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  • Access by Xinjiang University

Ultralow-Dissipation Superfluid Micromechanical Resonator

F. Souris, X. Rojas*, P. H. Kim, and J. P. Davis

  • Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada

  • *Present address: Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
  • jdavis@ualberta.ca

Phys. Rev. Applied 7, 044008 – Published 17 April, 2017

DOI: https://doi.org/10.1103/PhysRevApplied.7.044008

Abstract

Micro- and nanomechanical resonators with ultralow dissipation have great potential as useful quantum resources. The superfluid micromechanical resonators presented here possess several advantageous characteristics: straightforward thermalization, dissipationless flow, and in situ tunability. We identify and quantitatively model the various dissipation mechanisms in two resonators, one fabricated from borosilicate glass and one from single-crystal quartz. As the resonators are cryogenically cooled into the superfluid state, the damping from thermal effects and from the normal-fluid component are strongly suppressed. At our lowest temperatures, damping is limited solely by internal dissipation in the substrate materials, and the resonators reach quality factors of up to 913 000 at 13 mK. By lifting this limitation through substrate-material choice and resonator design, modeling suggests that the resonators could reach quality factors as high as 108 at 100 mK, putting this architecture in an ideal position to harness mechanical quantum effects and to facilitate the study of superfluids in confined geometries.

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References (60)

  1. H. Miao, K. Srinivasan, and V. Aksyuk, A microelectromechanically controlled cavity optomechanical sensing system, New J. Phys. 14, 075015 (2012).
  2. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, A nanomechanical mass sensor with yoctogram resolution, Nat. Nanotechnol. 7, 301 (2012).
  3. P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, Nanoscale torsional optomechanics, Appl. Phys. Lett. 102, 053102 (2013).
  4. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, Quantum ground state and single-phonon control of a mechanical resonator, Nature (London) 464, 697 (2010).
  5. T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, Entangling mechanical motion with microwave fields, Science 342, 710 (2013).
  6. F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Mechanically Mediated Microwave Frequency Conversion in the Quantum Regime, Phys. Rev. Lett. 116, 043601 (2016).
  7. S. M. Meenehan, J. D. Cohen, S. Groblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Silicon optomechanical crystal resonator at millikelvin temperatures, Phys. Rev. A 90, 011803 (2014).
  8. K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, Low-loss superconducting resonant circuits using vacuum-gap-based microwave components, Appl. Phys. Lett. 96, 093502 (2010).
  9. P. H. Kim, B. D. Hauer, C. Doolin, F. Souris, and J. P. Davis, Approaching the standard quantum limit of mechanical torque sensing, Nat. Commun. 7, 13165 (2016).
  10. S. S. Verbridge, H. G. Craighead, and J. M. Parpia, A megahertz nanomechanical resonator with room temperature quality factor over a million, Appl. Phys. Lett. 92, 013112 (2008).
  11. M. Mitchell, B. Khanaliloo, D. P. Lake, T. Masuda, J. P. Hadden, and P. E. Barclay, Single-crystal diamond low-dissipation cavity optomechanics, Optica 3, 963 (2016).
  12. M. J. Burek, J. D. Cohen, S. M. Meenehan, N. El-Sawah, C. Chia, T. Ruelle, S. Meesala, J. Rochman, H. A. Atikian, M. Markham, D. J. Twitchen, M. D. Lukin, O. Painter, and M. Lončar, Diamond optomechanical crystals, Optica 3, 1404 (2016).
  13. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  14. L. A. De Lorenzo and K. C. Schwab, Superfluid optomechanics: Coupling of a superfluid to a superconducting condensate, New J. Phys. 16, 113020 (2014).
  15. X. Rojas and J. P. Davis, A superfluid nanomechanical resonator for quantum nanofluidics, Phys. Rev. B 91, 024503 (2015).
  16. G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, Laser cooling and control of excitations in superfluid helium, Nat. Phys. 12, 788 (2016).
  17. A. D. Kashkanova, A. B. Shkarin, C. D. Brown, N. E. Flowers-Jacobs, L. Childress, S. W. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. G. E. Harris, Superfluid Brillouin optomechanics, Nat. Phys. 13, 74 (2017).
  18. L. A. De Lorenzo and K. C. Schwab, Ultra-high Q acoustic resonance in superfluid He4, J. Low Temp. Phys. 186, 233 (2017).
  19. S. Singh, L. A. De Lorenzo, I. Pikovski, and K. C. Schwab, Detecting continuous gravitational waves with superfluid He4, arXiv:1606.04980.
  20. F. M. Gasparini, M. O. Kimball, K. P. Mooney, and M. Diaz-Avila, Finite-size scaling of He4 at the superfluid transition, Rev. Mod. Phys. 80, 1009 (2008).
  21. J. K. Perron and F. M. Gasparini, Critical Point Coupling and Proximity Effects in He4 at the Superfluid Transition, Phys. Rev. Lett. 109, 035302 (2012).
  22. A. B. Vorontsov and J. A. Sauls, Crystalline Order in Superfluid He3 Films, Phys. Rev. Lett. 98, 045301 (2007).
  23. J. J. Wiman and J. A. Sauls, Superfluid phases of He3 in nanoscale channels, Phys. Rev. B 92, 144515 (2015).
  24. S. B. Chung and S.-C. Zhang, Detecting the Majorana Fermion Surface State of He3B through Spin Relaxation, Phys. Rev. Lett. 103, 235301 (2009).
  25. T. Mizushima, Superfluid He3 in a restricted geometry with a perpendicular magnetic field, Phys. Rev. B 86, 094518 (2012).
  26. H. Wu and J. A. Sauls, Majorana excitations, spin and mass currents on the surface of topological superfluid He3B, Phys. Rev. B 88, 184506 (2013).
  27. L. V. Levitin, R. G. Bennett, A. Casey, B. Cowan, J. Saunders, D. Drung, Th. Schurig, and J. M. Parpia, Phase diagram of the topological superfluid He3 confined in a nanoscale slab geometry, Science 340, 841 (2013).
  28. J. Taniguchi, Y. Aoki, and M. Suzuki, Superfluidity of liquid He4 confined to one-dimensional straight nanochannel structures, Phys. Rev. B 82, 104509 (2010).
  29. J. Taniguchi, K. Demura, and M. Suzuki, Dynamical superfluid response of He4 confined in a nanometer-size channel, Phys. Rev. B 88, 014502 (2013).
  30. A. Duh, A. Suhel, B. D. Hauer, R. Saeedi, P. H. Kim, T. S. Biswas, and J. P. Davis, Microfluidic and nanofluidic cavities for quantum fluids experiments, J. Low Temp. Phys. 168, 31 (2012).
  31. X. Rojas, B. D. Hauer, A. J. R. MacDonald, P. Saberi, Y. Yang, and J. P. Davis, Ultrasonic interferometer for first-sound measurements of confined liquid He4, Phys. Rev. B 89, 174508 (2014).
  32. S. Backhaus and E.Yu. Backhaus, Thermoviscous effects in steady and oscillating flow of an isotropic superfluid: Theory, J. Low Temp. Phys. 109, 511 (1997).
  33. J. S. Brooks, B. B. Sabo, P. C. Schubert, and W. Zimmermann, Jr., Helmholtz-resonator measurements of the superfluid density of liquid He4 in submicrometer-diameter channels, Phys. Rev. B 19, 4524 (1979).
  34. S. W. Van Sciver, Helium Cryogenics, 2nd ed. (Springer, New York, 2012), p. 193.
  35. J. W. Gardner and A. C. Anderson, Low-temperature specific heat and thermal conductivity of neutron-irradiated crystalline quartz, Phys. Rev. B 23, 474 (1981).
  36. J. Classen, C. Enss, C. Bechinger, G. Weiss, and S. Hunklinger, Low frequency acoustic and dielectric measurements on glasses, Ann. Phys. (Berlin) 506, 315 (1994).
  37. K. A. Topp and D. G. Cahill, Elastic properties of several amorphous solids and disordered crystals below 100 K, Z. Phys. B 101, 235 (1996).
  38. A. D. Fefferman, R. O. Pohl, A. T. Zehnder, and J. M. Parpia, Acoustic Properties of Amorphous Silica between 1 and 500 mK, Phys. Rev. Lett. 100, 195501 (2008).
  39. S. Galliou, J. Imbaud, M. Goryachev, R. Bourquin, and P. Abbé, Losses in high quality quartz crystal resonators at cryogenic temperatures, Appl. Phys. Lett. 98, 091911 (2011).
  40. S. Galliou, M. Goryachev, R. Bourquin, P. Abbé, J.-P. Aubry, and M. E. Tobar, Extremely low loss phonon-trapping cryogenic acoustic cavities for future physical experiments, Sci. Rep. 3, 2132 (2013).
  41. J. Classen, T. Burkert, C. Enss, and S. Hunklinger, Anomalous Frequency Dependence of the Internal Friction of Vitreous Silica, Phys. Rev. Lett. 84, 2176 (2000).
  42. D. Schmoranzer, M. La Mantia, G. Sheshin, I. Gritsenko, A. Zadorozhko, M. Rotterand, and L. Skrbek, Acoustic emission by quartz tuning forks and other oscillating structures in cryogenic He4 fluids, J. Low Temp. Phys. 163, 317 (2011).
  43. Y. Tao, J. M. Boss, B. Moores, and C. L. Degen, Single-crystal diamond nanomechanical resonators with quality factors exceeding one million, Nat. Commun. 5, 3638 (2014).
  44. M. Yuan, V. Singh, Y. M. Blanter, and G. A. Steele, Large cooperativity and microkelvin cooling with a three-dimensional optomechanical cavity, Nat. Commun. 6, 8491 (2015).
  45. R. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, 7th ed. (McGraw-Hill, New York, 1992), p. 488.
  46. A. K. Raychaudhuri and S. Hunklinger, Low frequency elastic properties of glasses at low temperatures—Implications on the tunneling model, Z. Phys. B 57, 113 (1984).
  47. S. Backhaus, K. Schwab, A. Loshak, S. Pereverzev, N. Bruckner, J. C. Davis, and R. E. Packard, Thermoviscous effects in steady and oscillating flow of superfluid He4: Experiments, J. Low Temp. Phys. 109, 527 (1997).
  48. J. S. Brooks and R. J. Donnelly, The calculated thermodynamic properties of superfluid helium-4, J. Phys. Chem. Ref. Data 6, 51 (1977).
  49. O. Avenel and E. Varoquaux, Observation of Singly Quantized Dissipation Events Obeying the Josephson Frequency Relation in the Critical Flow of Superfluid He4 through an Aperture, Phys. Rev. Lett. 55, 2704 (1985).
  50. B. P. Beecken and W. Zimmermann, Search for an ac Josephson effect in superfluid He4 using a low-frequency acoustic resonator, Phys. Rev. B 35, 74 (1987).
  51. R. Donnelly and C. Barenghi, The observed properties of liquid helium at the saturated vapor pressure, J. Phys. Chem. Ref. Data 27, 1217 (1998).
  52. D. S. Greywall, Thermal-conductivity measurements in liquid He4 below 0.7 K, Phys. Rev. B 23, 2152 (1981).
  53. G. L. Pollack, Kapitza resistance, Rev. Mod. Phys. 41, 48 (1969).
  54. F. Pobell, Matter and Methods at Low Temperatures, 3rd ed. (Springer, New York, 2007), p. 71.
  55. M. Sciacca and L. Galantucci, Effective thermal conductivity of superfluid helium: Laminar, turbulent and ballistic regimes, Commun. Appl. Ind. Math. 7, 111 (2016).
  56. M. Greenspan, Piston radiator: Some extensions of the theory, J. Acoust. Soc. Am. 65, 608 (1979).
  57. P. M. Morse, Vibration and Sound, 2nd ed. (McGraw-Hill, New York, 1948), p. 326.
  58. X. Rojas, A. Haziot, V. Bapst, S. Balibar, and H. J. Maris, Anomalous Softening of He4 Crystals, Phys. Rev. Lett. 105, 145302 (2010).
  59. F. Souris, A. D. Fefferman, A. Haziot, N. Garroum, J. R. Beamish, and S. Balibar, Search for dislocation free helium 4 crystals, J. Low Temp. Phys. 178, 149 (2015).
  60. R. N. Kleiman, G. Agnolet, and D. J. Bishop, Two-Level Systems Observed in the Mechanical Properties of Single-Crystal Silicon at Low Temperatures, Phys. Rev. Lett. 59, 2079 (1987).

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