Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Photon-number entanglement generated by sequential excitation of a two-level atom


Entanglement and spontaneous emission are fundamental quantum phenomena that drive many applications of quantum physics. During the spontaneous emission of light from an excited two-level atom, the atom briefly becomes entangled with the photonic field. Here we show that this natural process can be used to produce photon-number entangled states of light distributed in time. By exciting a quantum dot—an artificial two-level atom—with two sequential π-pulses, we generate a photon-number Bell state. We characterize this state using time-resolved intensity and phase correlation measurements. Furthermore, we theoretically show that applying longer sequences of pulses to a two-level atom can produce a series of multi-temporal mode entangled states with properties intrinsically related to the Fibonacci sequence. Our results on photon-number entanglement can be further exploited to generate new states of quantum light with applications in quantum technologies.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Generation of photon-number Bell states.
Fig. 2: Characterization of intensity.
Fig. 3: Characterization of coherence.

Data availability

The experimental data that support the findings of this study are available in figshare at


  1. Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. A “Schrödinger cat” superposition state of an atom. Science 272, 1131–1136 (1996).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012).

    Article  ADS  Google Scholar 

  3. Slodička, L. et al. Atom–atom entanglement by single-photon detection. Phys. Rev. Lett. 110, 083603 (2013).

    Article  ADS  Google Scholar 

  4. Blinov, B. B., Moehring, D. L., Duan, L. M. & Monroe, C. Observation of entanglement between a single trapped atom and a single photon. Nature 428, 153–157 (2004).

    Article  ADS  Google Scholar 

  5. Wilk, T., Webster, S. C., Kuhn, A. & Rempe, G. Single-atom single-photon quantum interface. Science 317, 488–490 (2007).

    Article  ADS  Google Scholar 

  6. De Greve, K. et al. Quantum-dot spin–photon entanglement via frequency downconversion to telecom wavelength. Nature 491, 421–425 (2012).

    Article  ADS  Google Scholar 

  7. Brunel, C., Lounis, B., Tamarat, P. & Orrit, M. Triggered source of single photons based on controlled single molecule fluorescence. Phys. Rev. Lett. 83, 2722–2725 (1999).

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Neumann, P. et al. multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008).

    Article  ADS  Google Scholar 

  10. Schwartz, I. et al. Deterministic generation of a cluster state of entangled photons. Science 354, 434–437 (2016).

    Article  ADS  Google Scholar 

  11. Besse, J.-C. et al. Realizing a deterministic source of multipartite-entangled photonic qubits. Nat. Commun. 11, 4877 (2020).

    Article  ADS  Google Scholar 

  12. Saavedra, C., Gheri, K. M., Törmä, P., Cirac, J. I. & Zoller, P. Controlled source of entangled photonic qubits. Phys. Rev. A 61, 062311 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  13. Schön, C., Solano, E., Verstraete, F., Cirac, J. I. & Wolf, M. M. Sequential generation of entangled multiqubit states. Phys. Rev. Lett. 95, 110503 (2005).

    Article  ADS  Google Scholar 

  14. Schön, C., Hammerer, K., Wolf, M. M., Cirac, J. I. & Solano, E. Sequential generation of matrix-product states in cavity QED. Phys. Rev. A 75, 032311 (2007).

    Article  ADS  Google Scholar 

  15. Maître, X. et al. Quantum memory with a single photon in a cavity. Phys. Rev. Lett. 79, 769–772 (1997).

    Article  ADS  Google Scholar 

  16. Specht, H. P. et al. A single-atom quantum memory. Nature 473, 190–193 (2011).

    Article  ADS  Google Scholar 

  17. Cirac, J. I., Zoller, P., Kimble, H. J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).

    Article  ADS  Google Scholar 

  18. Chou, C.-W. et al. Functional quantum nodes for entanglement distribution over scalable quantum networks. Science 316, 1316–1320 (2007).

    Article  ADS  Google Scholar 

  19. Yuan, Z.-S. et al. Experimental demonstration of a BDCZ quantum repeater node. Nature 454, 1098–1101 (2008).

    Article  ADS  Google Scholar 

  20. Daiss, S. et al. A quantum-logic gate between distant quantum-network modules. Science 371, 614–617 (2021).

    Article  ADS  Google Scholar 

  21. Weisskopf, V. & Wigner, E. Berechnung der natürlichen linienbreite auf grund der diracschen lichttheorie. Zeit. Phys. 63, 54–73 (1930).

    Article  ADS  MATH  Google Scholar 

  22. Blow, K. J., Loudon, R., Phoenix, S. J. D. & Shepherd, T. J. Continuum fields in quantum optics. Phys. Rev. A 42, 4102–4114 (1990).

    Article  ADS  Google Scholar 

  23. Hussain, N., Imoto, N. & Loudon, R. Quantum theory of dynamic interference experiments. Phys. Rev. A 45, 1987–1996 (1992).

    Article  ADS  Google Scholar 

  24. Özdemir, Ş. K., Miranowicz, A., Koashi, M. & Imoto, N. Pulse-mode quantum projection synthesis: effects of mode mismatch on optical state truncation and preparation. Phys. Rev. A 66, 053809 (2002).

    Article  ADS  Google Scholar 

  25. Van Enk, S. J. Single-particle entanglement. Phys. Rev. A 72, 064306 (2005).

    Article  ADS  Google Scholar 

  26. Specht, H. P. et al. Phase shaping of single-photon wave packets. Nat. Photon. 3, 469–472 (2009).

    Article  ADS  Google Scholar 

  27. Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  28. Hilaire, P. et al. Deterministic assembly of a charged-quantum-dot–micropillar cavity device. Phys. Rev. B 102, 195402 (2020).

    Article  ADS  Google Scholar 

  29. Kuhlmann, A. V. et al. A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode. Rev. Sci. Instrum. 84, 073905 (2013).

    Article  ADS  Google Scholar 

  30. Stievater, T. H. et al. Rabi oscillations of excitons in single quantum dots. Phys. Rev. Lett. 87, 133603 (2001).

    Article  ADS  Google Scholar 

  31. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    Article  ADS  Google Scholar 

  32. 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).

  33. Ollivier, H. et al. Hong-Ou-mandel interference with imperfect single photon sources. Phys. Rev. Lett. 126, 063602 (2021).

    Article  ADS  Google Scholar 

  34. Loredo, J. C. et al. Generation of non-classical light in a photon-number superposition. Nat. Photon. 13, 803–808 (2019).

    Article  ADS  Google Scholar 

  35. Wein, S. C. Modelling Markovian LightMatter Interactions for Quantum Optical Devices in the Solid State. PhD thesis, Univ. Calgary (2021).

  36. Wootters, W. K. Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27–44 (2001).

  37. Korzh, B. et al. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat. Photon. 14, 250–255 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. Tomm, N. et al. A bright and fast source of coherent single photons. Nat. Nanotechnol. 16, 399–403 (2021).

  40. Wang, C. et al. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 562, 101–104 (2018).

    Article  ADS  Google Scholar 

  41. Law, C. K. & Eberly, J. H. Arbitrary control of a quantum electromagnetic field. Phys. Rev. Lett. 76, 1055–1058 (1996).

    Article  ADS  Google Scholar 

  42. Cosacchi, M. et al. On-demand generation of higher-order fock states in quantum-dot–cavity systems. Phys. Rev. Res. 2, 033489 (2020).

    Article  Google Scholar 

  43. Cosacchi, M. et al. Schrödinger cat states in quantum-dot-cavity systems. Phys. Rev. Res. 3, 023088 (2021).

    Article  Google Scholar 

  44. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001).

    Article  ADS  Google Scholar 

  45. Erhard, M., Krenn, M. & Zeilinger, A. Advances in high-dimensional quantum entanglement. Nat. Rev. Phys. 2, 365–381 (2020).

    Article  Google Scholar 

  46. Ollivier, H. et al. Reproducibility of high-performance quantum dot single-photon sources. ACS Photon. 7, 1050–1059 (2020).

    Article  Google Scholar 

  47. Kuhlmann, A. V. et al. A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode. Rev. Sci. Instrum. 84, 073905 (2013).

    Article  ADS  Google Scholar 

  48. Loredo, J. C. et al. Generation of non-classical light in a photon-number superposition. Nat. Photon. 13, 803–808 (2019).

    Article  ADS  Google Scholar 

  49. Flagg, E. B., Polyakov, S. V., Thomay, T. & Solomon, G. S. Dynamics of nonclassical light from a single solid-state quantum emitter. Phys. Rev. Lett. 109, 163601 (2012).

    Article  ADS  Google Scholar 

  50. Hilaire, P. et al. Deterministic assembly of a charged-quantum-dot–micropillar cavity device. Phys. Rev. B 102, 195402 (2020).

    Article  ADS  Google Scholar 

Download references


P.S. acknowledges support from the ERC PoC PhoW, the IAD—ANR support ASTRID programme project (grant. no. ANR-18-ASTR-0024 LIGHT), the QuantERA ERA-NET Cofund in Quantum Technologies (project HIPHOP), the FET OPEN QLUSTER, and the French RENATECH network, a public grant overseen by the French National Research Agency (ANR) as part of the Investissements d’Avenir programme (Labex NanoSaclay, grant no. ANR-10-LABX-0035). J.C.L. acknowledges the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association. A.A., M.M. and S.C.W acknowledge support from the Foundational Questions Institute Fund (grant no. FQXi-IAF19-01 to A.A and S.C.W, and FQXi-IAF19-05 to A.A. and M.M.), as well as the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie (grant agreement no. 861097 to A.A., M.M. and S.C.W.). A.A. and M.M also acknowledge support from the ANR Research Collaborative Project Qu-DICE (grant no. ANR-PRC-CES47 to A.A and M.M.), the Templeton World Charity Foundation Inc (grant no. TWCF0338 to A.A. and M.M.) and the John Templeton Foundation (grant no. 61835 to A.A.). C.S. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant and Strategic Project Grant programs, as well as the National Research Council’s High-Throughput Secure Networks program. S.C.W. also acknowledges support from the NSERC Canadian Graduate Scholarships (grant nos 668347 and 677972) and the SPIE Education Scholarship program. S.C.W. and C.A.-S. acknowledge A. González-Tudela, C. Sánchez-Muñoz, T. Huber and N. Sinclair for fruitful discussions. C.A.-S. thanks K. Bencheikh and F. Raineri for providing technical assistance in the experimental set-up.

Author information

Authors and Affiliations



The experiments were conducted by J.C.L. and C.A.-S. Data analysis was carried out by S.C.W. and C.A.-S. with help from J.C.L. and P.H. Theoretical modelling was performed by S.C.W., M.M., C.S. and A.A, with help from J.C.L and C.A.-S. Cavity devices were fabricated by A.H. and N.S. from samples grown by A.L. based on a design of L.L. Etching was performed by I.S. The manuscript was written by S.C.W. and C.A.-S. with assistance from C.S. and P.S. and input from all authors. The project was supervised by C.A.-S. with the collaboration of C.S. and P.S.

Corresponding authors

Correspondence to Stephen C. Wein or Carlos Antón-Solanas.

Ethics declarations

Competing interests

N.S. is a co-founder—and P.S. is a scientific advisor and co-founder—of the single-photon-source company Quandela. The other authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Adam Miranowicz, Tracy Northup and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Theory derivations and the extended experimental analysis, and Supplementary Figs. 1–7.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wein, S.C., Loredo, J.C., Maffei, M. et al. Photon-number entanglement generated by sequential excitation of a two-level atom. Nat. Photon. 16, 374–379 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing