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  • Letter
  • Open Access

Hyperfine interaction limits polarization entanglement of photons from semiconductor quantum dots

Christian Schimpf1,*, Francesco Basso Basset2, Maximilian Aigner1, Wolfgang Attenender1, Laia Ginés3, Gabriel Undeutsch1, Marcus Reindl1, Daniel Huber1, Dorian Gangloff4 et al.

Evgeny A. Chekhovich5, Christian Schneider6, Sven Höfling7, Ana Predojević3, Rinaldo Trotta2, and Armando Rastelli1

  • 1Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, 4040 Linz, Austria
  • 2Department of Physics, Sapienza University of Rome, 00185 Rome, Italy
  • 3Department of Physics, Stockholm University, 106 91 Stockholm, Sweden
  • 4Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
  • 5Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
  • 6Institute of Physics, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
  • 7Julius-Maximilians-Universität Würzburg, Physikalisches Institut, Lehrstuhl für Technische Physik, Am Hubland, 97074 Würzburg, Germany

  • *christian.schimpf@eng.ox.ac.uk
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Phys. Rev. B 108, L081405 – Published 15 August, 2023

DOI: https://doi.org/10.1103/PhysRevB.108.L081405

Abstract

Excitons in quantum dots are excellent sources of polarization-entangled photon pairs, but a quantitative understanding of their interaction with the nuclear spin bath is still missing. Here we investigate the role of hyperfine energy shifts using experimentally accessible parameters and derive an upper limit to the achievable entanglement fidelity. Our results are consistent with all available literature, indicate that spin noise is often the dominant process limiting the entanglement in InGaAs quantum dots, and suggest routes to alleviate its effect.

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References (61)

  1. P. Senellart, G. Solomon, and A. White, High-performance semiconductor quantum-dot single-photon sources, Nat. Nanotechnol. 12, 1026 (2017).
  2. N. Tomm, A. Javadi, N. O. Antoniadis, D. Najer, M. C. Löbl, A. R. Korsch, R. Schott, S. R. Valentin, A. D. Wieck, A. Ludwig, and R. J. Warburton, A bright and fast source of coherent single photons, Nat. Nanotechnol. 16, 399 (2021).
  3. J. Liu, R. Su, Y. Wei, B. Yao, S. F. Covre da Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli, J. Li, and X. Wang, A solid-state source of strongly entangled photon pairs with high brightness and indistinguishability, Nat. Nanotechnol. 14, 586 (2019).
  4. H. Wang, H. Hu, T. H. Chung, J. Qin, X. Yang, J. P. Li, R. Z. Liu, H. S. Zhong, Y. M. He, X. Ding, Y. H. Deng, Q. Dai, Y. H. Huo, S. Höfling, C. Y. Lu, and J. W. Pan, On-Demand Semiconductor Source of Entangled Photons Which Simultaneously Has High Fidelity, Efficiency, and Indistinguishability, Phys. Rev. Lett. 122, 113602 (2019).
  5. H. Vural, S. L. Portalupi, and P. Michler, Perspective of self-assembled InGaAs quantum-dots for multi-source quantum implementations, Appl. Phys. Lett. 117, 030501 (2020).
  6. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, Regulated and Entangled Photons from a Single Quantum Dot, Phys. Rev. Lett. 84, 2513 (2000).
  7. N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, Entangled Photon Pairs from Semiconductor Quantum Dots, Phys. Rev. Lett. 96, 130501 (2006).
  8. R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, Improved fidelity of triggered entangled photons from single quantum dots, New J. Phys. 8, 29 (2006).
  9. R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, Triggered polarization-entangled photon pairs from a single quantum dot up to 30 K, New J. Phys. 9, 315 (2007).
  10. C. L. Salter, R. M. Stevenson, I. Farrer, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, An entangled-light-emitting diode, Nature (London) 465, 594 (2010).
  11. A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, Ultrabright source of entangled photon pairs, Nature (London) 466, 217 (2010).
  12. G. Juska, V. Dimastrodonato, L. O. Mereni, A. Gocalinska, and E. Pelucchi, Towards quantum-dot arrays of entangled photon emitters, Nat. Photon. 7, 527 (2013).
  13. M. Müller, S. Bounouar, K. D. Jöns, M. Glässl, and P. Michler, On-demand generation of indistinguishable polarization-entangled photon pairs, Nat. Photon. 8, 224 (2014).
  14. R. Trotta, J. S. Wildmann, E. Zallo, O. G. Schmidt, and A. Rastelli, Highly entangled photons from hybrid piezoelectric-semiconductor quantum dot devices, Nano Lett. 14, 3439 (2014).
  15. F. Olbrich, J. Höschele, M. Müller, J. Kettler, S. Luca Portalupi, M. Paul, M. Jetter, and P. Michler, Polarization-entangled photons from an InGaAs-based quantum dot emitting in the telecom C-band, Appl. Phys. Lett. 111, 133106 (2017).
  16. T. Müller, J. Skiba-Szymanska, A. B. Krysa, J. Huwer, M. Felle, M. Anderson, R. M. Stevenson, J. Heffernan, D. A. Ritchie, and A. J. Shields, A quantum light-emitting diode for the standard telecom window around 1550 nm, Nat. Commun. 9, 862 (2018).
  17. K. D. Zeuner, K. D. Jöns, L. Schweickert, C. Reuterskiöld Hedlund, C. Nuñez Lobato, T. Lettner, K. Wang, S. Gyger, E. Schöll, S. Steinhauer, M. Hammar, and V. Zwiller, On-demand generation of entangled photon pairs in the telecom C-band with InAs quantum dots, ACS Photonics 8, 2337 (2021).
  18. R. Winik, D. Cogan, Y. Don, I. Schwartz, L. Gantz, E. R. Schmidgall, N. Livneh, R. Rapaport, E. Buks, and D. Gershoni, On-demand source of maximally entangled photon pairs using the biexciton-exciton radiative cascade, Phys. Rev. B 95, 235435 (2017).
  19. A. Fognini, A. Ahmadi, M. Zeeshan, J. T. Fokkens, S. J. Gibson, N. Sherlekar, S. J. Daley, D. Dalacu, P. J. Poole, K. D. Jöns, V. Zwiller, and M. E. Reimer, Dephasing free photon entanglement with a quantum dot, ACS Photonics 6, 1656 (2019).
  20. M. Anderson, T. Müller, J. Skiba-Szymanska, A. B. Krysa, J. Huwer, R. M. Stevenson, J. Heffernan, D. A. Ritchie, and A. J. Shields, Gigahertz-Clocked Teleportation of Time-Bin Qubits with a Quantum Dot in the Telecommunication C Band, Phys. Rev. Appl. 13, 054052 (2020).
  21. D. Huber, M. Reindl, S. F. Covre da Silva, C. Schimpf, J. Martín-Sánchez, H. Huang, G. Piredda, J. Edlinger, A. Rastelli, and R. Trotta, Strain-Tunable GaAs Quantum Dot: A Nearly Dephasing-Free Source of Entangled Photon Pairs on Demand, Phys. Rev. Lett. 121, 033902 (2018).
  22. M. Gurioli, Z. Wang, A. Rastelli, T. Kuroda, and S. Sanguinetti, Droplet epitaxy of semiconductor nanostructures for quantum photonic devices, Nat. Mater. 18, 799 (2019).
  23. S. F. Covre da Silva, G. Undeutsch, B. Lehner, S. Manna, T. M. Krieger, M. Reindl, C. Schimpf, R. Trotta, and A. Rastelli, GaAs quantum dots grown by droplet etching epitaxy as quantum light sources, Appl. Phys. Lett. 119, 120502 (2021).
  24. L. Zhai, G. N. Nguyen, C. Spinnler, J. Ritzmann, M. C. Löbl, A. D. Wieck, A. Ludwig, A. Javadi, and R. J. Warburton, Quantum interference of identical photons from remote GaAs quantum dots, Nat. Nanotechnol. 17, 829 (2022).
  25. M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots, Phys. Rev. B 65, 195315 (2002).
  26. A. J. Hudson, R. M. Stevenson, A. J. Bennett, R. J. Young, C. A. Nicoll, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, Coherence of an Entangled Exciton-Photon State, Phys. Rev. Lett. 99, 266802 (2007).
  27. U. Hohenester, G. Pfanner, and M. Seliger, Phonon-Assisted Decoherence in the Production of Polarization-Entangled Photons in a Single Semiconductor Quantum Dot, Phys. Rev. Lett. 99, 047402 (2007).
  28. A. Reigue, J. Iles-Smith, F. Lux, L. Monniello, M. Bernard, F. Margaillan, A. Lemaitre, A. Martinez, D. P. S. McCutcheon, J. Mørk, R. Hostein, and V. Voliotis, Probing Electron-Phonon Interaction through Two-Photon Interference in Resonantly Driven Semiconductor Quantum Dots, Phys. Rev. Lett. 118, 233602 (2017).
  29. T. Seidelmann, C. Schimpf, T. K. Bracht, M. Cosacchi, A. Vagov, A. Rastelli, D. E. Reiter, and V. M. Axt, Two-Photon Excitation Sets Fundamental Limit to Entangled Photon Pair Generation from Quantum Emitters, Phys. Rev. Lett. 129, 193604 (2022).
  30. T. Seidelmann, T. K. Bracht, B. U. Lehner, C. Schimpf, M. Cosacchi, M. Cygorek, A. Vagov, A. Rastelli, D. E. Reiter, and V. M. Axt, Two-photon excitation with finite pulses unlocks pure dephasing-induced degradation of entangled photons emitted by quantum dots, Phys. Rev. B 107, 235304 (2023).
  31. I. A. Merkulov, A. L. Efros, and M. Rosen, Electron spin relaxation by nuclei in semiconductor quantum dots, Phys. Rev. B 65, 205309 (2002).
  32. B. Urbaszek, X. Marie, T. Amand, O. Krebs, P. Voisin, P. Malentinsky, A. Högele, and A. Imamoglu, Nuclear spin physics in quantum dots: An optical investigation, Rev. Mod. Phys. 85, 79 (2013).
  33. A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, Charge noise and spin noise in a semiconductor quantum device, Nat. Phys. 9, 570 (2013).
  34. T. Kuroda, T. Mano, N. Ha, H. Nakajima, H. Kumano, B. Urbaszek, M. Jo, M. Abbarchi, Y. Sakuma, K. Sakoda, I. Suemune, X. Marie, and T. Amand, Symmetric quantum dots as efficient sources of highly entangled photons: Violation of Bell's inequality without spectral and temporal filtering, Phys. Rev. B 88, 041306(R) (2013).
  35. D. Huber, M. Reindl, Y. Huo, H. Huang, J. S. Wildmann, O. G. Schmidt, A. Rastelli, and R. Trotta, Highly indistinguishable and strongly entangled photons from symmetric GaAs quantum dots, Nat. Commun. 8, 15506 (2017).
  36. R. Keil, M. Zopf, Y. Chen, B. Höfer, J. Zhang, F. Ding, and O. G. Schmidt, Solid-state ensemble of highly entangled photon sources at rubidium atomic transitions, Nat. Commun. 8, 15501 (2017).
  37. Y. M. He, Y. He, Y. J. Wei, D. Wu, M. Atatüre, C. Schneider, S. Höfling, M. Kamp, C. Y. Lu, and J. W. Pan, On-demand semiconductor single-photon source with near-unity indistinguishability, Nat. Nanotechnol. 8, 213 (2013).
  38. T. Braun, S. Betzold, N. Lundt, M. Kamp, S. Höfling, and C. Schneider, Impact of ex situ rapid thermal annealing on magneto-optical properties and oscillator strength of In(Ga)As quantum dots, Phys. Rev. B 93, 155307 (2016).
  39. J. Zhang, J. S. Wildmann, F. Ding, R. Trotta, Y. Huo, E. Zallo, D. Huber, A. Rastelli, and O. G. Schmidt, High yield and ultrafast sources of electrically triggered entangled-photon pairs based on strain-tunable quantum dots, Nat. Commun. 6, 10067 (2015).
  40. R. Stockill, C. Le Gall, C. Matthiesen, L. Huthmacher, E. Clarke, M. Hugues, and M. Atatüre, Quantum dot spin coherence governed by a strained nuclear environment, Nat. Commun. 7, 12745 (2016).
  41. D. A. Gangloff, G. Éthier-Majcher, C. Lang, E. V. Denning, J. H. Bodey, D. M. Jackson, E. Clarke, M. Hugues, C. Le Gall, and M. Atatüre, Quantum interface of an electron and a nuclear ensemble, Science 364, 62 (2019).
  42. L. Zaporski, N. Shofer, J. H. Bodey, S. Manna, G. Gillard, M. H. Appel, C. Schimpf, S. F. Covre da Silva, J. Jarman, G. Delamare, G. Park, U. Haeusler, E. A. Chekhovich, A. Rastelli, D. A. Gangloff, M. Atatüre, and C. Le Gall, Ideal refocusing of an optically active spin qubit under strong hyperfine interactions, Nat. Nanotechnol. 18, 257 (2023).
  43. E. Welander, J. Hildmann, and G. Burkard, Influence of hyperfine interaction on the entanglement of photons generated by biexciton recombination, arXiv:1409.6521.
  44. B. Eble, C. Testelin, P. Desfonds, F. Bernardot, A. Balocchi, T. Amand, A. Miard, A. Lemaître, X. Marie, and M. Chamarro, Hole–Nuclear Spin Interaction in Quantum Dots, Phys. Rev. Lett. 102, 146601 (2009).
  45. G. Éthier-Majcher, D. Gangloff, R. Stockill, E. Clarke, M. Hugues, C. Le Gall, and M. Atatüre, Improving a Solid-State Qubit through an Engineered Mesoscopic Environment, Phys. Rev. Lett. 119, 130503 (2017).
  46. D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, Ultrafast optical spin echo in a single quantum dot, Nat. Photon. 4, 367 (2010).
  47. S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V. M. Axt, T. Kuhn, and A. Zrenner, Two-photon Rabi oscillations in a single InxGa1−xAs/GaAs quantum dot, Phys. Rev. B 73, 125304 (2006).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.L081405 for details about the modeling of the entangled two-photon states, the used QD samples and devices, the experimental methods used to acquire the measured data, the temperature and charge-noise dependence of the measurements, and for a list of relevant parameters of each QD included in this work. It also contains Ref. [61].
  49. C. Schimpf, M. Reindl, P. Klenovský, T. Fromherz, S. F. Covre da Silva, J. Hofer, C. Schneider, S. Höfling, R. Trotta, and A. Rastelli, Resolving the temporal evolution of line broadening in single quantum emitters, Opt. Express 27, 35290 (2019).
  50. J. Neuwirth, F. Basso Basset, M. B. Rota, J.-G. Hartel, M. Sartison, S. F. Covre da Silva, K. D. Jöns, A. Rastelli, and R. Trotta, A multipair-free source of entangled photons in the solid state, Phys. Rev. B 106, L241402 (2022).
  51. A. Bennett, Y. M. Pooley, N. R. Stevenson, M. Ward, R. Patel, A. B. de La Giroday, N. Sköld, I. Farrer, C. Nicoll, D. Ritchie et al., Electric-field-induced coherent coupling of the exciton states in a single quantum dot, Nat. Phys. 6, 947 (2010).
  52. T. Lettner, S. Gyger, K. D. Zeuner, L. Schweickert, S. Steinhauer, C. Reuterskiöld Hedlund, S. Stroj, A. Rastelli, M. Hammar, R. Trotta, K. D. Jöns, and V. Zwiller, Strain-controlled quantum dot fine structure for entangled photon generation at 1550 nm, Nano Lett. 21, 10501 (2021).
  53. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Measurement of qubits, Phys. Rev. A 64, 052312 (2001).
  54. W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett. 80, 2245 (1998).
  55. T. Belhadj, T. Amand, A. Kunold, C. M. Simon, T. Kuroda, M. Abbarchi, T. Mano, K. Sakoda, S. Kunz, X. Marie, and B. Urbaszek, Impact of heavy hole-light hole coupling on optical selection rules in GaAs quantum dots, Appl. Phys. Lett. 97, 051111 (2010).
  56. C. Tonin, R. Hostein, V. Voliotis, R. Grousson, A. Lemaitre, and A. Martinez, Polarization properties of excitonic qubits in single self-assembled quantum dots, Phys. Rev. B 85, 155303 (2012).
  57. J. D. Plumhof, R. Trotta, V. Křápek, E. Zallo, P. Atkinson, S. Kumar, A. Rastelli, and O. G. Schmidt, Tuning of the valence band mixing of excitons confined in GaAs/AlGaAs quantum dots via piezoelectric-induced anisotropic strain, Phys. Rev. B 87, 075311 (2013).
  58. C. Bulutay, Quadrupolar spectra of nuclear spins in strained InxGa1−xAs quantum dots, Phys. Rev. B 85, 115313 (2012).
  59. E. V. Denning, D. A. Gangloff, M. Atatüre, J. Mørk, and C. Le Gall, Collective Quantum Memory Activated by a Driven Central Spin, Phys. Rev. Lett. 123, 140502 (2019).
  60. D. Huber, B. U. Lehner, D. Csontosová, M. Reindl, S. Schuler, S. F. Covre da Silva, P. Klenovský, and A. Rastelli, Single-particle-picture breakdown in laterally weakly confining GaAs quantum dots, Phys. Rev. B 100, 235425 (2019).
  61. L. Wang, A. Rastelli, and O. G. Schmidt, Structural and optical properties of In(Ga)As/GaAs quantum dots treated by partial capping and annealing, J. Appl. Phys. 100, 064313 (2006).

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Phys. Rev. B 108, L081405– Published 15 August, 2023
  • Received 18 February 2023
  • Revised 27 April 2023
  • Accepted 17 July 2023
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