/R763CtuW">photonic crystal</a> 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 <a href="/facts/Stranski-Krastanov_growth/uKeB3IMx">Stranski-Krastanov growth</a> mode, but other materials and growth methods such as local droplet etching <a class="footnote-ref" id="fnref:14" href="#fn:14">14</a><a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> have been used. A list of different experimental realizations is shown below:

<ul><li>Micropillars: In this approach, quantum dots are grown between two <a href="/facts/Distributed_bragg_reflector/UfJMWTLm">distributed bragg reflectors</a> (DBR mirrors). The DBRs are typically both grown by <a href="/facts/Molecular_beam_epitaxy/zIhe0lMv">molecular beam epitaxy</a> (MBE). For the mirrors two materials with different <a href="/facts/Refractive_index/yjkzvgeE">indices of refraction</a> are grown in alternate order. Their lattice parameters should match to prevent strain. A possible combination is a combination of <a href="/facts/Aluminum_arsenide/Ke8qJeGc">aluminum arsenide</a> and <a href="/facts/Gallium_arsenide/BakLFjpp">gallium arsenide</a>-layers.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a><a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> After the first DBR, material with smaller <a href="/facts/Band_gap/IjIeh95l">band gap</a> 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.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> 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.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a> The edges thus must be as smooth as possible to minimize losses. This can be achieved by structuring the sample with <a href="/facts/Electron_beam_lithography/KILHHdKk">Electron beam lithography</a> and processing the pillars with <a href="/facts/Reactive_ion_etching/sugH0RUh">reactive ion etching</a>.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a></li></ul>
<ul><li>Tunable micro-cavities hosting quantum dots can be also used as single-photon source.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a><a class="footnote-ref" id="fnref:22" href="#fn:22">22</a> 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 <a href="/facts/Semiconductor/zFf3mGTE">semiconductor</a>. 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 <a href="/facts/Diode/JyaoyGnk">diode</a> structures.<a class="footnote-ref" id="fnref:23" href="#fn:23">23</a> A disadvantage of the micro-cavity system is that it requires additional mechanical components to tune the cavity which increases the overall system size.</li></ul>
<ul><li>Microlens and <a href="/facts/Solid_immersion_lens/mVc8HAXD">solid immersion lens</a>: To increase the brightness of a quantum dot single-photon source, also microlens structures have been used.<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a> The concept is to reduce losses due to <a href="/facts/Total_internal_reflection/Tm0M62NQ">total internal reflection</a> similar to what can be achieved with a solid immersion lens.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a></li></ul>
<ul><li>Other single-photon sources are nanobeam or photonic crystal waveguides <a class="footnote-ref" id="fnref:26" href="#fn:26">26</a><a class="footnote-ref" id="fnref:27" href="#fn:27">27</a><a class="footnote-ref" id="fnref:28" href="#fn:28">28</a> 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.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> 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.</li></ul>
<h3>Verification of emission of single photons</h3>
Single photon sources exhibit <a href="/facts/Photon_antibunching/FWGyBnHY">antibunching</a>. 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 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 τ
 )
 
 
 {\displaystyle g^{(2)}(\tau )}
 
. A photon source is antibunched if 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 0
 )
 
 
 {\displaystyle g^{(2)}(0)}
 
 ≤ 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 τ
 )
 
 
 {\displaystyle g^{(2)}(\tau )}
 
.<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a> For an ideal single photon source, 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 0
 )
 =
 0
 
 
 {\displaystyle g^{(2)}(0)=0}
 
. Experimentally, 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 τ
 )
 
 
 {\displaystyle g^{(2)}(\tau )}
 
 is measured using the <a href="/facts/Hanbury_Brown_and_Twiss_effect/BUfkpgAa">Hanbury Brown and Twiss effect</a>. Using resonant excitation schemes, experimental values for 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 0
 )
 
 
 {\displaystyle g^{(2)}(0)}
 
 are typically in the regime of just a few percent.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a><a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> Values down to 
 
 
 
 
 g
 
 (
 2
 )
 
 
 (
 0
 )
 =
 7.5
 ×
 
 10
 
 −
 5
 
 
 
 
 {\displaystyle g^{(2)}(0)=7.5\times 10^{-5}}
 
 have been reached without resonant excitation.<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a>

<h3>Indistinguishability of the emitted photons</h3>
For applications the photons emitted by a single photon source must be <a href="/facts/Identical_particles/qg0mHeVR">indistinguishable</a>. 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 <a href="/facts/Hong-Ou-Mandel_effect/TI5TFnmM">Hong-Ou-Mandel effect</a> is used. Two photons of the source are prepared so that they enter a 50:50 <a href="/facts/Beam_splitter/3PFoofER">beam splitter</a> at the same time from the two different input channels. A <a href="/facts/Photodetector/7cSkXS6s">detector</a> 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.<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a> Experimentally, almost perfect indistinguishability is found.<a class="footnote-ref" id="fnref:35" href="#fn:35">35</a><a class="footnote-ref" id="fnref:36" href="#fn:36">36</a>

<h2 id="applications">Applications</h2>
Single-photon sources are of great importance in quantum communication science. They can be used for truly random number generators.<a class="footnote-ref" id="fnref:37" href="#fn:37">37</a> Single photons entering a beam splitter exhibit inherent <a href="/facts/Quantum_indeterminacy/v9omYD5e">quantum indeterminacy</a>. Random numbers are used extensively in simulations using the <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo method</a>.
Furthermore, single photon sources are essential in <a href="/facts/Quantum_cryptography/FPqPdNXT">quantum cryptography</a>. The <a href="/facts/BB84/8d2G3lfC">BB84</a><a class="footnote-ref" id="fnref:38" href="#fn:38">38</a> scheme is a <a href="/facts/Provable_security/2kQS1WId">provable secure</a> <a href="/facts/Quantum_key_distribution/aJ4aQ6yw">quantum key distribution</a> scheme. It works with a light source that perfectly emits only one photon at a time. Due to the <a href="/facts/No-cloning_theorem/cLYH4pQE">no-cloning theorem</a>,<a class="footnote-ref" id="fnref:39" href="#fn:39">39</a> 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 <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>.<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Optical_microcavity/0XkrTxzk">Optical microcavity</a></li>
<li><a href="/facts/Quantum_dot/K5Ytv8Yw">Quantum dot</a></li>
<li><a href="/facts/Single-photon_source/nAmXRF58">Single-photon source</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn: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 10.1.1.178.4356. doi:10.1209/0295-5075/1/4/004. S2CID 250837011. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn: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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn: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:quant-ph/0501013. Bibcode:2005PhRvB..71x1304K. doi:10.1103/PhysRevB.71.241304. S2CID 119442776. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn: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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn: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:10.1063/1.3610677. ISSN 0034-6748. PMID 21806165. <a href="https://doi.org/10.1063%2F1.3610677" target="_blank">https://doi.org/10.1063%2F1.3610677</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">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:10.1063/1.3610677. ISSN 0034-6748. PMID 21806165. <a href="https://doi.org/10.1063%2F1.3610677" target="_blank">https://doi.org/10.1063%2F1.3610677</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">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:1203.6171. Bibcode:2012NatSR...2..321B. doi:10.1038/srep00321. PMC 3307054. PMID 22432053. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3307054" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3307054</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">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:1407.0691. Bibcode:2014Natur.514..343K. doi:10.1038/nature13832. PMID 25318523. S2CID 4470179. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Gold, Peter (2015). "Quantenpunkt-Mikroresonatoren als Bausteine für die Quantenkommunikation". {{cite journal}}: Cite journal requires |journal= (help) <a href="/wiki/Template:Cite_journal" target="_blank">/wiki/Template:Cite_journal</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">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:10.1063/1.3610677. ISSN 0034-6748. PMID 21806165. <a href="https://doi.org/10.1063%2F1.3610677" target="_blank">https://doi.org/10.1063%2F1.3610677</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">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:1507.04937. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID 26799002. S2CID 206266974. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">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:1507.04937. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID 26799002. S2CID 206266974. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">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:2103.15083. Bibcode:2019NatMa..18..799G. doi:10.1038/s41563-019-0355-y. ISSN 1476-1122. PMID 31086322. S2CID 155091956. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">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): 4745. arXiv:2003.00023. Bibcode:2020NatCo..11.4745Z. doi:10.1038/s41467-020-18625-z. ISSN 2041-1723. PMC 7506537. PMID 32958795. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7506537" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7506537</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">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:1507.04937. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID 26799002. S2CID 206266974. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">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:1510.06499. Bibcode:2016NaPho..10..340S. doi:10.1038/nphoton.2016.23. S2CID 119281960. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">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. S2CID 122998636. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">Gold, Peter (2015). "Quantenpunkt-Mikroresonatoren als Bausteine für die Quantenkommunikation". {{cite journal}}: Cite journal requires |journal= (help) <a href="/wiki/Template:Cite_journal" target="_blank">/wiki/Template:Cite_journal</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">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:2007.12654. Bibcode:2021NatNa..16..399T. doi:10.1038/s41565-020-00831-x. ISSN 1748-3387. PMID 33510454. S2CID 220769410. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Ding, Xing; Guo, Yong-Peng; Xu, Mo-Chi; Liu, Run-Ze; Zou, Geng-Yan; Zhao, Jun-Yi; Ge, Zhen-Xuan; Zhang, Qi-Hang; Liu, Hua-Liang; Wang, Lin-Jun; Chen, Ming-Cheng; Wang, Hui; He, Yu-Ming; Huo, Yong-Heng; Lu, Chao-Yang; Pan, Jian-Wei (2023). "High-efficiency single-photon source above the loss-tolerant threshold for efficient linear optical quantum computing". arXiv:2311.08347 [quant-ph]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">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:1812.08662. Bibcode:2019Natur.575..622N. doi:10.1038/s41586-019-1709-y. ISSN 0028-0836. PMID 31634901. S2CID 204832937. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">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 5485799. PMID 28670600. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5485799" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5485799</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">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. arXiv:1901.09721. Bibcode:2019NanoL..19.2404S. doi:10.1021/acs.nanolett.8b05132. ISSN 1530-6984. PMC 6463245. PMID 30862165. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6463245" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6463245</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">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. arXiv:1706.04422. Bibcode:2018NatNa..13..835L. doi:10.1038/s41565-018-0188-x. ISSN 1748-3387. PMID 30013218. S2CID 205568107. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">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. arXiv:2003.08919. Bibcode:2020SciA....6.8268U. doi:10.1126/sciadv.abc8268. ISSN 2375-2548. PMC 7725451. PMID 33298444. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7725451" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7725451</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">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. Bibcode:2015ApPhL.107b1101R. doi:10.1063/1.4926729. ISSN 0003-6951. <a href="https://doi.org/10.1063%2F1.4926729" target="_blank">https://doi.org/10.1063%2F1.4926729</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">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:1811.10962. Bibcode:2019Optic...6..524P. doi:10.1364/OPTICA.6.000524. ISSN 2334-2536. S2CID 117682842. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">Paul, H (1982). "Photon antibunching". Reviews of Modern Physics. 54 (4): 1061–1102. Bibcode:1982RvMP...54.1061P. doi:10.1103/RevModPhys.54.1061. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">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:1507.04937. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID 26799002. S2CID 206266974. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">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:1510.06499. Bibcode:2016NaPho..10..340S. doi:10.1038/nphoton.2016.23. S2CID 119281960. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">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. arXiv:1712.06937. Bibcode:2018ApPhL.112i3106S. doi:10.1063/1.5020038. ISSN 0003-6951. S2CID 21749500. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
<li id="fn:34">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></li>
<li id="fn:35">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:1510.06499. Bibcode:2016NaPho..10..340S. doi:10.1038/nphoton.2016.23. S2CID 119281960. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></li>
<li id="fn:36">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:1507.04937. Bibcode:2016PhRvL.116a0401P. doi:10.1103/PhysRevLett.116.010401. PMID 26799002. S2CID 206266974. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></li>
<li id="fn:37">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:10.1063/1.3610677. ISSN 0034-6748. PMID 21806165. <a href="https://doi.org/10.1063%2F1.3610677" target="_blank">https://doi.org/10.1063%2F1.3610677</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></li>
<li id="fn:38">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 Archived 2020-01-30 at the Wayback Machine <a href="http://researcher.watson.ibm.com/researcher/files/us-bennetc/BB84highest.pdf" target="_blank">http://researcher.watson.ibm.com/researcher/files/us-bennetc/BB84highest.pdf</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></li>
<li id="fn:39">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. <a href="/wiki/Nature_(journal)" target="_blank">/wiki/Nature_(journal)</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></li>
<li id="fn:40">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 10.1.1.178.4356. doi:10.1209/0295-5075/1/4/004. S2CID 250837011. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></li>
</ol>

Quantum dot single-photon source open-in-new

Quantum dot single-photon source