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Fully Suspended Nano-beams for Quantum Fluids

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Abstract

Non-invasive probes are keystones of fundamental research. Their size and maneuverability (in terms of, for example, speed, dissipated power) define their applicability range for a specific use. As such, solid-state physics possesses, e.g. atomic force microscopy (AFM), scanning tunneling microscopy (STM), or scanning SQUID microscopy. In comparison, quantum fluids (superfluid \(^{3}\)He, \(^{4}\)He) are still lacking probes able to sense them (in a fully controllable manner) down to their smallest relevant lengthscales, namely the coherence length \(\xi _{0}\). In this work, we report on the fabrication and cryogenic characterisation of fully suspended (hanging over an open window, with no substrate underneath) \({\text {Si}}_{3} {\text {N}}_{4}\) nano-beams, of width down to 50 nm and quality factor up to \(10^{5}\). As a benchmark experiment we used them to investigate the Knudsen boundary layer of a rarefied gas: \(^{4}\)He at very low pressures. The absence of the rarefaction effect due to the nearby chip surface discussed in Gazizulin et al. (Phys Rev Lett 120:036802, 2018. https://doi.org/10.1103/PhysRevLett.120.036802) is attested, while we report on the effect of the probe size itself.

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References

  1. R.R. Gazizulin, O. Maillet, X. Zhou, A. Maldonado Cid, O. Bourgeois, E. Collin, Surface-induced near-field scaling in the Knudsen layer of a rarefied gas. Phys. Rev. Lett. 120, 036802 (2018). https://doi.org/10.1103/PhysRevLett.120.036802

    Article  ADS  Google Scholar 

  2. S.R. Stalp, L. Skrbek, R.J. Donnelly, Decay of grid turbulence in a finite channel. Phys. Rev. Lett. 82, 4831–4834 (1999). https://doi.org/10.1103/PhysRevLett.82.4831

    Article  ADS  Google Scholar 

  3. X.-L. Qi, T.L. Hughes, S. Raghu, S.-C. Zhang, Time-reversal-invariant topological superconductors and superfluids in two and three dimensions. Phys. Rev. Lett. 102, 187001 (2009). https://doi.org/10.1103/PhysRevLett.102.187001

    Article  ADS  Google Scholar 

  4. D.I. Bradley, Y.M. Bunkov, D.J. Cousins, M.P. Enrico, S.N. Fisher, M.R. Follows, A.M. Guénault, W.M. Hayes, G.R. Pickett, T. Sloan, Potential dark matter detector? The detection of low energy neutrons by superfluid \(^{3}\)He. Phys. Rev. Lett. 75, 1887–1890 (1995). https://doi.org/10.1103/PhysRevLett.75.1887

    Article  ADS  Google Scholar 

  5. G. Volovik, The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003). https://doi.org/10.1093/acprof:oso/9780199564842.001.0001

    Book  MATH  Google Scholar 

  6. M. Niemetz, R. Hänninen, W. Schoepe, On the transition from potential flow to turbulence around a microsphere oscillating in superfluid \(^{4}\)He. J. Low Temp. Phys. 187, 195–220 (2017). https://doi.org/10.1007/s10909-017-1745-7

    Article  ADS  Google Scholar 

  7. A.M. Guénault, V. Keith, C.J. Kennedy, S.G. Mussett, G.R. Pickett, The mechanical behavior of a vibrating wire in superfluid \(^{3}\)He-B in the ballistic limit. J. Low Temp. Phys. 62, 511–523 (1986). https://doi.org/10.1007/BF00683408

    Article  ADS  Google Scholar 

  8. D. Bradley, S. Fisher, A. Guénault, R.P. Haley, C.R. Lawson, G.R. Pickett, R. Schanen, M. Skyba, V. Tsepelin, D.E. Zmeev, Breaking the superfluid speed limit in a fermionic condensate. Nat. Phys. 12, 1017–1021 (2016). https://doi.org/10.1038/nphys3813

    Article  Google Scholar 

  9. D.O. Clubb, O.V.L. Buu, R.M. Bowley, R. Nyman, J.R. Owers-Bradley, Quartz tuning fork viscometers for helium liquids. J. Low Temp. Phys. 136, 1–13 (2004). https://doi.org/10.1023/B:JOLT.0000035368.63197.16

    Article  ADS  Google Scholar 

  10. D. Schmoranzer, M. La Mantia, G. Sheshin, I. Gritsenko, A. Zadorozhko, M. Rotter, L. Skrbek, Acoustic emission by quartz tuning forks and other oscillating structures in cryogenic \(^{4}\)He fluids. J. Low Temp. Phys. 163, 317–344 (2011). https://doi.org/10.1007/s10909-011-0353-1

    Article  ADS  Google Scholar 

  11. A. Guthrie, R.P. Haley, A. Jennings, S. Kafanov, O. Kolosov, M. Mucientes, M.T. Noble, Y.A. Pashkin, G.R. Pickett, V. Tsepelin, D.E. Zmeev, V. Efimov, Multimode probing of superfluid \(^4\)He by tuning forks. Appl. Phys. Lett. 115(11), 113103 (2019). https://doi.org/10.1063/1.5121023

    Article  ADS  Google Scholar 

  12. M. Defoort, S. Dufresnes, S.L. Ahlstrom, D.I. Bradley, R.P. Haley, A.M. Guénault, E.A. Guise, G.R. Pickett, M. Poole, A.J. Wood, V. Tsepelin, S.N. Fisher, H. Godfrin, E. Collin, Probing Bogoliubov quasiparticles in superfluid \(^{3}\)He with a ‘vibrating-wire like’ MEMS device. J. Low Temp. Phys. 183, 284–291 (2016). https://doi.org/10.1007/s10909-015-1392-9

    Article  ADS  Google Scholar 

  13. A. Guthrie, S. Kafanov, M.T. Noble, Y.A. Pashkin, G.R. Pickett, V. Tsepelin, A.A. Dorofeev, V.A. Krupenin, D.E. Presnov, Nanoscale real-time detection of quantum vortices at millikelvin temperatures. Nat. Commun. 12, 2645 (2021). https://doi.org/10.1038/s41467-021-22909-3

    Article  ADS  Google Scholar 

  14. A.M. Guénault, A. Guthrie, R.P. Haley, S. Kafanov, Y.A. Pashkin, G.R. Pickett, M. Poole, R. Schanen, V. Tsepelin, D.E. Zmeev, E. Collin, O. Maillet, R. Gazizulin, Probing superfluid \(^{4}\)He with high-frequency nanomechanical resonators down to millikelvin temperatures. Phys. Rev. B 100, 020506 (2019). https://doi.org/10.1103/PhysRevB.100.020506

    Article  ADS  Google Scholar 

  15. A.M. Guénault, A. Guthrie, R.P. Haley, S. Kafanov, Y.A. Pashkin, G.R. Pickett, V. Tsepelin, D.E. Zmeev, E. Collin, R. Gazizulin, O. Maillet, Detecting a phonon flux in superfluid \(^{4}\)He by a nanomechanical resonator. Phys. Rev. B 101, 060503 (2020). https://doi.org/10.1103/PhysRevB.101.060503

    Article  ADS  Google Scholar 

  16. D.I. Bradley, R. George, A.M. Guénault, R.P. Haley, S. Kafanov, M.T. Noble, Y.A. Pashkin, G.R. Pickett, M. Poole, J.R. Prance, M. Sarsby, R. Schanen, V. Tsepelin, T. Wilcox, D.E. Zmeev, Operating nanobeams in a quantum fluid. Sci. Rep. 7, 4876 (2017). https://doi.org/10.1038/s41598-017-04842-y

    Article  ADS  Google Scholar 

  17. C. Regal, J. Teufel, K. Lehnert, Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys. 4, 555–560 (2008). https://doi.org/10.1038/nphys974

    Article  Google Scholar 

  18. E. Sage, M. Sansa, S. Fostner, M. Defoort, M. Gély, A.K. Naik, R. Morel, L. Duraffourg, M.L. Roukes, T. Alava, G. Jourdan, E. Colinet, C. Masselon, A. Brenac, S. Hentz, Single-particle mass spectrometry with arrays of frequency-addressed nanomechanical resonators. Nat. Commun. 9, 3283 (2018). https://doi.org/10.1038/s41467-018-05783-4

    Article  ADS  Google Scholar 

  19. M. Defoort, K.J. Lulla, T. Crozes, O. Maillet, O. Bourgeois, E. Collin, Slippage and boundary layer probed in an almost ideal gas by a nanomechanical oscillator. Phys. Rev. Lett. 113, 136101 (2014). https://doi.org/10.1103/PhysRevLett.113.136101

    Article  ADS  Google Scholar 

  20. D. Vollhardt, P. Woelfle, The Superfluid Phases of Helium 3 (CRC Press, Boca Raton, 1990). https://doi.org/10.1201/b12808

    Book  Google Scholar 

  21. A.W. Baggaley, V. Tsepelin, C.F. Barenghi, S.N. Fisher, G.R. Pickett, Y.A. Sergeev, N. Suramlishvili, Visualizing pure quantum turbulence in superfluid \(^{3}\)He: Andreev reflection and its spectral properties. Phys. Rev. Lett. 115, 015302 (2015). https://doi.org/10.1103/PhysRevLett.115.015302

    Article  ADS  Google Scholar 

  22. A.N. Cleland, M.L. Roukes, External control of dissipation in a nanometer-scale radiofrequency mechanical resonator. Sens. Actuators A Phys. 72(3), 256–261 (1999). https://doi.org/10.1016/S0924-4247(98)00222-2

    Article  Google Scholar 

  23. R. Lifshitz, M.C. Cross, Nonlinear dynamics of nanomechanical and micromechanical resonators, in Reviews of Nonlinear Dynamics and Complexity. ed. by H.G. Schuster (Wiley, Weinheim, 2008), pp. 1–52. https://doi.org/10.1002/9783527626359.ch1

    Chapter  MATH  Google Scholar 

  24. M. Defoort, Dynamique non-linéaire dans les systèmes nano-électromécanique à basses températures. Theses, Université de Grenoble (2014). https://hal.archives-ouvertes.fr/tel-01332665

  25. D.R. Brumley, M. Willcox, J.E. Sader, Oscillation of cylinders of rectangular cross section immersed in fluid. Phys. Fluids 22, 052001 (2010). https://doi.org/10.1063/1.3397926

    Article  ADS  MATH  Google Scholar 

  26. R.B. Bhiladvala, Z.J. Wang, Effect of fluids on the q factor and resonance frequency of oscillating micrometer and nanometer scale beams. Phys. Rev. E 69, 036307 (2004). https://doi.org/10.1103/PhysRevE.69.036307

    Article  ADS  Google Scholar 

  27. V. Kara, V. Yakhot, K.L. Ekinci, Generalized Knudsen number for unsteady fluid flow. Phys. Rev. Lett. 118, 074505 (2017). https://doi.org/10.1103/PhysRevLett.118.074505

    Article  ADS  Google Scholar 

  28. V. Kara, Y.-I. Sohn, H. Atikian, V. Yakhot, M. Lončar, K.L. Ekinci, Nanofluidics of single-crystal diamond nanomechanical resonators. Nano Lett. 15, 8070–8076 (2015). https://doi.org/10.1021/acs.nanolett.5b03503

    Article  ADS  Google Scholar 

  29. A. Noury, J. Vergara-Cruz, P. Morfin, B. Plaçais, M.C. Gordillo, J. Boronat, S. Balibar, A. Bachtold, Layering transition in superfluid helium adsorbed on a carbon nanotube mechanical resonator. Phys. Rev. Lett. 122, 165301 (2019). https://doi.org/10.1103/PhysRevLett.122.165301

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge the use of the Néel Nanofab facility, and fruitful discussions with Rasul Gazizulin, Benjamin Pigeau and Jean-Philippe Poizat. The authors acknowledge the support from ERC StG Grant UNIGLASS No. 714692, and ERC CoG grant ULT-NEMS No. 647917. The research leading to these results has received funding from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement No. 824109, the European Microkelvin Platform (EMP).

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  1. Institut Néel, Univ. Grenoble Alpes, 25 rue des Martyrs, 38042, Grenoble, France

    Ilya Golokolenov, Baptiste Alperin, Bruno Fernandez, Andrew Fefferman & Eddy Collin

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  1. Ilya Golokolenov
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Golokolenov, I., Alperin, B., Fernandez, B. et al. Fully Suspended Nano-beams for Quantum Fluids. J Low Temp Phys 210, 550–561 (2023). https://doi.org/10.1007/s10909-022-02722-y

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