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.

  • Letter
  • Published:

Generation of Fock states in a superconducting quantum circuit

Nature volume 454, pages 310–314 (2008)Cite this article

Abstract

Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics1. The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, whereas the harmonic oscillator represents the most linear, with an infinite number of evenly spaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state2. Quantum behaviour in an oscillator is most obvious in Fock states, which are states with specific numbers of energy quanta, but such states are hard to create3,4,5,6,7. Here we demonstrate the controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit8, which is a close approximation to a two-level spin system, coupled to a microwave resonator, which acts as a harmonic oscillator, to prepare and analyse pure Fock states with up to six photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Device description and spectroscopy.
Figure 2: Preparation and measurement of Fock states.
Figure 3: Preparation and measurement of coherent states.
Figure 4: Population analysis of coherent states.

Similar content being viewed by others

References

  1. Cohen-Tannoudji, C., Diu, B. & Laloë, F. Quantum Mechanics Vol. 1, Ch. 4 5 (Wiley, New York, 2006)

    MATH  Google Scholar 

  2. Haroche, S. & Raimond, J.-M. Exploring the Quantum — Atoms, Cavities and Photons Ch. 3 (Oxford Univ. Press, Oxford, UK, 2006)

    Book  Google Scholar 

  3. Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett. 76, 1796–1799 (1996)

    Article  ADS  CAS  Google Scholar 

  4. Cirac, J. I., Blatt, R., Parkins, A. S. & Zoller, P. Preparation of Fock states by observation of quantum jumps in an ion trap. Phys. Rev. Lett. 70, 762–765 (1993)

    Article  ADS  CAS  Google Scholar 

  5. Varcoe, B. T. H., Brattke, S., Weidinger, M. & Walther, H. Preparing pure photon number states of the radiation field. Nature 403, 743–746 (2000)

    Article  ADS  CAS  Google Scholar 

  6. Bertet, P. et al. Generating and probing a two-photon Fock state with a single atom in a cavity. Phys. Rev. Lett. 88, 143601 (2002)

    Article  ADS  CAS  Google Scholar 

  7. Waks, E., Dimanti, E. & Yamamoto, Y. Generation of photon number states. N. J. Phys. 8, 4 (2006)

    Article  Google Scholar 

  8. Devoret, M. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Quantum Inf. Process. 3, 163–203 (2004)

    Article  Google Scholar 

  9. Guerlin, C. et al. Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889–893 (2007)

    Article  ADS  CAS  Google Scholar 

  10. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    Article  ADS  CAS  Google Scholar 

  11. Johansson, J. et al. Vacuum Rabi oscillations in a macroscopic superconducting qubit LC oscillator system. Phys. Rev. Lett. 96, 127006 (2006)

    Article  ADS  CAS  Google Scholar 

  12. Houck, A. A. et al. Generating single microwave photons in a circuit. Nature 449, 328–331 (2007)

    Article  ADS  CAS  Google Scholar 

  13. Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007)

    Article  ADS  Google Scholar 

  14. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)

    Article  ADS  CAS  Google Scholar 

  15. Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007)

    Article  ADS  CAS  Google Scholar 

  16. Astafiev, O. et al. Single artificial-atom lasing. Nature 449, 588–590 (2007)

    Article  ADS  CAS  Google Scholar 

  17. Liu, Y.-X., Wei, L. F. & Nori, F. Generation of nonclassical photon states using a superconducting qubit in a microcavity. Europhys. Lett. 67, 941–947 (2004)

    Article  ADS  CAS  Google Scholar 

  18. Brune, M. et al. Quantum Rabi oscillation: A direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800–1803 (1996)

    Article  ADS  CAS  Google Scholar 

  19. Steffen, M. et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys. Rev. Lett. 97, 050502 (2006)

    Article  ADS  Google Scholar 

  20. Neeley, M. et al. Transformed dissipation in superconducting quantum circuits. Phys. Rev. B 77, 180508(R) (2008)

    Article  ADS  Google Scholar 

  21. O’Connell, A. D. et al. Microwave dielectric loss at single photon energies and millikelvin temperatures. Appl. Phys. Lett. 92, 112903 (2008)

    Article  ADS  Google Scholar 

  22. Neeley, M. et al. Process tomography of quantum memory in a Josephson phase qubit coupled to a two-level state. Nature Phys. advance online publication 10.1038/nphys972 (27 April 2008)

  23. Devoret, M. H., Esteve, D., Martinis, J. M. & Urbina, C. Effect of an adjustable admittance on the macroscopic energy levels of a current biased Josephson junction. Phys. Scr. T25, 118–121 (1989)

    Article  ADS  Google Scholar 

  24. Devoret, M. H. et al. in Quantum Tunnelling in Condensed Media (eds Kagan, Y. & Leggett, A. J.) Ch. 6 337–338 (Elsevier, Amsterdam, 1992)

    Google Scholar 

  25. Jaynes, E. & Cummings, F. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1963)

    Article  Google Scholar 

  26. Lucero, E. et al. High-fidelity gates in a Josephson qubit. Phys. Rev. Lett. (in the press); preprint at 〈http://arxiv.org/abs/0802.0903〉 (2008)

  27. Lu, N. Effects of dissipation on photon statistics and the lifetime of a pure number state. Phys. Rev. A 40, 1707–1708 (1989)

    Article  ADS  CAS  Google Scholar 

  28. Faist, A., Geneux, E., Meystre, P. & Quattropani, P. Coherent radiation in interaction with two-level system. Helv. Phys. Acta 45, 956–959 (1972)

    Google Scholar 

  29. Eberly, J. H., Narozhny, N. B. & Sanchez-Mondragon, J. J. Periodic spontaneous collapse and revival in a simple quantum model. Phys. Rev. Lett. 44, 1323–1326 (1980)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank M. Geller for theoretical input. Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. This work was supported by IARDA under grant W911NF-04-1-0204 and by the NSF under grants CCF-0507227 and DMR-0605818.

Author information

Author notes

  1. E. M. Weig

    Present address: Present address: Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, 80539 München, Germany.,

Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, California 93106, USA,

    Max Hofheinz, E. M. Weig, M. Ansmann, Radoslaw C. Bialczak, Erik Lucero, M. Neeley, A. D. O’Connell, H. Wang, John M. Martinis & A. N. Cleland

Authors
  1. Max Hofheinz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. M. Weig
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Ansmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Radoslaw C. Bialczak
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Erik Lucero
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Neeley
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. D. O’Connell
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. H. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. John M. Martinis
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. A. N. Cleland
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Cleland.

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hofheinz, M., Weig, E., Ansmann, M. et al. Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008). https://doi.org/10.1038/nature07136

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07136

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