Skip to main content

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.

Hong–Ou–Mandel interference of two phonons in trapped ions

Nature volume 527, pages 74–77 (2015)Cite this article

Subjects

Abstract

The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong–Ou–Mandel effect1. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose–Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong–Ou–Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right2,3,4, and could have implications for the quantum simulation of bosonic particles5,6 and analogue quantum computation via boson sampling7.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Figure 1: Conceptual diagrams of phonon hopping dynamics and two-phonon interference.
Figure 2: Experimental results for phonon dynamics.
Figure 3: Measurement of fidelity of the state.

References

  1. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between 2 photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987)

    Article  ADS  CAS  Google Scholar 

  2. Brown, K. R. et al. Coupled quantized mechanical oscillators. Nature 471, 196–199 (2011)

    Article  ADS  CAS  Google Scholar 

  3. Harlander, M., Lechner, R., Brownnutt, M., Blatt, R. & Hänsel, W. Trapped-ion antennae for the transmission of quantum information. Nature 471, 200–203 (2011)

    Article  ADS  CAS  Google Scholar 

  4. Haze, S., Tateishi, Y., Noguchi, A., Toyoda, K. & Urabe, S. Observation of phonon hopping in radial vibrational modes of trapped ions. Phys. Rev. A 85, 031401(R) (2012)

    Article  ADS  Google Scholar 

  5. Porras, D. & Cirac, J. I. Bose-Einstein condensation and strong-correlation behavior of phonons in ion traps. Phys. Rev. Lett. 93, 263602 (2004)

    Article  ADS  CAS  Google Scholar 

  6. Toyoda, K., Matsuno, Y., Noguchi, A., Haze, S. & Urabe, S. Experimental realization of a quantum phase transition of polaritonic excitations. Phys. Rev. Lett. 111, 160501 (2013)

    Article  ADS  Google Scholar 

  7. Shen, C., Zhang, Z. & Duan, L. M. Scalable implementation of boson sampling with trapped ions. Phys. Rev. Lett. 112, 050504 (2014)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  9. Beugnon, J. et al. Quantum interference between two single photons emitted by independently trapped atoms. Nature 440, 779–782 (2006)

    Article  ADS  CAS  Google Scholar 

  10. Kaltenbaek, R., Blauensteiner, B., Zukowski, M., Aspelmeyer, M. & Zeilinger, A. Experimental interference of independent photons. Phys. Rev. Lett. 96, 240502 (2006)

    Article  ADS  Google Scholar 

  11. Maunz, P. et al. Quantum interference of photon pairs from two remote trapped atomic ions. Nature Phys. 3, 538–541 (2007)

    Article  ADS  CAS  Google Scholar 

  12. Lang, C. et al. Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies. Nature Phys. 9, 345–348 (2013)

    Article  ADS  CAS  Google Scholar 

  13. Kaufman, A. M. et al. Two-particle quantum interference in tunnel-coupled optical tweezers. Science 345, 306–309 (2014)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Lopes, R. et al. Atomic Hong–Ou–Mandel experiment. Nature 520, 66–68 (2015)

    Article  ADS  CAS  Google Scholar 

  15. Liu, R. C., Odom, B., Yamamoto, Y. & Tarucha, S. Quantum interference in electron collision. Nature 391, 263–265 (1998)

    Article  ADS  CAS  Google Scholar 

  16. Bocquillon, E. et al. Coherence and indistinguishability of single electrons emitted by independent sources. Science 339, 1054–1057 (2013)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  18. Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007)

    Article  ADS  CAS  Google Scholar 

  19. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)

    Article  ADS  CAS  Google Scholar 

  20. Mølmer, K. & Sørensen, A. Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 82, 1835–1838 (1999)

    Article  ADS  Google Scholar 

  21. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000)

    Article  ADS  CAS  Google Scholar 

  22. Broome, M. A. et al. Photonic boson sampling in a tunable circuit. Science 339, 794–798 (2013)

    Article  ADS  CAS  Google Scholar 

  23. Spring, J. B. et al. Boson sampling on a photonic chip. Science 339, 798–801 (2013)

    Article  ADS  CAS  Google Scholar 

  24. Tillmann, M. et al. Experimental boson sampling. Nature Photon. 7, 540–544 (2013)

    Article  ADS  CAS  Google Scholar 

  25. Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nature Photon. 7, 545–549 (2013)

    Article  ADS  CAS  Google Scholar 

  26. Aspelmeyer, M., Kippenberg, T. J. & Marquard, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank Y. Yamamoto for suggestions made at the early stages of this study, and K. Hayasaka for comments on the manuscript. This work was supported by JSPS KAKENHI, grant number 26400418.

Author information

Author notes

  1. Atsushi Noguchi

    Present address: † Present address: Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan.,

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Kenji Toyoda, Ryoto Hiji, Atsushi Noguchi & Shinji Urabe

Authors
  1. Kenji Toyoda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryoto Hiji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Atsushi Noguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shinji Urabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.U., K.T. and A.N. designed this study. A.N. and R.H. conducted the experiment. R.H. wrote an early version of the manuscript. K.T. revised and completed the manuscript.

Corresponding author

Correspondence to Kenji Toyoda.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Toyoda, K., Hiji, R., Noguchi, A. et al. Hong–Ou–Mandel interference of two phonons in trapped ions. Nature 527, 74–77 (2015). https://doi.org/10.1038/nature15735

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature15735

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

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