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Analog information processing at the quantum limit with a Josephson ring modulator

Nature Physics volume 6, pages 296–302 (2010)Cite this article

Abstract

Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, they always degrade the information by adding noise. Quantum mechanics puts a limit on how small this degradation can be. Theoretically, the minimum noise energy added by a phase-preserving amplifier to the signal it processes amounts at least to half a photon at the signal frequency. Here we propose a practical microwave device that can fulfil the minimal requirements to reach the quantum limit. The availability of such a device is of importance for the readout of solid-state qubits, and more generally for the measurement of very weak signals in various areas of science. We discuss how this device can be the basic building block for a variety of practical applications, such as amplification, noiseless frequency conversion, dynamic cooling and production of entangled signal pairs.

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Figure 1: Electrical modes and energy states of the Josephson ring modulator.
Figure 2: Description of the Josephson parametric converter.
Figure 3: Gain of the JPC.
Figure 4: Main constraint on the gain × bandwidth product of the JPC.

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References

  1. Shimoda, K., Takahasi, H. & Townes, C. H. Fluctuations in amplification of quanta with application to Maser amplifiers. J. Phys. Soc. Jpn 12, 686–700 (1957).

    Article  ADS  Google Scholar 

  2. Haus, H. A. & Mullen, J. A. Quantum noise in linear amplifiers. Phys. Rev. 128, 2407–2413 (1962).

    Article  ADS  Google Scholar 

  3. Caves, C. M. Quantum limits on noise in linear amplifiers. Phys. Rev. D 26, 1817–1839 (1982).

    Article  ADS  Google Scholar 

  4. Tien, P. K. Parametric amplification and frequency mixing in propagating circuits. J. Appl. Phys. 29, 1347–1357 (1958).

    Article  ADS  Google Scholar 

  5. Louisell, W. H. Coupled Mode and Parametric Electronics (John Wiley, 1960).

    Google Scholar 

  6. Louisell, W. H., Yariv, A. & Siegman, A. E. Quantum fluctuations and noise in parametric processes. I. Phys. Rev. 124, 1646–1654 (1961).

    Article  ADS  Google Scholar 

  7. Gordon, J. P., Louisell, W. H. & Walker, L. R. Quantum fluctuations and noise in parametric processes. II. Phys. Rev. 129, 481–485 (1963).

    Article  ADS  Google Scholar 

  8. André, M.-O., Mück, M., Clarke, J., Gail, J. & Heiden, C. Radio-frequency amplifier with tenth-kelvin noise temperature based on a microstrip direct current. Appl. Phys. Lett. 75, 698–700 (1999).

    Article  ADS  Google Scholar 

  9. Spietz, L., Irwin, K. & Aumentado, J. Input impedance and gain of a gigahertz amplifier using a dc superconducting quantum interference device in a quarter wave resonator. Appl. Phys. Lett. 93, 082506 (2008).

    Article  ADS  Google Scholar 

  10. Yurke, B. et al. Observation of parametric amplification and deamplification in a Josephson parametric amplifier. Phys. Rev. A 39, 2519–2533 (1989).

    Article  ADS  Google Scholar 

  11. Yurke, B. Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier. Phys. Rev. Lett. 60, 764–767 (1988).

    Article  ADS  Google Scholar 

  12. Movshovich, R. et al. Observation of zero-point noise squeezing via a Josephson-parametric amplifier. Phys. Rev. Lett. 65, 1419–1422 (1990).

    Article  ADS  Google Scholar 

  13. 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  Google Scholar 

  14. Lupaşcu, A. et al. Quantum non-demolition measurement of a superconducting two-level system. Nature Phys. 3, 119–125 (2007).

    Article  ADS  Google Scholar 

  15. Mika, A., 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 

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

    Article  ADS  Google Scholar 

  17. Castellanos-Beltran, M. A. & Lehnert, K. W. Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator. Appl. Phys. Lett. 91, 083509 (2007).

    Article  ADS  Google Scholar 

  18. Castellanos-Beltrana, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 928–931 (2008).

    ADS  Google Scholar 

  19. Tholeń, E. A. Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators. Appl. Phys. Lett. 90, 253509 (2007).

    Article  ADS  Google Scholar 

  20. Yamamoto, T. et al. Flux-driven Josephson parametric amplifier. Appl. Phys. Lett. 93, 042510 (2008).

    Article  ADS  Google Scholar 

  21. Zhang, Q., Ruskov, R. & Korotkov, A. N. Continuous quantum feedback of coherent oscillations in a solid-state qubit. Phys. Rev. B 72, 245322 (2005).

    Article  ADS  Google Scholar 

  22. Korotkov, A. N. Simple quantum feedback of a solid-state qubit. Phys. Rev. B 71, 201305 (2005).

    Article  ADS  Google Scholar 

  23. Pozar, D. M. Microwave Engineering 629 (Wiley, 2005).

    Google Scholar 

  24. Devoret, M. H. Quantum Fluctuations: Les Houches Session LXIII (Elsevier, 1997).

    Google Scholar 

  25. Yurke, B. & Denker, J. S. Quantum network theory. Phys. Rev. A 29, 1419–1437 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  26. Caldeira, A. O. & Legget, A. J. Quantum tunneling in a dissipative system. Ann. Phys. 149, 374–456 (1983).

    Article  ADS  Google Scholar 

  27. Mears, C. A Quantum-limited heterodyne detection of millimetre waves using superconducting tantalum tunnel junctions. Appl. Phys. Lett. 57, 2487–2489 (1990).

    Article  ADS  Google Scholar 

  28. Wahlstein, S., Rudner, S. & Claeson, T. Arrays of Josephson tunnel junctions as parametric amplifiers. J. Appl. Phys. 49, 4248–4263 (1979).

    Article  ADS  Google Scholar 

  29. Mygind, N., Perdersen, F., Soerensen, O. H., Dueholm, B. & Levinsen, M. T. Low-noise parametric amplification at 35 GHz in a single Josephson tunnel junction. Appl. Phys. Lett. 35, 91–93 (1979).

    Article  ADS  Google Scholar 

  30. Bryant, P., Wiesenfeld, K. & McNamara, B. Noise rise in parametric amplifiers. Phys. Rev. B 36, 752–755 (1987).

    Article  ADS  Google Scholar 

  31. Bjork, G. & Yamamoto, Y. Generation of nonclassical photon states using correlated photon pairs and linear feedforward. Phys. Rev. A 37, 4229–4239 (1984).

    Article  ADS  Google Scholar 

  32. Grosshans, F. & Grangier, P. Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002).

    Article  ADS  Google Scholar 

  33. Siddiqi, I. et al. RF-driven Josephson bifurcation amplifier for quantum measurement. Phys. Rev. Lett. 93, 207002 (2004).

    Article  ADS  Google Scholar 

  34. Metcalfe, M. et al. Measuring the decoherence of a quantronium qubit with the cavity bifurcation amplifier. Phys. Rev. B 76, 174516 (2007).

    Article  ADS  Google Scholar 

  35. Guillemin, V. & Sternberg, S. Symplectic Techniques in Physics (Cambridge Univ. Press, 1984).

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by NSA through ARO grant number W911NF-05-01-0365, the Keck foundation and the NSF through grant number DMR-032-5580. M.H.D. acknowledges partial support from College de France. We are indebted to B. Abdo for help with the proof corrections.

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Authors and Affiliations

  1. Department of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520-8284, USA

    N. Bergeal, R. Vijay, V. E. Manucharyan, R. J. Schoelkopf, S. M. Girvin & M. H. Devoret

  2. Department of Physics, University of California, Berkeley, California 94720-7300, USA

    R. Vijay & I. Siddiqi

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  1. N. Bergeal
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  2. R. Vijay
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  3. V. E. Manucharyan
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  6. S. M. Girvin
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  7. M. H. Devoret
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Contributions

M.H.D. proposed the original idea of the ring modulator. N.B. and M.H.D. developed the device, carried out the theoretical analysis and wrote the article. R.V., V.E.M. and I.S. contributed extensively to discussions of the results. S.M.G. introduced all authors to the multifunctional aspect of three-wave mixing. R.J.S. contributed by his knowledge of ultralow-noise microwave circuits and measurements.

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Correspondence to N. Bergeal or M. H. Devoret.

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The authors declare no competing financial interests.

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Bergeal, N., Vijay, R., Manucharyan, V. et al. Analog information processing at the quantum limit with a Josephson ring modulator. Nature Phys 6, 296–302 (2010). https://doi.org/10.1038/nphys1516

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