Thank you for visiting nature.com. 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.

# Generation of non-classical light in a photon-number superposition

## Abstract

Generating light in a pure quantum state is essential for advancing optical quantum technologies. However, controlling its photon number remains elusive. Optical fields with zero and one photon can be produced by single atoms, but, so far, this has been limited to generating incoherent mixtures or coherent superpositions with a very small one-photon term. Here, we report the on-demand generation of quantum superpositions of zero, one and two photons via coherent control of an artificial atom. Driving the system up to full atomic inversion leads to quantum superpositions of vacuum and one photon, with their relative populations controlled by the driving laser intensity. A stronger driving of the system, with 2π pulses, results in a coherent superposition of vacuum, one and two photons, with the two-photon term exceeding the one-photon component, a state allowing phase super-resolving interferometry. Our results open new paths for optical quantum technologies with access to the photon-number degree of freedom.

## Relevant articles

• ### Quantum channel correction outperforming direct transmission

Nature Communications Open Access 05 April 2022

## Access options

\$32.00

All prices are NET prices.

## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

## References

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

2. Erhard, M., Fickler, R., Krenn, M. & Zeilinger, A. Twisted photons: new quantum perspectives in high dimensions. Light Sci. Appl. 7, 17146 (2018).

3. Waks, E., Diamanti, E. & Yamamoto, Y. Generation of photon number states. New J. Phys. 8, 4 (2006).

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

5. Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).

6. Scarani, V. et al. The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009).

7. Bunandar, D. et al. Metropolitan quantum key distribution with silicon photonics. Phys. Rev. X 8, 021009 (2018).

8. Brida, G., Genovese, M. & Ruo Berchera, I. Experimental realization of sub-shot-noise quantum imaging. Nat. Photon. 4, 227–230 (2010).

9. Schwartz, O. et al. Superresolution microscopy with quantum emitters. Nano Lett. 13, 5832–5836 (2013).

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

11. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007).

12. Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010).

13. Loredo, J. C. et al. Measuring entanglement in a photonic embedding quantum simulator. Phys. Rev. Lett. 116, 070503 (2016).

14. Chen, M.-C. et al. Efficient measurement of multiparticle entanglement with embedding quantum simulator. Phys. Rev. Lett. 116, 070502 (2016).

15. Santagati, R. et al. Witnessing eigenstates for quantum simulation of Hamiltonian spectra. Sci. Adv. 4, eaap9646 (2018).

16. O’Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C. & Branning, D. Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003).

17. Patel, R. B., Ho, J., Ferreyrol, F., Ralph, T. C. & Pryde, G. J. A quantum Fredkin gate. Sci. Adv. 2, e1501531 (2016).

18. Wang, X.-L. et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015).

19. Takeda, S., Fuwa, M., van Loock, P. & Furusawa, A. Entanglement swapping between discrete and continuous variables. Phys. Rev. Lett. 114, 100501 (2015).

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

21. 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).

22. Senellart, P., Solomon, G. & White, A. High-performance semiconductor quantum-dot single-photon sources. Nat. Nanotechnol. 12, 1026–1039 (2017).

23. Kirsanske, G. et al. Indistinguishable and efficient single photons from a quantum dot in a planar nanobeam waveguide. Phys. Rev. B 96, 165306 (2017).

24. Lombardi, E., Sciarrino, F., Popescu, S. & De Martini, F. Teleportation of a vacuum-one-photon qubit. Phys. Rev. Lett. 88, 070402 (2002).

25. Gabriel, C. et al. A generator for unique quantum random numbers based on vacuum states. Nat. Photon. 4, 711–715 (2010).

26. Bimbard, E., Jain, N., MacRae, A. & Lvovsky, A. I. Quantum-optical state engineering up to the two-photon level. Nat. Photon. 4, 243–247 EP (2010).

27. Fuwa, M., Takeda, S., Zwierz, M., Wiseman, H. M. & Furusawa, A. Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements. Nat. Commun. 6, 6665 (2015).

28. Grangier, P., Roger, G. & Aspect, A. Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. Europhys. Lett. 1, 173–179 (1986).

29. Lounis, B. & Moerner, W. E. Single photons on demand from a single molecule at room temperature. Nature 407, 491–493 (2000).

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

31. Michler, P. et al. Quantum correlation among photons from a single quantum dot at room temperature. Nature 406, 968–970 (2000).

32. Jessen, P. S. et al. Observation of quantized motion of Rb atoms in an optical field. Phys. Rev. Lett. 69, 49–52 (1992).

33. Nguyen, H. S. et al. Ultra-coherent single photon source. Appl. Phys. Lett. 99, 261904 (2011).

34. Matthiesen, C., Vamivakas, A. N. & Atature, M. Subnatural linewidth single photons from a quantum dot. Phys. Rev. Lett. 108, 093602 (2012).

35. Matthiesen, C. et al. Phase-locked indistinguishable photons with synthesized waveforms from a solid-state source. Nat. Commun. 4, 1600 (2013).

36. Proux, R. et al. Measuring the photon coalescence time window in the continuous-wave regime for resonantly driven semiconductor quantum dots. Phys. Rev. Lett. 114, 067401 (2015).

37. Schulte, C. H. H. et al. Quadrature squeezed photons from a two-level system. Nature 525, 222–225 (2015).

38. Giesz, V. et al. Coherent manipulation of a solid-state artificial atom with few photons. Nat. Commun. 7, 11986 (2016).

39. Dousse, A. et al. Controlled light–matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography. Phys. Rev. Lett. 101, 267404 (2008).

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

41. Fischer, K. A. et al. Signatures of two-photon pulses from a quantum two-level system. Nat. Phys. 13, 649–654 (2017).

42. 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).

43. Fischer, K. A., Trivedi, R. & Lukin, D. Particle emission from open quantum systems. Phys. Rev. A 98, 023853 (2018).

44. Grange, T. et al. Reducing phonon-induced decoherence in solid-state single-photon sources with cavity quantum electrodynamics. Phys. Rev. Lett. 118, 253602 (2017).

45. Valente, D. et al. Monitoring stimulated emission at the single-photon level in one-dimensional atoms. Phys. Rev. A 85, 023811 (2012).

46. Sayrin, C. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011).

47. Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).

48. Munoz, C. S. et al. Emitters of n-photon bundles. Nat. Photon. 8, 550–555 (2014).

49. Ralph, T. C., Gilchrist, A., Milburn, G. J., Munro, W. J. & Glancy, S. Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003).

50. Lund, A. P., Ralph, T. C. & Haselgrove, H. L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett. 100, 030503 (2008).

51. Gilchrist, A. et al. Schrödinger cats and their power for quantum information processing. J. Opt. B 6, 5828–5833 (2004).

## Acknowledgements

This work was partially supported by ERC Starting Grant no. 277885 QD-CQED, the French Agence Nationale pour la Recherche (grant ANR SPIQE and USSEPP), the French RENATECH network and a public grant overseen by the French National Research Agency (ANR) as part of the Investissements d’Avenir programme (Labex NanoSaclay, reference ANR-10-LABX-0035). J.C.L. and C.A. acknowledge support from Marie Skłodowska-Curie Individual Fellowships SMUPHOS and SQUAPH, respectively. We thank N. Carlon Zambon for providing technical assistance throughout the project.

## Author information

Authors

### Contributions

The experiments were conducted by J.C.L. and C.A. with help from P.H., C.M., H.O. and L.D.S. Data analysis was carried out by C.A. and J.C.L. The theoretical modelling was done by A.A., B.R., O.K., C.A. and J.C.L. The cavity devices were fabricated by A.H. and N.S. from samples grown by A.L., and the etching was done by I.S. The manuscript was written by J.C.L., C.A. and P.S. with input from all authors. The project was supervised by L.L., A.A., O.K. and P.S.

### Corresponding authors

Correspondence to J. C. Loredo, C. Antón or P. Senellart.

## Ethics declarations

### Competing interests

N.S. is co-founder, and P.S. is scientific advisor and co-founder, of the single-photon-source company Quandela.

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

## Supplementary information

### Supplementary Information

Supplementary notes and figures.

## Rights and permissions

Reprints and Permissions

Loredo, J.C., Antón, C., Reznychenko, B. et al. Generation of non-classical light in a photon-number superposition. Nat. Photonics 13, 803–808 (2019). https://doi.org/10.1038/s41566-019-0506-3

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41566-019-0506-3

• ### Quantum channel correction outperforming direct transmission

• Sergei Slussarenko
• Morgan M. Weston
• Geoff J. Pryde

Nature Communications (2022)

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

• Stephen C. Wein
• Juan C. Loredo
• Carlos Antón-Solanas

Nature Photonics (2022)