Quantum repeaters with individual rare-earth ions at telecommunication wavelengths
Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| Published: | 2018-09-13, volume 2, page 93 |
| Eprint: | arXiv:1712.05356v3 |
| Doi: | https://doi.org/10.22331/q-2018-09-13-93 |
| Citation: | Quantum 2, 93 (2018). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We present a quantum repeater scheme that is based on individual erbium and europium ions. Erbium ions are attractive because they emit photons at telecommunication wavelength, while europium ions offer exceptional spin coherence for long-term storage. Entanglement between distant erbium ions is created by photon detection. The photon emission rate of each erbium ion is enhanced by a microcavity with high Purcell factor, as has recently been demonstrated. Entanglement is then transferred to nearby europium ions for storage. Gate operations between nearby ions are performed using dynamically controlled electric-dipole coupling. These gate operations allow entanglement swapping to be employed in order to extend the distance over which entanglement is distributed. The deterministic character of the gate operations allows improved entanglement distribution rates in comparison to atomic ensemble-based protocols. We also propose an approach that utilizes multiplexing in order to enhance the entanglement distribution rate.
► BibTeX data
► References
[1] T. Jennewein and B. Higgins, Physics World 26, 52 (2013).
https://doi.org/10.1088/2058-7058/26/03/37
[2] P. Komar, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, Nat. Phys. 10, 582 (2014).
https://doi.org/10.1038/nphys3000
[3] D. Gottesman, T. Jennewein, and S. Croke, Phys. Rev. Lett. 109, 070503 (2012).
https://doi.org/10.1103/PhysRevLett.109.070503
[4] H. J. Kimble, Nature 453, 1023 (2008).
https://doi.org/10.1038/nature07127
[5] C. Simon, Nat. Photonics 11, 678– (2017).
https://doi.org/10.1038/s41566-017-0032-0
[6] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).
https://doi.org/10.1103/PhysRevLett.81.5932
[7] N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Rev. Mod. Phys. 83, 33 (2011).
https://doi.org/10.1103/RevModPhys.83.33
[8] W. P. Grice, Phys. Rev. A 84, 042331 (2011).
https://doi.org/10.1103/PhysRevA.84.042331
[9] S. Wein, K. Heshami, C. A. Fuchs, H. Krovi, Z. Dutton, W. Tittel, and C. Simon, Phys. Rev. A 94, 032332 (2016).
https://doi.org/10.1103/PhysRevA.94.032332
[10] N. Sangouard, R. Dubessy, and C. Simon, Phys. Rev. A 79, 042340 (2009).
https://doi.org/10.1103/PhysRevA.79.042340
[11] S. Ritter, C. Nolleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mucke, E. Figueroa, J. Bochmann, and G. Rempe, Nature 484, 195 (2012).
https://doi.org/10.1038/nature11023
[12] A. Reiserer and G. Rempe, Rev. Mod. Phys. 87, 1379 (2015).
https://doi.org/10.1103/RevModPhys.87.1379
[13] H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. Blok, L. Robledo, T. Taminiau, M. Markham, D. Twitchen, L. Childress, et al., Nature 497, 86 (2013).
https://doi.org/10.1038/nature12016
[14] B. Hensen, H. Bernien, A. E. Dreau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellan, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Nature 526, 682 (2015).
https://doi.org/10.1038/nature15759
[15] D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L. M. Duan, and C. Monroe, Nature 449, 68 (2007).
https://doi.org/10.1038/nature06118
[16] L. Slodička, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, Phys. Rev. Lett. 110, 083603 (2013).
https://doi.org/10.1103/PhysRevLett.110.083603
[17] K. J. Morse, R. J. Abraham, A. DeAbreu, C. Bowness, T. S. Richards, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. Thewalt, et al., Science advances 3, e1700930 (2017).
https://doi.org/10.1126/sciadv.1700930
[18] A. Delteil, Z. Sun, W. Gao, E. Togan, S. Faelt, and A. Imamoglu, Nat. Phys. 12, 218 (2016).
https://doi.org/10.1038/nphys3605
[19] R. Stockill, M. J. Stanley, L. Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, C. Le Gall, and M. Atatüre, Phys. Rev. Lett. 119, 010503 (2017).
https://doi.org/10.1103/PhysRevLett.119.010503
[20] W. Tittel, M. Afzelius, T. Chaneliere, R. L. Cone, S. Kröll, S. A. Moiseev, and M. Sellars, Laser & Photonics Rev. 4, 244 (2010).
https://doi.org/10.1002/lpor.200810056
[21] F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, C. Simon, and W. Tittel, J. Mod. Opt. 60, 1519 (2013).
https://doi.org/10.1080/09500340.2013.856482
[22] S. Wu, G. Han, D. J. Milliron, S. Aloni, V. Altoe, D. V. Talapin, B. E. Cohen, and P. J. Schuck, Proc. Natl. Acad. Sci. 106, 10917 (2009).
https://doi.org/10.1073/pnas.0904792106
[23] Y. Chu, N. de Leon, B. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. Zibrov, A. Yacoby, D. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. Lukin, Nano Letters 14, 1982 (2014).
https://doi.org/10.1021/nl404836p
[24] D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, Science 325, 70 (2009).
https://doi.org/10.1126/science.1173684
[25] R. G. Neuhauser, K. T. Shimizu, W. K. Woo, S. A. Empedocles, and M. G. Bawendi, Phys. Rev. Lett. 85, 3301 (2000).
https://doi.org/10.1103/PhysRevLett.85.3301
[26] R. de Sousa and S. Das Sarma, Phys. Rev. B 68, 115322 (2003).
https://doi.org/10.1103/PhysRevB.68.115322
[27] K. Xia, R. Kolesov, Y. Wang, P. Siyushev, R. Reuter, T. Kornher, N. Kukharchyk, A. D. Wieck, B. Villa, S. Yang, and J. Wrachtrup, Phys. Rev. Lett. 115, 093602 (2015).
https://doi.org/10.1103/PhysRevLett.115.093602
[28] B. Lauritzen, J. Minář, H. De Riedmatten, M. Afzelius, N. Sangouard, C. Simon, and N. Gisin, Phys. Rev. Lett. 104, 080502 (2010).
https://doi.org/10.1103/PhysRevLett.104.080502
[29] M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, et al., Phys. Rev. Lett. 104, 040503 (2010).
https://doi.org/10.1103/PhysRevLett.104.040503
[30] G. Heinze, C. Hubrich, and T. Halfmann, Phys. Rev. Lett. 111, 033601 (2013).
https://doi.org/10.1103/PhysRevLett.111.033601
[31] C. Laplane, P. Jobez, J. Etesse, N. Gisin, and M. Afzelius, Phys. Rev. Lett. 118, 210501 (2017).
https://doi.org/10.1103/PhysRevLett.118.210501
[32] M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Nature 517, 177 (2015a).
https://doi.org/10.1038/nature14025
[33] T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, et al., arXiv preprint arXiv:1803.07520 (2018).
arXiv:1803.07520
[34] A. M. Dibos, M. Raha, C. M. Phenicie, and J. D. Thompson, Phys. Rev. Lett. 120, 243601 (2018).
https://doi.org/10.1103/PhysRevLett.120.243601
[35] R. Kolesov, K. Xia, R. Reuter, R. Stöhr, A. Zappe, J. Meijer, P. Hemmer, and J. Wrachtrup, Nat. Commun. 3, 1029 (2012).
https://doi.org/10.1038/ncomms2034
[36] C. Yin, M. Rancic, G. G. de Boo, N. Stavrias, J. C. McCallum, M. J. Sellars, and S. Rogge, Nature 497, 91 (2013).
https://doi.org/10.1038/nature12081
[37] T. Utikal, E. Eichhammer, L. Petersen, A. Renn, S. Götzinger, and V. Sandoghdar, Nat. Commun. 5, 3627 (2014).
https://doi.org/10.1038/ncomms4627
[38] T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, Nat. Commun. 6, 8206 (2015b).
https://doi.org/10.1038/ncomms9206
[39] T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, Science 357, 1392 (2017).
https://doi.org/10.1126/science.aan5959
[40] J. J. Longdell and M. J. Sellars, Phys. Rev. A 69, 032307 (2004).
https://doi.org/10.1103/PhysRevA.69.032307
[41] J. J. Longdell, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 93, 130503 (2004).
https://doi.org/10.1103/PhysRevLett.93.130503
[42] A. Reiserer, N. Kalb, M. S. Blok, K. J. van Bemmelen, T. H. Taminiau, R. Hanson, D. J. Twitchen, and M. Markham, Phys. Rev. X 6, 021040 (2016).
https://doi.org/10.1103/PhysRevX.6.021040
[43] S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310 (2005).
https://doi.org/10.1103/PhysRevA.71.060310
[44] G. Liu and B. Jacquier, Spectroscopic properties of rare earths in optical materials, Vol. 83 (Springer Science & Business Media, 2006).
https://doi.org/10.1007/3-540-28209-2
[45] D. McAuslan, J. J. Longdell, and M. Sellars, Phys. Rev. A 80, 062307 (2009).
https://doi.org/10.1103/PhysRevA.80.062307
[46] N. Ohlsson, R. K. Mohan, and S. Kröll, Opt. Commun. 201, 71 (2002).
https://doi.org/10.1016/S0030-4018(01)01666-2
[47] S. Altner, G. Zumofen, U. Wild, and M. Mitsunaga, Phys. Rev. B 54, 17493 (1996).
https://doi.org/10.1103/PhysRevB.54.17493
[48] C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, Phys. Rev. Lett. 98, 190503 (2007).
https://doi.org/10.1103/PhysRevLett.98.190503
[49] O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, Phys. Rev. Lett. 98, 060502 (2007).
https://doi.org/10.1103/PhysRevLett.98.060502
[50] N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, Phys. Rev. Lett. 113, 053603 (2014).
https://doi.org/10.1103/PhysRevLett.113.053603
[51] L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
https://doi.org/10.1038/35106500
[52] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Nat. Commun. 8 (2017).
https://doi.org/10.1038/ncomms15043
[53] C. W. Thiel, W. R. Babbitt, and R. L. Cone, Phys. Rev. B 85, 174302 (2012).
https://doi.org/10.1103/PhysRevB.85.174302
[54] T. Kornher, K. Xia, R. Kolesov, N. Kukharchyk, R. Reuter, P. Siyushev, R. Stöhr, M. Schreck, H. W. Becker, B. Villa, A. D. Wieck, and J. Wrachtrup, Appl. Phys. Lett. 108, 053108 (2016).
https://doi.org/10.1063/1.4941403
[55] M. Davanco, J. Liu, L. Sapienza, C.-Z. Zhang, J. V. De Miranda Cardoso, V. Verma, R. Mirin, S. W. Nam, L. Liu, and K. Srinivasan, Nat. Commun. 8, 889 (2017).
https://doi.org/10.1038/s41467-017-00987-6
[56] E. Murray, D. J. P. Ellis, T. Meany, F. F. Floether, J. P. Lee, J. P. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, A. J. Bennett, and A. J. Shields, Appl. Phys. Lett. 107, 171108 (2015).
https://doi.org/10.1063/1.4935029
[57] J.-H. Kim, S. Aghaeimeibodi, C. J. K. Richardson, R. P. Leavitt, D. Englund, and E. Waks, Nano Letters 17, 7394 (2017).
https://doi.org/10.1021/acs.nanolett.7b03220
[58] S. R. Hastings-Simon, B. Lauritzen, M. U. Staudt, J. L. M. van Mechelen, C. Simon, H. de Riedmatten, M. Afzelius, and N. Gisin, Phys. Rev. B 78, 085410 (2008).
https://doi.org/10.1103/PhysRevB.78.085410
[59] T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, Phys. Rev. B 73, 075101 (2006).
https://doi.org/10.1103/PhysRevB.73.075101
[60] S. Probst, H. Rotzinger, A. V. Ustinov, and P. A. Bushev, Phys. Rev. B 92, 014421 (2015).
https://doi.org/10.1103/PhysRevB.92.014421
[61] O. Guillot-Noël, H. Vezin, P. Goldner, F. Beaudoux, J. Vincent, J. Lejay, and I. Lorgeré, Phys. Rev. B 76, 180408 (2007).
https://doi.org/10.1103/PhysRevB.76.180408
[62] E. Fraval, M. J. Sellars, A. Morrison, and A. Ferris, J. Lumin. 107, 347 (2004).
https://doi.org/10.1016/j.jlumin.2003.12.021
[63] R. M. Macfarlane and R. M. Shelby, Spectroscopy of Solids Containing Rare Earth Ions, edited by A. A. Kaplyanskii and R. M. Macfarlane (North Holland, Amsterdam, 1987).
https://doi.org/10.1016/c2009-0-12176-1
[64] P. Siyushev, K. Xia, R. Reuter, M. Jamali, N. Zhao, N. Yang, C. Duan, N. Kukharchyk, A. Wieck, R. Kolesov, et al., Nat. Commun. 5 (2014).
https://doi.org/10.1038/ncomms4895
[65] B. Lauritzen, S. R. Hastings-Simon, H. de Riedmatten, M. Afzelius, and N. Gisin, Phys. Rev. A 78, 043402 (2008).
https://doi.org/10.1103/PhysRevA.78.043402
[66] J. Minář, B. Lauritzen, H. de Riedmatten, M. Afzelius, C. Simon, and N. Gisin, New J. Phys. 11, 113019 (2009).
https://doi.org/10.1088/1367-2630/11/11/113019
[67] R. M. Macfarlane, J. Lumin. 125, 156 (2007), festschrift in Honor of Academician Alexander A. Kaplyanskii.
https://doi.org/10.1016/j.jlumin.2006.08.012
[68] J. H. Wesenberg, K. Mølmer, L. Rippe, and S. Kröll, Phys. Rev. A 75, 012304 (2007).
https://doi.org/10.1103/PhysRevA.75.012304
[69] Y. Sun, T. Böttger, C. W. Thiel, and R. L. Cone, Phys. Rev. B 77, 085124 (2008).
https://doi.org/10.1103/PhysRevB.77.085124
[70] F. M. Pichanick, P. G. H. Sandars, and G. K. Woodgate, Proc. Royal Soc. A 257, 277 (1960).
https://doi.org/10.1098/rspa.1960.0150
[71] C. O'Brien, T. Zhong, A. Faraon, and C. Simon, Phys. Rev. A 94, 043807 (2016).
https://doi.org/10.1103/PhysRevA.94.043807
[72] T. Grange, G. Hornecker, D. Hunger, J.-P. Poizat, J.-M. Gérard, P. Senellart, and A. Auffèves, Phys. Rev. Lett. 114, 193601 (2015).
https://doi.org/10.1103/PhysRevLett.114.193601
[73] T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, Phys. Rev. B 79, 115104 (2009).
https://doi.org/10.1103/PhysRevB.79.115104
[74] A. E. Lita, A. J. Miller, and S. W. Nam, Opt. Express 16, 3032 (2008).
https://doi.org/10.1364/OE.16.003032
[75] F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, et al., Nat. Photonics 7, 210 (2013).
https://doi.org/10.1038/nphoton.2013.13
[76] J. G. Bartholomew, R. L. Ahlefeldt, and M. J. Sellars, Phys. Rev. B 93, 014401 (2016).
https://doi.org/10.1103/PhysRevB.93.014401
[77] M. Grimau Puigibert, G. H. Aguilar, Q. Zhou, F. Marsili, M. D. Shaw, V. B. Verma, S. W. Nam, D. Oblak, and W. Tittel, Phys. Rev. Lett. 119, 083601 (2017).
https://doi.org/10.1103/PhysRevLett.119.083601
[78] K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
https://doi.org/10.1038/s41566-018-0132-5
[79] M. Rančić, M. P. Hedges, R. L. Ahlefeldt, and M. J. Sellars, Nat. Phys. (2017), 10.1038/nphys4254.
https://doi.org/10.1038/nphys4254
[80] B. Car, L. Veissier, A. Louchet-Chauvet, J.-L. Le Gouët, and T. Chanelière, Phys. Rev. Lett. 120, 197401 (2018).
https://doi.org/10.1103/PhysRevLett.120.197401
Cited by
[1] Sumeet Khatri, Corey T. Matyas, Aliza U. Siddiqui, and Jonathan P. Dowling, "Practical figures of merit and thresholds for entanglement distribution in quantum networks", Physical Review Research 1 2, 023032 (2019).
[2] Kenneth Sharman, Faezeh Kimiaee Asadi, Stephen C Wein, and Christoph Simon, "Quantum repeaters based on individual electron spins and nuclear-spin-ensemble memories in quantum dots", Quantum 5, 570 (2021).
[3] Thomas Jennewein, Christoph Simon, André Fougères, François Babin, Faezeh Kimiaee Asadi, Katanya B. Kuntz, Mathieu Maisonneuve, Brian Moffat, Kimia Mohammadi, and Denis Panneton, "QEYSSat 2.0—white paper on satellite-based quantum communication missions in Canada", Canadian Journal of Physics 103 4, 328 (2025).
[4] Jia-Wei Ji, Faezeh Kimiaee Asadi, Khabat Heshami, and Christoph Simon, "Noncryogenic Quantum Repeaters with hot Hybrid Alkali-Noble Gases", Physical Review Applied 19 5, 054063 (2023).
[5] Sourabh Kumar, Nikolai Lauk, and Christoph Simon, "Towards long-distance quantum networks with superconducting processors and optical links", Quantum Science and Technology 4 4, 045003 (2019).
[6] Jia-Wei Ji, Yu-Feng Wu, Stephen C. Wein, Faezeh Kimiaee Asadi, Roohollah Ghobadi, and Christoph Simon, "Proposal for room-temperature quantum repeaters with nitrogen-vacancy centers and optomechanics", Quantum 6, 669 (2022).
[7] Guus Avis, Francisco Ferreira da Silva, Tim Coopmans, Axel Dahlberg, Hana Jirovská, David Maier, Julian Rabbie, Ariana Torres-Knoop, and Stephanie Wehner, "Requirements for a processing-node quantum repeater on a real-world fiber grid", npj Quantum Information 9 1, 100 (2023).
[8] F Kimiaee Asadi, S C Wein, and C Simon, "Protocols for long-distance quantum communication with single 167Er ions", Quantum Science and Technology 5 4, 045015 (2020).
[9] Rinat A. Akhmedzhanov, Yurii Yu. Balega, Andrey D. Deev, and Aleksei A. Kalachev, "Quantum repeaters: current research trends and latest achievements", Physics-Uspekhi 68 09, 857 (2025).
[10] Mucheng Guo, Wanting Xiao, Zongfeng Li, Weiye Sun, Matthew J. Sellars, Rose L. Ahlefeldt, Ping Wang, Shuping Liu, Fudong Wang, and Manjin Zhong, "Towards telecom-compatible quantum nodes using erbium-doped stoichiometric EuCl3 ⋅ 6H2O crystals", npj Quantum Information 12 1, 57 (2026).
[11] Tim Coopmans, Robert Knegjens, Axel Dahlberg, David Maier, Loek Nijsten, Julio de Oliveira Filho, Martijn Papendrecht, Julian Rabbie, Filip Rozpędek, Matthew Skrzypczyk, Leon Wubben, Walter de Jong, Damian Podareanu, Ariana Torres-Knoop, David Elkouss, and Stephanie Wehner, "NetSquid, a NETwork Simulator for QUantum Information using Discrete events", Communications Physics 4 1, 164 (2021).
[12] Ali Akbar, Zahid Hussain, Farhan Sadiq, Sajjad Hussain, Imran Sadiq, Sadaf Naz, Samreen Saeed, Muhammad Shahbaz, Latif Ullah Khan, Saira Riaz, and Shahzad Naseem, "Insight into the local atomic structure, optical, magnetic, and electrical polarization properties of Eu³+-substituted R-type hexagonal ferrite", Journal of Sol-Gel Science and Technology 117 3, 81 (2026).
[13] Mahsa Karimi, Faezeh Kimiaee Asadi, Stephen C. Wein, and Christoph Simon, "Comparing the performance of practical two-qubit gates for individual 171Yb ions in yttrium orthovanadate", Quantum 10, 2075 (2026).
[14] Koji Azuma, Stefan Bäuml, Tim Coopmans, David Elkouss, and Boxi Li, "Tools for quantum network design", AVS Quantum Science 3 1, 014101 (2021).
[15] Faezeh Kimiaee Asadi, Jia-Wei Ji, and Christoph Simon, "Proposal for transduction between microwave and optical photons using Er167 -doped yttrium orthosilicate", Physical Review A 105 6, 062608 (2022).
[16] Chetan Deshmukh, Eduardo Beattie, Bernardo Casabone, Samuele Grandi, Diana Serrano, Alban Ferrier, Philippe Goldner, David Hunger, and Hugues de Riedmatten, "Detection of single ions in a nanoparticle coupled to a fiber cavity", Optica 10 10, 1339 (2023).
[17] Bernardo Casabone, Chetan Deshmukh, Shuping Liu, Diana Serrano, Alban Ferrier, Thomas Hümmer, Philippe Goldner, David Hunger, and Hugues de Riedmatten, "Dynamic control of Purcell enhanced emission of erbium ions in nanoparticles", Nature Communications 12 1, 3570 (2021).
[18] E. Shchukin, F. Schmidt, and P. van Loock, "Waiting time in quantum repeaters with probabilistic entanglement swapping", Physical Review A 100 3, 032322 (2019).
[19] Yisheng Lei, Faezeh Kimiaee Asadi, Tian Zhong, Alex Kuzmich, Christoph Simon, and Mahdi Hosseini, "Quantum optical memory for entanglement distribution", Optica 10 11, 1511 (2023).
[20] Zhidong Fang, Hirotake Kajii, Masahiko Kondow, Yasufumi Fujiwara, and Jun Tatebayashi, "Demonstration of enhanced Er luminescence in nanobeam photonic crystal nanocavities based on Er,O-codoped GaAs", Japanese Journal of Applied Physics 64 2, 025001 (2025).
[21] Jingyi Lu, Shunan Zhao, Fangfang Wei, and Keith Man‐Chung Wong, "Design, Synthesis and Photophysical Studies of Luminescent Rhodium(III) Complexes in Near‐Infrared Region", European Journal of Inorganic Chemistry 26 11, e202200792 (2023).
[22] Shobhit Gupta, Yizhong Huang, Shihan Liu, Yuxiang Pei, Qiang Gao, Shuolong Yang, Natasha Tomm, Richard J. Warburton, and Tian Zhong, "Dual epitaxial telecom spin-photon interfaces with long-lived coherence", Nature Communications 16 1, 9814 (2025).
[23] F. Kimiaee Asadi, S. C. Wein, and C. Simon, "Cavity-assisted controlled phase-flip gates", Physical Review A 102 1, 013703 (2020).
[24] Robert M. Pettit, Farhang Hadad Farshi, Sean E. Sullivan, Álvaro Véliz-Osorio, and Manish Kumar Singh, "A perspective on the pathway to a scalable quantum internet using rare-earth ions", Applied Physics Reviews 10 3, 031307 (2023).
[25] Tomohiro Yamazaki and Koji Azuma, "Linear-Optical Fusion Boosted by High-Dimensional Entanglement", Physical Review Letters 134 20, 200801 (2025).
[26] Rinat A. Akhmedzhanov, Yurii Yu. Balega, Andrey D. Deev, and Aleksei A. Kalachev, "Quantum repeaters: current research trends and latest achievements", Uspekhi Fizicheskih Nauk 195 09, 909 (2025).
[27] Junyi Wang, Feifei Huang, JiaBo Li, Bingpeng Li, Ying Tian, and Shiqing Xu, "Broadband tunable infrared emission of Ni2+-doped ZnGa/AlO4 integrated transparent glass ceramics", Infrared Physics & Technology 133, 104805 (2023).
[28] Daniel B. Higginbottom, Faezeh Kimiaee Asadi, Camille Chartrand, Jia-Wei Ji, Laurent Bergeron, Michael L.W. Thewalt, Christoph Simon, and Stephanie Simmons, "Memory and Transduction Prospects for Silicon T Center Devices", PRX Quantum 4 2, 020308 (2023).
[29] Koji Azuma, Sophia E. Economou, David Elkouss, Paul Hilaire, Liang Jiang, Hoi-Kwong Lo, and Ilan Tzitrin, "Quantum repeaters: From quantum networks to the quantum internet", Reviews of Modern Physics 95 4, 045006 (2023).
[30] J. Chacaliaza-Ricaldi, V.A.G. Rivera, I.C. Pinto, Y. Messaddeq, and E. Marega, "Germanate-tellurite glasses with low Er3+ ions concentration and their radiative emissions", Journal of Non-Crystalline Solids 638, 123063 (2024).
[31] Mohammed K. Alqedra, Chetan Deshmukh, Shuping Liu, Diana Serrano, Sebastian P. Horvath, Safi Rafie-Zinedine, Abdullah Abdelatief, Lars Rippe, Stefan Kröll, Bernardo Casabone, Alban Ferrier, Alexandre Tallaire, Philippe Goldner, Hugues de Riedmatten, and Andreas Walther, "Optical coherence properties of Kramers' rare-earth ions at the nanoscale for quantum applications", Physical Review B 108 7, 075107 (2023).
[32] Ruo-Ran Meng, Xiao Liu, Ming Jin, Zong-Quan Zhou, Chuan-Feng Li, and Guang-Can Guo, "Solid-state quantum nodes based on color centers and rare-earth ions coupled with fiber Fabry–Pérot microcavities", Chip 3 1, 100081 (2024).
[33] Eva M. González-Ruiz, Hugo Jacinto, and Nicolas Sangouard, Optica Quantum 2.0 Conference and Exhibition QM2A.5 (2025) ISBN:978-1-957171-48-7.
[34] Shi‐Hai Wei, Bo Jing, Xue‐Ying Zhang, Jin‐Yu Liao, Chen‐Zhi Yuan, Bo‐Yu Fan, Chen Lyu, Dian‐Li Zhou, You Wang, Guang‐Wei Deng, Hai‐Zhi Song, Daniel Oblak, Guang‐Can Guo, and Qiang Zhou, "Towards Real‐World Quantum Networks: A Review", Laser & Photonics Reviews 16 3, 2100219 (2022).
[35] Shahrzad Taherizadegan, Faezeh Kimiaee Asadi, Jia-Wei Ji, Daniel Higginbottom, and Christoph Simon, "Exploring the feasibility of probabilistic and deterministic quantum gates between T centers in silicon", Quantum Science and Technology 11 2, 025031 (2026).
[36] Stephen C. Wein, Jia-Wei Ji, Yu-Feng Wu, Faezeh Kimiaee Asadi, Roohollah Ghobadi, and Christoph Simon, "Analyzing photon-count heralded entanglement generation between solid-state spin qubits by decomposing the master-equation dynamics", Physical Review A 102 3, 033701 (2020).
[37] A. A. Kalachev, "Quantum Repeaters: Current Developments and Prospects", Bulletin of the Lebedev Physics Institute 50 S12, S1312 (2023).
[38] Adam Kinos, Andreas Walther, Stefan Kröll, and Lars Rippe, "Complete analysis of a realistic fiber-based quantum repeater scheme", Physical Review Research 7 3, 033199 (2025).
[39] Jia-Wei Ji, Shinichi Sunami, Seigo Kikura, Akihisa Goban, and Christoph Simon, "Global quantum network with ground-based single-atom memories in optical cavities and satellite links", Physical Review Applied 25 2, 024050 (2026).
[40] Amirhossein Alizadehkhaledi, Adriaan L. Frencken, Frank C. J. M. van Veggel, and Reuven Gordon, "Isolating Nanocrystals with an Individual Erbium Emitter: A Route to a Stable Single-Photon Source at 1550 nm Wavelength", Nano Letters 20 2, 1018 (2020).
[41] Savo Glisic and Beatriz Lorenzo, "Optimum 6G/7G quantum network design: Survey", Optics Communications 608, 131883 (2026).
[42] Jacob P. Covey, Alp Sipahigil, Szilard Szoke, Neil Sinclair, Manuel Endres, and Oskar Painter, "Telecom-Band Quantum Optics with Ytterbium Atoms and Silicon Nanophotonics", Physical Review Applied 11 3, 034044 (2019).
[43] Wolfgang Tittel, Mikael Afzelius, Adam Kinos, Lars Rippe, and Andreas Walther, "Quantum networks using rare-earth ions", Quantum Science and Technology 10 3, 033002 (2025).
[44] Xu Feng, Liting Lin, Rui Duan, Jianrong Qiu, and Shifeng Zhou, "Transition metal ion activated near-infrared luminescent materials", Progress in Materials Science 129, 100973 (2022).
[45] Tim Coopmans, Sebastiaan Brand, and David Elkouss, "Improved analytical bounds on delivery times of long-distance entanglement", Physical Review A 105 1, 012608 (2022).
[46] Sumeet Khatri, "Towards a General Framework for Practical Quantum Network Protocols", arXiv:2412.20472, (2024).
The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 14:21:39) and SAO/NASA ADS (last updated successfully 2026-08-09 14:21:41). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.