Quantum dot single-photon source

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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.

Contents

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

Figure 1: Schematic structure of an optical microcavity with a single quantum dot placed between two layers of DBR's. This structure works as a single photon source. Optical Microresonator.png
Figure 1: Schematic structure of an optical microcavity with a single quantum dot placed between two layers of DBR's. This structure works as 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 (see Fig. 2) reduces the significance of linewidth broadening due to noise.

Figure 2: The decay of a linewidth broadened excited state results in the emission of a photon of frequency ho. The linewidth broadening is a result of the finite lifetime of the excited state. Linewidth.png
Figure 2: The decay of a linewidth broadened excited state results in the emission of a photon of frequency ħω. The linewidth broadening is a result of the finite lifetime of the excited state.

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 -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:

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 . A photon source is antibunched if . [24] For an ideal single photon source, . Experimentally, is measured using the Hanbury Brown and Twiss effect. Using resonant excitation schemes, experimental values for are typically in the regime of just a few percent. [10] [13] Values down to 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]

See also

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References

  1. 1 2 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.
  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: quant-ph/0501013 . 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. 1 2 3 4 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.
  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: 1203.6171 . Bibcode:2012NatSR...2E.321B. doi:10.1038/srep00321. PMC   3307054 . 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: 1407.0691 . Bibcode:2014Natur.514..343K. doi:10.1038/nature13832. PMID   25318523. S2CID   4470179.
  9. 1 2 Gold, Peter (2015). "Quantenpunkt-Mikroresonatoren als Bausteine für die Quantenkommunikation".Cite journal requires |journal= (help)
  10. 1 2 3 4 5 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.
  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: 2103.15083 . 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   7506537 .
  13. 1 2 3 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.
  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: 2007.12654 . 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: 1812.08662 . 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   5485799 .
  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   6463245 .
  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   7725451 .
  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: 1811.10962 . 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.