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dc SQUID: Noise and optimization

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Abstract

A computer model is described for the dc SQUID in which the two Josephson junctions are nonhysteretic, resistively shunted tunnel junctions. In the absence of noise, current-voltage(I–V) characteristics are obtained as functions of the applied flux, Φ a , SQUID inductanceL, junction critical currentI 0 , and shunt resistanceR. The effects of asymmetry inL, I 0 , andR are discussed.I–V characteristics, flux-voltage transfer functions, and low-frequency spectral densities of the voltage noise are obtained at experimentally interesting values of the parameters in the presence of Johnson noise in the resistive shunts. The transfer functions and voltage spectral densities are used to calculate the flux and energy resolution of the SQUID operated as an open-loop, small-signal amplifier. The resolution of the SQUID with ac flux modulation is discussed. The flux resolution calculated for the SQUID of Clarke, Goubau, and Ketchen is1.6 × 10 −5 Φ 0 Hz−1/2, approximately one-half the experimental value. Optimization of the SQUID resolution is discussed: It is shown that the optimum operating condition is β=2LI 0 /Φ 0 ≈1. Finally, some speculations are made on the ultimate performance of the tunnel junction dc SQUID. When the dominant noise source is Johnson noise in the resistive shunts, the energy resolution per Hz is4k B T(πLC)1/2, whereC is the junction capacitance, and the constraintR=(Φ 0 /2πCI 0 )1/2 has been imposed. This result implies that the energy resolution is proportional to (junction area)1/2. In the limiteI 0 R ≫k B T, the dominant noise source is shot noise in the junctions; for β=1, the energy resolution per Hz is then approximatelyh/2.

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References

  1. R. C. Jaklevic, J. Lambe, A. H. Silver, and J. E. Mercereau,Phys. Rev. Lett. 12, 159 (1964);Phys. Rev. Lett. 14, 887 (1965);Phys. Rev. 140, A1628 (1965).

    Google Scholar 

  2. J. Clarke, W. M. Goubau, and M. B. Ketchen,J. Low Temp. Phys. 25, 99 (1976).

    Google Scholar 

  3. M. Tinkham,Introduction to Superconductivity (McGraw-Hill, 1975), p. 214.

  4. J. E. Zimmerman and A. H. Silver,Phys. Rev. 141, 367 (1966).

    Google Scholar 

  5. E. O. Schulz-DuBois, IBM Research RZ 564 (April 13, 1973).

  6. A. Th. A. M. De Waele and R. De Bruyn Ouboter,Physica 41, 225 (1969).

    Google Scholar 

  7. A. Th. A. M. De Waele and R. De Bruyn Ouboter,Physica 42, 626 (1969).

    Google Scholar 

  8. T. A. Fulton,Solid State Commun. 8, 1353 (1970).

    Google Scholar 

  9. J. Clarke and J. L. Paterson,Appl. Phys. Lett. 19, 469 (1971).

    Google Scholar 

  10. W.-T. Tsang and T. Van Duzer,J. Appl. Phys. 46, 4573 (1975).

    Google Scholar 

  11. T. A. Fulton, L. N. Dunkleberger, and R. C. Dynes,Phys. Rev. B 6, 855 (1972).

    Google Scholar 

  12. W.-T. Tsang and T. Van Duzer,J. Appl. Phys. 47, 2656 (1976).

    Google Scholar 

  13. F. Auracher, Ph.D. thesis, University of California, Berkeley (1973).

    Google Scholar 

  14. V. Ambegaokar and B. I. Halperin,Phys. Rev. Lett. 22, 1364 (1969).

    Google Scholar 

  15. T. A. Fulton,IEEE Trans. Magn. MAG-11, 749 (1975).

    Google Scholar 

  16. A. N. Vystavkin, V. N. Gubankov, L. S. Kuzmin, K. K. Likharev, V. V. Migulin, and V. K. Semenov,Rev. Phys. Appl. 9, 79 (1974).

    Google Scholar 

  17. C. Tesche and J. Clarke,IEEE Trans. Magn. MAG-13, 859 (1977).

    Google Scholar 

  18. W. C. Stewart,Appl. Phys. Lett. 12, 277 (1968); D. E. McCumber,J. Appl. Phys. 39, 3113 (1968).

    Google Scholar 

  19. J. Clarke,Phil. Mag. 13, 115 (1966).

    Google Scholar 

  20. M. B. Ketchen, W. M. Goubau, J. Clarke, and G. B. Donaldson,IEEE Trans. Magn. MAG-13, 372 (1977).

    Google Scholar 

  21. L. Solymar,Superconductive Tunneling and Applications (Chapman and Hall, London, 1972), p. 202.

    Google Scholar 

  22. J. Clarke and J. L. Paterson, unpublished.

  23. L. G. Aslamazov, A. I. Larkin, and Yu.N. Orchinnikov,Zh. Eksp. Teor. Fig. 28, 171 (1969).

    Google Scholar 

  24. A. J. Dahm, A. Denenstein, D. N. Langenberg, W. H. Parker, D. Rogovin, and D. J. Scalapino,Phys. Rev. Lett. 22, 1416 (1969).

    Google Scholar 

  25. M. J. Stephen,Phys. Rev. Lett. 21, 1629 (1968).

    Google Scholar 

  26. G. A. Hawkins and J. Clarke,J. Appl. Phys. 47, 1616 (1976).

    Google Scholar 

  27. A. Van der Ziel,Noise (Prentice-Hall, New York, 1954), p. 320.

    Google Scholar 

  28. J. Kadlec and K. H. Gunlach, preprint.

  29. S. Basaviah and J. H. Greiner,J. Appl. Phys. 47, 4201 (1976).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of California, Berkeley, California

    Claudia D. Tesche & John Clarke

  2. Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, California

    Claudia D. Tesche & John Clarke

Authors
  1. Claudia D. Tesche
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  2. John Clarke
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Work supported by the U.S. ERDA.

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Tesche, C.D., Clarke, J. dc SQUID: Noise and optimization. J Low Temp Phys 29, 301–331 (1977). https://doi.org/10.1007/BF00655097

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  • DOI: https://doi.org/10.1007/BF00655097

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