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The Damping of a Quartz Tuning Fork in Superfluid 3He-B at Low Temperatures

  • D. I. Bradley
  • P. Crookston
  • S. N. Fisher
  • A. Ganshin
  • A. M. Guénault
  • R. P. Haley
  • M. J. Jackson
  • G. R. Pickett
  • R. Schanen
  • V. Tsepelin
Article

Abstract

We have measured the damping on a quartz tuning fork in the B-phase of superfluid 3He at low temperatures, below 0.3T c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid 3He-B and in superfluid 4He at low temperatures. In superfluid 4He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid 3He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid 3He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid 4He.

Keywords

Superfluid 3He-B Andreev reflection Vibrating structures Critical velocity 

PACS

67.40.Vs 67.57.De 67.57.-z 47.37.+q 43.58.Hp 

References

  1. 1.
    P. Günther, U.Ch. Fischer, K. Dransfeld, Appl. Phys. B 48, 89 (1989) CrossRefADSGoogle Scholar
  2. 2.
    K. Karrai, R.D. Grober, Appl. Phys. Lett. 66, 1842 (1995) CrossRefADSGoogle Scholar
  3. 3.
    F.J. Giessibl, Appl. Phys. Lett. 73, 3956 (1998) CrossRefADSGoogle Scholar
  4. 4.
    D.O. Clubb, O.V.L. Buu, R.M. Bowley, R. Nyman, J.R. Owers-Bradley, J. Low Temp. Phys. 136(1–2), 1 (2004) CrossRefADSGoogle Scholar
  5. 5.
    R. Blaauwgeers, M. Blaz̆ková, M. C̆lovec̆ko, V.B. Eltsov, R. de Graaf, J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R.E. Solntsev, D.E. Zmeev, J. Low Temp. Phys. 146(5–6), 537 (2007) CrossRefADSGoogle Scholar
  6. 6.
    M. Blaz̆ková, M. C̆lovec̆ko, E. Gažo, L. Skrbek, P. Skyba, J. Low Temp. Phys. 148(3–4), 305 (2007) CrossRefADSGoogle Scholar
  7. 7.
    M. Blaz̆ková, D. Schmoranzer, L. Skrbek, Phys. Rev. E 75, 025302 (2007) CrossRefADSGoogle Scholar
  8. 8.
    M. Blaz̆ková, M. C̆lovec̆ko, V.B. Eltsov, E. Gaz̆o, R. de Graaf, J.J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R.E. Solntsev, W.F. Vinen, J. Low Temp. Phys. 150(3–4), 525 (2008) CrossRefADSGoogle Scholar
  9. 9.
    G.A. Sheshin, A.A. Zadorozhko, E.Y. Rudavskii, V.K. Chagovets, L. Skrbek, M. Blaz̆ková, Low Temp. Phys. 34, 875 (2008) CrossRefADSGoogle Scholar
  10. 10.
    M. Blaz̆ková, D. Schmoranzer, L. Skrbek, W.F. Vinen, Phys. Rev. B 79, 054522 (2009) CrossRefADSGoogle Scholar
  11. 11.
    D.I. Bradley, M.J. Fear, S.N. Fisher, A.M. Guénault, R.P. Haley, C.R. Lawson, P.V.E. McClintock, G.R. Pickett, R. Schanen, V. Tsepelin, L.A. Wheatland, J. Low Temp. Phys. 156(3–6), 116 (2009) CrossRefGoogle Scholar
  12. 12.
    M. Blaz̆ková, T.V. Chagovets, M. Rotter, D. Schmoranzer, L. Skrbek, J. Low Temp. Phys. 150(3–4), 194 (2008) CrossRefADSGoogle Scholar
  13. 13.
    M. Blaz̆ková, D. Schmoranzer, L. Skrbek, Low Temp. Phys. 34, 298 (2008) CrossRefADSGoogle Scholar
  14. 14.
    E.M. Pentti, J.T. Tuoriniemi, A.J. Salmela, A.P. Sebedash, J. Low Temp. Phys. 150(3–4), 555 (2008) CrossRefADSGoogle Scholar
  15. 15.
    D.I. Bradley, M. C̆lovec̆ko, E. Gažo, P. Skyba, J. Low Temp. Phys. 152(5–6), 147 (2008) CrossRefADSGoogle Scholar
  16. 16.
    M. Blažková, D. Schmoranzer, L. Skrbek, Phys. Rev. E 75, 025302 (2007) CrossRefADSGoogle Scholar
  17. 17.
    A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975) CrossRefADSGoogle Scholar
  18. 18.
    J.C. Wheatley, Rev. Mod. Phys. 47, 415 (1975) CrossRefADSGoogle Scholar
  19. 19.
    D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3, vol. 3 (Taylor & Francis, London, 1990) Google Scholar
  20. 20.
    E.R. Dobbs, Helium Three. International Series of Monographs on Physics, vol. 108 (Oxford University Press, Oxford, 2000) Google Scholar
  21. 21.
    S.N. Fisher, A.M. Guénault, C.J. Kennedy, G.R. Pickett, Phys. Rev. Lett. 63, 2566 (1989) CrossRefADSGoogle Scholar
  22. 22.
    C. Bäuerle, Y.M. Bunkov, S.N. Fisher, H. Godfrin, Phys. Rev. B 57, 14381 (1998) CrossRefADSGoogle Scholar
  23. 23.
    S.N. Fisher, A.M. Guénault, C.J. Kennedy, G.R. Pickett, Phys. Rev. Lett. 67, 1270 (1991) CrossRefADSGoogle Scholar
  24. 24.
    S.N. Fisher, A.M. Guénault, C.J. Kennedy, G.R. Pickett, Phys. Rev. Lett. 69, 1073 (1992) CrossRefADSGoogle Scholar
  25. 25.
    S.N. Fisher, A.M. Guénault, A.J. Hale, G.R. Pickett, J. Low Temp. Phys. 121(5–6), 393 (2000) CrossRefGoogle Scholar
  26. 26.
    S.N. Fisher, A.J. Hale, A.M. Guénault, G.R. Pickett, Phys. Rev. Lett. 86, 244 (2001) CrossRefADSGoogle Scholar
  27. 27.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, C.J. Matthews, G.R. Pickett, J. Low Temp. Phys. 134(1–2), 381 (2004) CrossRefADSGoogle Scholar
  28. 28.
    A.F. Andreev, Sov. Phys. JETP 19, 1228 (1964) Google Scholar
  29. 29.
    M.P. Enrico, S.N. Fisher, A.M. Guénault, G.R. Pickett, K. Torizuka, Phys. Rev. Lett. 70, 1846 (1993) CrossRefADSGoogle Scholar
  30. 30.
    C.F. Barenghi, Y.A. Sergeev, N. Suramlishvili, Phys. Rev. B 77, 104512 (2008) CrossRefADSGoogle Scholar
  31. 31.
    C.F́. Barenghi, Y.A. Sergeev, N. Suramlishvili, P.J. van Dijk, Phys. Rev. B 79, 024508 (2009) CrossRefADSGoogle Scholar
  32. 32.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, M.R. Lowe, G.R. Pickett, A. Rahm, R.C.V. Whitehead, Phys. Rev. Lett. 93, 235302 (2004) CrossRefADSGoogle Scholar
  33. 33.
    R.J. Watts-Tobin, S.N. Fisher, Physica B 165, 683 (1990) CrossRefADSGoogle Scholar
  34. 34.
    S.N. Fisher, G.R. Pickett, R.J. Watts-Tobin, J. Low Temp. Phys. 83(3–4), 225 (1991) CrossRefADSGoogle Scholar
  35. 35.
    M.P. Enrico, S.N. Fisher, R.J. Watts-Tobin, J. Low Temp. Phys. 98(1–2), 81 (1995) CrossRefADSGoogle Scholar
  36. 36.
    G.R. Pickett, S.N. Fisher, Physica B 329–333, 75 (2003) CrossRefGoogle Scholar
  37. 37.
    A.M. Guénault, V. Keith, C.J. Kennedy, S.G. Mussett, G.R. Pickett, J. Low Temp. Phys. 62(5–6), 511 (1986) CrossRefADSGoogle Scholar
  38. 38.
    P. Skyba, S.M. Holt, Private communication, in preparation Google Scholar
  39. 39.
    J.R. Morison, M.P. O’Brien, J.W. Johnson, S.A. Schaaf, Trans. Am. Inst. Min. Met. Eng. 189, 149 (1950) Google Scholar
  40. 40.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, V. Tsepelin, G.R. Pickett, K.L. Zaki, J. Low Temp. Phys. 154(3–4), 97 (2009) CrossRefADSGoogle Scholar
  41. 41.
    H. Yano, N. Hashimoto, A. Handa, M. Nakagawa, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 75, 012502 (2007) CrossRefADSGoogle Scholar
  42. 42.
    H. Yano, T. Ogawa, A. Mori, Y. Miura, Y. Nago, K. Obara, O. Ishikawa, T. Hata, J. Low Temp. Phys. 156(3–6), 132 (2009) CrossRefGoogle Scholar
  43. 43.
    D.J. Cousins, S.N. Fisher, A.M. Guénault, R.P. Haley, I.E. Miller, G.R. Pickett, G.N. Plenderleith, P. Skyba, P.Y.A. Thibault, M.G. Ward, J. Low Temp. Phys. 114(5–6), 547 (1999) CrossRefGoogle Scholar
  44. 44.
    C.J. Lambert, Physica B (Amsterdam) 165/166, 653 (1990) ADSGoogle Scholar
  45. 45.
    C.J. Lambert, Physica B 178, 294 (1992) CrossRefADSGoogle Scholar
  46. 46.
    W. Zhang, J. Kurkijärvi, E.V. Thuneberg, Phys. Lett. A 109, 238 (1985) CrossRefADSGoogle Scholar
  47. 47.
    W. Zhang, J. Kurkijärvi, E.V. Thuneberg, Phys. Rev. B 36, 1987 (1987) CrossRefADSGoogle Scholar
  48. 48.
    D.S. Greywall, Phys. Rev. B 33, 7520 (1986) CrossRefADSGoogle Scholar
  49. 49.
    N. Masuhara, B.C. Watson, M.W. Meisel, Phys. Rev. Lett. 85, 2537 (2000) CrossRefADSGoogle Scholar
  50. 50.
    D.I. Bradley, Phys. Rev. Lett. 84, 1252 (2000) CrossRefADSGoogle Scholar
  51. 51.
    Y. Nago, M. Inui, R. Kado, K. Obara, H. Yano, O. Ishikawa, T. Hata, J. Phys. Conf. Ser. 150, 032071 (2009) CrossRefADSGoogle Scholar
  52. 52.
    M. Niemetz, W. Schoepe, M. Krusius, Phys. Rev. Lett. 87, 059601 (2001) CrossRefADSGoogle Scholar
  53. 53.
    D.I. Bradley, G.R. Pickett, Phys. Rev. Lett. 87, 059602 (2001) CrossRefADSGoogle Scholar
  54. 54.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, M.R. Lowe, G.R. Pickett, A. Rahm, Physica B 329, 104 (2003) CrossRefADSGoogle Scholar
  55. 55.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K. Zaki, Phys. Rev. Lett. 95, 035302 (2005) CrossRefADSGoogle Scholar
  56. 56.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K. Zaki, in Low Temperature Physics, Parts A, B. AIP Conference Proceedings, vol. 850 (Amer. Inst. Phys., Melville, 2006), p. 173 Google Scholar
  57. 57.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, J. Roberts, S. O’Sullivan, V. Tsepelin, J. Low Temp. Phys. 148(3–4), 235 (2007) CrossRefADSGoogle Scholar
  58. 58.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K. Zaki, in Low Temperature Physics, Parts A, B. AIP Conference Proceedings, vol. 850 (Amer. Inst. Phys., Melville, 2006), p. 175 Google Scholar
  59. 59.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, K. Zaki, Phys. Rev. Lett. 96, 035301 (2006) CrossRefADSGoogle Scholar
  60. 60.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, M. Holmes, S. O’Sullivan, G.R. Pickett, V. Tsepelin, J. Low Temp. Phys. 150(3–4), 364 (2008) CrossRefADSGoogle Scholar
  61. 61.
    D.I. Bradley, S.N. Fisher, A.M. Guénault, R.P. Haley, S. O’Sullivan, G.R. Pickett, V. Tsepelin, Phys. Rev. Lett. 101, 065302 (2008) CrossRefADSGoogle Scholar
  62. 62.
    D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, K.L. Zaki, J. Low Temp. Phys. 138(3–4), 493 (2005) CrossRefADSGoogle Scholar
  63. 63.
    D. Charalambous, L. Skrbek, P.C. Hendry, P.V.E. McClintock, W.F. Vinen, Phys. Rev. E 74, 036307 (2006) CrossRefADSGoogle Scholar
  64. 64.
    H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. Lett. 92, 244501 (2004) CrossRefADSGoogle Scholar
  65. 65.
    H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E. McClintock, Phys. Rev. E 70, 056307 (2004) CrossRefADSGoogle Scholar
  66. 66.
    J. Jäger, B. Schuderer, W. Schoepe, Phys. Rev. Lett. 74, 566 (1995) CrossRefADSGoogle Scholar
  67. 67.
    R. Hänninen, M. Tsubota, W.F. Vinen, Phys. Rev. B 75, 064502 (2007) CrossRefADSGoogle Scholar
  68. 68.
    R. Hänninen, W. Schoepe, J. Low Temp. Phys. 153(5–6), 189 (2008) CrossRefADSGoogle Scholar
  69. 69.
    W.I. Glaberson, R.J. Donnelly, Phys. Rev. 141, 208 (1966) CrossRefADSGoogle Scholar
  70. 70.
    H. Yano, A. Handa, H. Nakagawa, K. Obara, O. Ishikawa, T. Hata, M. Nakagawa, J. Low Temp. Phys. 138(3–4), 561 (2005) CrossRefADSGoogle Scholar
  71. 71.
    N. Hashimoto, R. Goto, H. Yano, K. Obara, O. Ishikawa, T. Hata, Phys. Rev. B 76, 020504 (2007) CrossRefADSGoogle Scholar
  72. 72.
    R. Goto, S. Fujiyama, H. Yano, Y. Nago, N. Hashimoto, K. Obara, O. Ishikawa, M. Tsubota, T. Hata, Phys. Rev. Lett. 100, 045301 (2008) CrossRefADSGoogle Scholar
  73. 73.
    R. Hänninen, A. Mitani, M. Tsubota, in AIP Conference Proceedings, vol. 850 (Amer. Inst. Phys., Melville, 2006), p. 217 CrossRefGoogle Scholar
  74. 74.
    S. Fujiyama, M. Tsubota, Phys. Rev. B 79, 094513 (2009) CrossRefADSGoogle Scholar
  75. 75.
    V.M.H. Ruutu, Ü. Parts, J.H. Koivuniemi, N.B. Kopnin, M. Krusius, J. Low Temp. Phys. 107(1–2), 93 (1997) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • D. I. Bradley
    • 1
  • P. Crookston
    • 1
  • S. N. Fisher
    • 1
  • A. Ganshin
    • 1
  • A. M. Guénault
    • 1
  • R. P. Haley
    • 1
  • M. J. Jackson
    • 1
  • G. R. Pickett
    • 1
  • R. Schanen
    • 1
  • V. Tsepelin
    • 1
  1. 1.Physics DepartmentLancaster UniversityLancasterUK

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