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Phonon scattering inhibits simultaneous near-unity efficiency and indistinguishability in semiconductor single-photon sources


Semiconductor quantum dots (QDs) have recently emerged as a leading platform to generate highly indistinguishable photons efficiently, and this work addresses the timely question of how good these solid-state sources can ultimately be. We establish the crucial role of lattice relaxation in these systems in giving rise to trade-offs between indistinguishability and efficiency. We analyse the two source architectures most commonly employed: a QD embedded in a waveguide and a QD coupled to an optical cavity. For waveguides, we demonstrate that the broadband Purcell effect results in a simple inverse relationship, in which indistinguishability and efficiency cannot be simultaneously increased. For cavities, the frequency selectivity of the Purcell enhancement results in a more subtle trade-off, in which indistinguishability and efficiency can be increased simultaneously, although not arbitrarily, which limits a source with near-unity indistinguishability (>99%) to an efficiency of approximately 96% for realistic parameters.

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Figure 1: Lattice relaxation in QDs and the phonon SB.
Figure 2: Single-photon source architectures and emission spectra.
Figure 3: Indistinguishability and efficiency of the three source set-ups shown in Fig. 2.


  1. 1

    O'Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).

    ADS  Article  Google Scholar 

  2. 2

    Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

    ADS  Article  Google Scholar 

  3. 3

    Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    ADS  Article  Google Scholar 

  4. 4

    Pan, J. W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).

    ADS  Article  Google Scholar 

  5. 5

    Michler, P. et al. A quantum dot single-photon turnstile device. Science 290, 2282–2285 (2000).

    ADS  Article  Google Scholar 

  6. 6

    Santori, C., Pelton, M., Solomon, G., Dale, Y. & Yamamoto, Y. Triggered single photons from a quantum dot. Phys. Rev. Lett. 86, 1502–1505 (2001).

    ADS  Article  Google Scholar 

  7. 7

    Santori, C., Fattal, D., Vuckovic, J., Solomon, G. S. & Yamamoto, Y. Indistinguishable photons from a single-photon device. Nature 419, 594–597 (2002).

    ADS  Article  Google Scholar 

  8. 8

    Gazzano, O. et al. Bright solid-state sources of indistinguishable single photons. Nat. Commun. 4, 1425 (2013).

    ADS  Article  Google Scholar 

  9. 9

    Nowak, A. K. et al. Deterministic and electrically tunable bright single-photon source. Nat. Commun. 5, 3240 (2014).

    ADS  Article  Google Scholar 

  10. 10

    He, Y.-M. et al. On-demand semiconductor single-photon source with near-unity indistinguishability. Nat. Nanotech. 8, 213–217 (2013).

    ADS  Article  Google Scholar 

  11. 11

    Thoma, A. et al. Exploring dephasing of a solid-state quantum emitter via time- and temperature-dependent Hong–Ou–Mandel experiments. Phys. Rev. Lett. 116, 033601 (2016).

    ADS  Article  Google Scholar 

  12. 12

    Somaschi, N. et al. Near optimal single photon sources in the solid state. Nat. Photon. 10, 340–345 (2016).

    ADS  Article  Google Scholar 

  13. 13

    Ding, X. et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016).

    ADS  Article  Google Scholar 

  14. 14

    Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  15. 15

    Claudon, J. et al. A highly efficient single-photon source based on a quantum dot in a photonic nanowire. Nat. Photon. 4, 174–177 (2010).

    ADS  Article  Google Scholar 

  16. 16

    Arcari, M. et al. Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide. Phys. Rev. Lett. 113, 093603 (2014).

    ADS  Article  Google Scholar 

  17. 17

    Houel, J. et al. Probing single-charge fluctuations at a GaAs/AlAs interface using laser spectroscopy on a nearby InGaAs quantum dot. Phys. Rev. Lett. 108, 107401 (2012).

    ADS  Article  Google Scholar 

  18. 18

    Kuhlmann, A. V. et al. Charge noise and spin noise in a semiconductor quantum device. Nat. Phys. 9, 570–575 (2013).

    Article  Google Scholar 

  19. 19

    Kuhlmann, A. V. et al. Transform-limited single photons from a single quantum dot. Nat. Commun. 6, 8204 (2015).

    ADS  Article  Google Scholar 

  20. 20

    Ramsay, A. J. et al. Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots. Phys. Rev. Lett. 104, 017402 (2010).

    ADS  Article  Google Scholar 

  21. 21

    Ramsay, A. J. et al. Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots. Phys. Rev. Lett. 105, 177402 (2010).

    ADS  Article  Google Scholar 

  22. 22

    McCutcheon, D. P. S. & Nazir, A. Model of the optical emission of a driven semiconductor quantum dot: phonon-enhanced coherent scattering and off-resonant sideband narrowing. Phys. Rev. Lett. 110, 217401 (2013).

    ADS  Article  Google Scholar 

  23. 23

    Nazir, A. & McCutcheon, D. P. S. Modelling exciton–phonon interactions in optically driven quantum dots. J. Phys. Condens. Matter 28, 103002 (2016).

    ADS  Article  Google Scholar 

  24. 24

    Kaer, P., Lodahl, P., Jauho, A.-P. & Mørk, J. Microscopic theory of indistinguishable single-photon emission from a quantum dot coupled to a cavity: the role of non-Markovian phonon-induced decoherence. Phys. Rev. B 87, 081308 (2013).

    ADS  Article  Google Scholar 

  25. 25

    Kaer, P. & Mørk, J. Decoherence in semiconductor cavity QED systems due to phonon couplings. Phys. Rev. B 90, 035312 (2014).

    ADS  Article  Google Scholar 

  26. 26

    Iles-Smith, J., McCutcheon, D. P. S., Mørk, J. & Nazir, A. Limits to coherent scattering and photon coalescence from solid-state quantum emitters. Phys. Rev. B 95, 201305(R) (2017).

    ADS  Article  Google Scholar 

  27. 27

    Unsleber, S. et al. Two-photon interference from a quantum dot microcavity: persistent pure dephasing and suppression of time jitter. Phys. Rev. B 91, 075413 (2015).

    ADS  Article  Google Scholar 

  28. 28

    Aharonovich, I., Englund, D. & Toth, M. Solid-state single-photon emitters. Nat. Photon. 10, 631–641 (2016).

    ADS  Article  Google Scholar 

  29. 29

    Purcell, E. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946).

    Article  Google Scholar 

  30. 30

    Manga Rao, V. S. C. & Hughes, S. Single quantum-dot Purcell factor and β-factor in a photonic crystal waveguide. Phys. Rev. B 75, 205437 (2007).

    ADS  Article  Google Scholar 

  31. 31

    Kaer, P., Gregersen, N. & Mork, J. The role of phonon scattering in the indistinguishability of photons emitted from semiconductor cavity QED systems. New J. Phys. 15, 035027 (2013).

    ADS  Article  Google Scholar 

  32. 32

    Bylander, J., Robert-Philip, I. & Abram, I. Interference and correlation of two independent photons. Eur. Phys. J. D 22, 295–301 (2003).

    ADS  Article  Google Scholar 

  33. 33

    Kiraz, A., Atatüre, M. & Imamoğlu, A. Quantum-dot single-photon sources: prospects for applications in linear optics quantum-information processing. Phys. Rev. A 69, 032305 (2004).

    ADS  Article  Google Scholar 

  34. 34

    Muljarov, E. A. & Zimmermann, R. Dephasing in quantum dots: quadratic coupling to acoustic phonons. Phys. Rev. Lett. 93, 237401 (2004).

    ADS  Article  Google Scholar 

  35. 35

    Quilter, J. H. et al. Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation. Phys. Rev. Lett. 114, 137401 (2015).

    ADS  Article  Google Scholar 

  36. 36

    Bimberg, D., Grundmann, M. & Ledentsov, N. N. Quantum Dot Heterostructures (John Wiley & Sons, 1999).

  37. 37

    Zrenner, A. et al. Coherent properties of a two-level system based on a quantum-dot photodiode. Nature 418, 612–614 (2002).

    ADS  Article  Google Scholar 

  38. 38

    McCutcheon, D. P. S. & Nazir, A. Quantum dot Rabi rotations beyond the weak exciton–phonon coupling regime. New J. Phys. 12, 113042 (2010).

    ADS  Article  Google Scholar 

  39. 39

    Nazir, A. Photon statistics from a resonantly driven quantum dot. Phys. Rev. B 78, 153309 (2008).

    ADS  Article  Google Scholar 

  40. 40

    McCutcheon, D. P. S. Optical signatures of non-Markovian behavior in open quantum systems. Phys. Rev. A 93, 022119 (2016).

    ADS  Article  Google Scholar 

  41. 41

    Hornecker, G., Auffèves, A. & Grange, T. Influence of phonons on solid-state cavity–QED investigated using nonequilibrium Green's functions. Phys. Rev. B 95, 035404 (2017).

    ADS  Article  Google Scholar 

  42. 42

    Roy, C. & Hughes, S. Phonon-dressed Mollow triplet in the regime of cavity quantum electrodynamics: excitation-induced dephasing and nonperturbative cavity feeding effects. Phys. Rev. Lett. 106, 247403 (2011).

    ADS  Article  Google Scholar 

  43. 43

    Roy-Choudhury, K. & Hughes, S. Quantum theory of the emission spectrum from quantum dots coupled to structured photonic reservoirs and acoustic phonons. Phys. Rev. B 92, 205406 (2015).

    ADS  Article  Google Scholar 

  44. 44

    Iles-Smith, J. & Nazir, A. Quantum correlations of light and matter through environmental transitions. Optica 3, 207–211 (2016).

    ADS  Article  Google Scholar 

  45. 45

    Grange, T. et al. Cavity-funneled generation of indistinguishable single photons from strongly dissipative quantum emitters. Phys. Rev. Lett. 114, 193601 (2015).

    ADS  Article  Google Scholar 

  46. 46

    Tighineanu, P., Dreeßen, C. L., Flindt, C., Lodahl, P. & Sørensen, A. S. Phonon decoherence of quantum dots in photonic structures: broadening of the zero-phonon line and the role of dimensionality. Preprint at (2017).

  47. 47

    Androvitsaneas, P. et al. Charged quantum dot micropillar system for deterministic light-matter interactions. Phys. Rev. B 93, 241409 (2016).

    ADS  Article  Google Scholar 

  48. 48

    Eberly, J. H. & Wódkiewicz, K. The time-dependent physical spectrum of light. J. Opt. Soc. Am. 67, 1252–1261 (1977).

    ADS  Article  Google Scholar 

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The authors thank N. Gregersen for useful discussions. J.I.-S. and J.M. acknowledge support from the Danish Research Council (DFF-4181-00416) and Villum Fonden (NATEC Centre, grant 8692). A.N. is supported by the University of Manchester and the Engineering and Physical Sciences Research Council, grant number EP/N008154/1. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 703193.

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All the authors were involved in the conception, development and writing of the manuscript.

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Correspondence to Jake Iles-Smith.

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Iles-Smith, J., McCutcheon, D., Nazir, A. et al. Phonon scattering inhibits simultaneous near-unity efficiency and indistinguishability in semiconductor single-photon sources. Nature Photon 11, 521–526 (2017).

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