Letter | Published:

Synthesizing arbitrary quantum states in a superconducting resonator

Nature volume 459, pages 546549 (28 May 2009) | Download Citation

Subjects

Abstract

The superposition principle is a fundamental tenet of quantum mechanics. It allows a quantum system to be ‘in two places at the same time’, because the quantum state of a physical system can simultaneously include measurably different physical states. The preparation and use of such superposed states forms the basis of quantum computation and simulation1. The creation of complex superpositions in harmonic systems (such as the motional state of trapped ions2, microwave resonators3,4,5 or optical cavities6) has presented a significant challenge because it cannot be achieved with classical control signals. Here we demonstrate the preparation and measurement of arbitrary quantum states in an electromagnetic resonator, superposing states with different numbers of photons in a completely controlled and deterministic manner. We synthesize the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm7 that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator8. We completely characterize the resonator quantum state using Wigner tomography, which is equivalent to measuring the resonator’s full density matrix.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    & Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

  2. 2.

    et al. Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle. Phys. Rev. Lett. 90, 037902 (2003)

  3. 3.

    et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008)

  4. 4.

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

  5. 5.

    , & Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007)

  6. 6.

    , , , & Reversible state transfer between light and a single trapped atom. Phys. Rev. Lett. 98, 193601 (2007)

  7. 7.

    & Arbitrary control of a quantum electromagnetic field. Phys. Rev. Lett. 76, 1055–1058 (1996)

  8. 8.

    et al. Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008)

  9. 9.

    , & Energy-level quantization in the zero-voltage state of a current-biased Josephson junction. Phys. Rev. Lett. 55, 1543–1546 (1985)

  10. 10.

    & Superconducting quantum bits. Nature 453, 1031–1042 (2008)

  11. 11.

    et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)

  12. 12.

    et al. Quantum coherent tunable coupling of superconducting qubits. Science 316, 723–726 (2007)

  13. 13.

    , , & Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits. Nature 447, 836–839 (2007)

  14. 14.

    et al. Climbing the Jaynes-Cummings ladder and observing its nonlinearity in a cavity QED system. Nature 454, 315–318 (2008)

  15. 15.

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

  16. 16.

    et al. Generation of non-classical photon states using a superconducting qubit in a quantum electrodynamic microcavity. Europhys. Lett. 67, 941–947 (2004)

  17. 17.

    , & Quantum state engineering of the radiation field. Phys. Rev. Lett. 71, 1816–1819 (1993)

  18. 18.

    , , & Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. Phys. Rev. Lett. 70, 1244–1247 (1993)

  19. 19.

    & Direct probing of quantum phase space by photon counting. Phys. Rev. Lett. 76, 4344–4347 (1996)

  20. 20.

    & Method for direct measurement of the Wigner function in cavity QED and ion traps. Phys. Rev. Lett. 78, 2547–2550 (1997)

  21. 21.

    , , & Direct measurement of the Wigner function by photon counting. Phys. Rev. A 60, 674–677 (1999)

  22. 22.

    et al. Direct measurement of the Wigner function of a one-photon Fock state in a cavity. Phys. Rev. Lett. 89, 200402 (2002)

  23. 23.

    On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)

  24. 24.

    & Exploring the Quantum — Atoms, Cavities and Photons (Oxford Univ. Press, 2006)

  25. 25.

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

  26. 26.

    , & Measurement of the quantum states of squeezed light. Nature 387, 471–475 (1997)

  27. 27.

    & Synthesis and tomographic characterization of the displaced Fock state of light. Phys. Rev. A 66, 011801 (2002)

  28. 28.

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

  29. 29.

    et al. Measurement of the decay of Fock states in a superconducting quantum circuit. Phys. Rev. Lett. 101, 240401 (2008)

Download references

Acknowledgements

Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. We thank M. Geller for discussions. This work was supported by IARPA (grant W911NF-04-1-0204) and by the NSF (grant CCF-0507227).

Author Contributions M.H. performed the experiments and analysed the data. H.W. improved the resonator design and fabricated the sample. J.M.M. and E.L. designed the custom electronics and M.H. developed the calibrations for it. M.A. and M.N. provided software infrastructure. All authors contributed to the fabrication process, qubit design or experimental set-up. M.H., J.M.M. and A.N.C. conceived the experiment and co-wrote the paper.

Author information

Affiliations

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

    • Max Hofheinz
    • , H. Wang
    • , M. Ansmann
    • , Radoslaw C. Bialczak
    • , Erik Lucero
    • , M. Neeley
    • , A. D. O'Connell
    • , D. Sank
    • , J. Wenner
    • , John M. Martinis
    •  & A. N. Cleland

Authors

  1. Search for Max Hofheinz in:

  2. Search for H. Wang in:

  3. Search for M. Ansmann in:

  4. Search for Radoslaw C. Bialczak in:

  5. Search for Erik Lucero in:

  6. Search for M. Neeley in:

  7. Search for A. D. O'Connell in:

  8. Search for D. Sank in:

  9. Search for J. Wenner in:

  10. Search for John M. Martinis in:

  11. Search for A. N. Cleland in:

Corresponding author

Correspondence to A. N. Cleland.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Methods and Data, Supplementary Figures S1-S3 with Legends and Supplementary References.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature08005

Further reading

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.