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Suppression of the superfluid Kelvin-Helmholtz instability due to massive vortex cores, friction and confinement

Published 18 Mar 2024 in cond-mat.quant-gas and physics.flu-dyn | (2403.11987v2)

Abstract: We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform.

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References (78)
  1. H. von Helmholtz, Über discontinuirliche Flüssigkeits-Bewegungen, Akademie der Wissenschaften zu Berlin (1868).
  2. W. Thomson, XLVI. Hydrokinetic solutions and observations, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42(281), 362 (1871).
  3. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Books on Physics Series. Dover Publications, ISBN 9780486640716 (1981).
  4. L. Landau and E. Lifshitz, Fluid mechanics, Pergamon Press, 2nd edn. (1987).
  5. F. Charru, Hydrodynamic instabilities, vol. 37, Cambridge University Press, 10.1017/CBO9780511975172 (2011).
  6. G. Klaassen and W. Peltier, The onset of turbulence in finite-amplitude Kelvin–Helmholtz billows, Journal of Fluid Mechanics 155, 1 (1985).
  7. A. Mashayek and W. Peltier, The ‘zoo’of secondary instabilities precursory to stratified shear flow transition. Part 2 The influence of stratification, Journal of fluid mechanics 708, 45 (2012), 10.1017/jfm.2012.294.
  8. S. Thorpe, Transitional phenomena and the development of turbulence in stratified fluids: A review, Journal of Geophysical Research: Oceans 92(C5), 5231 (1987).
  9. S. Thorpe, On the Kelvin–Helmholtz route to turbulence, Journal of Fluid Mechanics 708, 1 (2012), 10.1017/jfm.2012.383.
  10. Atmospheric Kelvin–Helmholtz billows captured by the MU radar, lidars and a fish-eye camera, Earth, Planets and Space 70, 1 (2018), 10.1186/s40623-018-0935-0.
  11. Extensive studies of large-amplitude Kelvin–Helmholtz billows in the lower atmosphere with VHF middle and upper atmosphere radar, Quarterly Journal of the Royal Meteorological Society 137(657), 1019 (2011), 10.1002/qj.807.
  12. H. Li and H. Yamazaki, Observations of a Kelvin-Helmholtz billow in the ocean, Journal of oceanography 57, 709 (2001), 10.1023/A:1021284409498.
  13. Ocean mixing by Kelvin-Helmholtz instability, Oceanography 25(2), 140 (2012).
  14. C. P. McNally, W. Lyra and J.-C. Passy, A well-posed Kelvin–Helmholtz instability test and comparison, The Astrophysical Journal Supplement Series 201(2), 18 (2012), 10.1088/0067-0049/201/2/18.
  15. A. Mastrano and A. Melatos, Kelvin—Helmholtz instability and circulation transfer at an isotropic—anisotropic superfluid interface in a neutron star, Monthly Notices of the Royal Astronomical Society 361(3), 927 (2005), 10.1111/j.1365-2966.2005.09219.x.
  16. L. Rayleigh, On the stability, or instability, of certain fluid motions, Proceedings of the London Mathematical Society 1(1), 57 (1879).
  17. A. J. Leggett, Superfluidity, Rev. Mod. Phys. 71, S318 (1999), 10.1103/RevModPhys.71.S318.
  18. Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999), 10.1103/RevModPhys.71.463.
  19. Theory of ultracold atomic Fermi gases, Rev. Mod. Phys. 80, 1215 (2008), 10.1103/RevModPhys.80.1215.
  20. I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013), 10.1103/RevModPhys.85.299.
  21. M. Tsubota, M. Kobayashi and H. Takeuchi, Quantum hydrodynamics, Physics Reports 522(3), 191 (2013), 10.1016/j.physrep.2012.09.007.
  22. Observation of von Kármán Vortex Street in an Atomic Superfluid Gas, Phys. Rev. Lett. 117, 245301 (2016), 10.1103/PhysRevLett.117.245301.
  23. K. Sasaki, N. Suzuki and H. Saito, Bénard–von Kármán Vortex Street in a Bose-Einstein Condensate, Phys. Rev. Lett. 104, 150404 (2010), 10.1103/PhysRevLett.104.150404.
  24. G. Stagg, N. Parker and C. Barenghi, Quantum analogues of classical wakes in Bose–Einstein condensates, Journal of Physics B: Atomic, Molecular and Optical Physics 47(9), 095304 (2014), 10.1088/0953-4075/47/9/095304.
  25. G. W. Stagg, N. G. Parker and C. F. Barenghi, Superfluid Boundary Layer, Phys. Rev. Lett. 118, 135301 (2017), 10.1103/PhysRevLett.118.135301.
  26. S. Gautam and D. Angom, Rayleigh-Taylor instability in binary condensates, Phys. Rev. A 81, 053616 (2010), 10.1103/PhysRevA.81.053616.
  27. Interface dynamics of a two-component Bose-Einstein condensate driven by an external force, Phys. Rev. A 83, 043623 (2011), 10.1103/PhysRevA.83.043623.
  28. Rayleigh-Taylor instability in a two-component Bose-Einstein condensate with rotational symmetry, Phys. Rev. A 85, 013602 (2012), 10.1103/PhysRevA.85.013602.
  29. Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate, Phys. Rev. A 80, 063611 (2009), 10.1103/PhysRevA.80.063611.
  30. Shear Flow and Kelvin-Helmholtz Instability in Superfluids, Phys. Rev. Lett. 89, 155301 (2002), 10.1103/PhysRevLett.89.155301.
  31. Dynamics of vortices and interfaces in superfluid 3He, Reports on Progress in Physics 69(12), 3157 (2006), 10.1088/0034-4885/69/12/R03.
  32. S. Korshunov, Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid, Journal of Experimental and Theoretical Physics Letters 75, 423 (2002), 10.1134/1.1490015.
  33. Explosive Development of the Kelvin-Helmholtz Quantum Instability on the He-II Free Surface, J. Exp. Theor. Phys. 129, 651 (2019), 10.1134/S1063776119100157.
  34. G. E. Volovik, On the Kelvin-Helmholtz instability in superfluids, Journal of Experimental and Theoretical Physics Letters 75, 418 (2002), 10.1134/1.1490014.
  35. Quantum Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates, Phys. Rev. B 81, 094517 (2010), 10.1103/PhysRevB.81.094517.
  36. Crossover between Kelvin-Helmholtz and counter-superflow instabilities in two-component Bose-Einstein condensates, Phys. Rev. A 82, 063604 (2010), 10.1103/PhysRevA.82.063604.
  37. E. Lundh and J.-P. Martikainen, Kelvin-Helmholtz instability in two-component Bose gases on a lattice, Phys. Rev. A 85, 023628 (2012), 10.1103/PhysRevA.85.023628.
  38. Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities, Phys. Rev. A 89, 013631 (2014), 10.1103/PhysRevA.89.013631.
  39. H. Kokubo, K. Kasamatsu and H. Takeuchi, Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids, Phys. Rev. A 104, 023312 (2021), 10.1103/PhysRevA.104.023312.
  40. H. Kokubo, K. Kasamatsu and H. Takeuchi, Vorticity Distribution in Quantum Kelvin–Helmholtz Instability of Binary Bose–Einstein Condensates, Journal of Low Temperature Physics pp. 1–8 (2022), doi.org/10.1007/s10909-021-02660-1.
  41. Interface dynamics of strongly interacting binary superfluids, arXiv preprint arXiv:2401.09189 (2024).
  42. Kelvin-Helmholtz instability in a single-component atomic superfluid, Phys. Rev. A 97, 053608 (2018), 10.1103/PhysRevA.97.053608.
  43. H. Aref, On the equilibrium and stability of a row of point vortices, Journal of Fluid Mechanics 290, 167 (1995).
  44. L. Giacomelli and I. Carusotto, Interplay of Kelvin-Helmholtz and superradiant instabilities of an array of quantized vortices in a two-dimensional Bose-Einstein condensate, SciPost Phys. 14, 025 (2023), 10.21468/SciPostPhys.14.2.025.
  45. Crystallization of bosonic quantum Hall states in a rotating quantum gas, Nature 601(7891), 58 (2022), 10.1038/s41586-021-04170-2.
  46. Universality of the superfluid Kelvin-Helmholtz instability by single-vortex tracking, arXiv preprint arXiv:2303.12631 (2023), 10.48550/arXiv.2303.12631.
  47. C. Caroli, P. De Gennes and J. Matricon, Bound fermion states on a vortex line in a type ii superconductor, Physics Letters 9(4), 307 (1964).
  48. E. Šimánek, Reactive effects of core fermion excitations on the inertial mass of a vortex, Journal of low temperature physics 100, 1 (1995).
  49. M. Machida and T. Koyama, Structure of a Quantized Vortex near the BCS-BEC Crossover in an Atomic Fermi Gas, Phys. Rev. Lett. 94, 140401 (2005), 10.1103/PhysRevLett.94.140401.
  50. Sound emission and annihilations in a programmable quantum vortex collider, Nature 600(7887), 64 (2021), 10.1038/s41586-021-04047-4.
  51. Dissipative Dynamics of Quantum Vortices in Fermionic Superfluid, Phys. Rev. Lett. 130, 043001 (2023), 10.1103/PhysRevLett.130.043001.
  52. T. H. Havelock, LII. The stability of motion of rectilinear vortices in ring formation, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 11(70), 617 (1931).
  53. G. J. Mertz, Stability of body-centered polygonal configurations of ideal vortices, The Physics of Fluids 21(7), 1092 (1978).
  54. G. P. Bewley, D. P. Lathrop and K. R. Sreenivasan, Visualization of quantized vortices, Nature 441(7093), 588 (2006), 10.1038/441588a.
  55. Magnus-force model for active particles trapped on superfluid vortices, Phys. Rev. A 101, 053601 (2020), 10.1103/PhysRevA.101.053601.
  56. A. Griffin, T. Nikuni and E. Zaremba, Bose-condensed gases at finite temperatures, Cambridge University Press, 10.1017/CBO9780511575150 (2009).
  57. Vortex Precession in Bose-Einstein Condensates: Observations with Filled and Empty Cores, Phys. Rev. Lett. 85, 2857 (2000), 10.1103/PhysRevLett.85.2857.
  58. K. J. H. Law, P. G. Kevrekidis and L. S. Tuckerman, Stable Vortex–Bright-Soliton Structures in Two-Component Bose-Einstein Condensates, Phys. Rev. Lett. 105, 160405 (2010), 10.1103/PhysRevLett.105.160405.
  59. Magnetic defects in an imbalanced mixture of two Bose-Einstein condensates, Phys. Rev. A 97, 063615 (2018), 10.1103/PhysRevA.97.063615.
  60. Vortices with massive cores in a binary mixture of Bose-Einstein condensates, Phys. Rev. A 101, 013630 (2020), 10.1103/PhysRevA.101.013630.
  61. V. P. Ruban, Instabilities of a Filled Vortex in a Two-Component Bose–Einstein Condensate, JETP Letters 113(8), 532 (2021), 10.1134/S0021364021080117.
  62. Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates, Phys. Rev. A 103, 023311 (2021), 10.1103/PhysRevA.103.023311.
  63. Dynamics of a massive superfluid vortex in rksuperscript𝑟𝑘{r}^{k}italic_r start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT confining potentials, Phys. Rev. A 106, 063307 (2022), 10.1103/PhysRevA.106.063307.
  64. Massive superfluid vortices and vortex necklaces on a planar annulus, SciPost Phys. 15, 057 (2023), 10.21468/SciPostPhys.15.2.057.
  65. A. Chaika, A. Richaud and A. Yakimenko, Making ghost vortices visible in two-component Bose-Einstein condensates, Phys. Rev. Res. 5, 023109 (2023), 10.1103/PhysRevResearch.5.023109.
  66. A. Bellettini, A. Richaud and V. Penna, Relative dynamics of quantum vortices and massive cores in binary BECs, Eur. Phys. J. Plus 138, 676 (2023), https://doi.org/10.1140/epjp/s13360-023-04294-6.
  67. Stability of quantized vortices in two-component condensates, Phys. Rev. Res. 5, 033201 (2023), 10.1103/PhysRevResearch.5.033201.
  68. Mass-driven vortex collisions in flat superfluids, Phys. Rev. A 107, 053317 (2023), 10.1103/PhysRevA.107.053317.
  69. G. Teschl, Ordinary differential equations and dynamical systems, vol. 140, American Mathematical Soc., 10.1090/gsm/140 (2012).
  70. Imprinting Persistent Currents in Tunable Fermionic Rings, Phys. Rev. X 12, 041037 (2022), 10.1103/PhysRevX.12.041037.
  71. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4superscriptnormal-He4{}^{4}\mathrm{He}start_FLOATSUPERSCRIPT 4 end_FLOATSUPERSCRIPT roman_He: Line-line and line-boundary interactions, Phys. Rev. B 31, 5782 (1985), 10.1103/PhysRevB.31.5782.
  72. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4superscriptnormal-He4{}^{4}\mathrm{He}start_FLOATSUPERSCRIPT 4 end_FLOATSUPERSCRIPT roman_He: Homogeneous superfluid turbulence, Phys. Rev. B 38, 2398 (1988), 10.1103/PhysRevB.38.2398.
  73. Vortex mutual friction in superfluid 3 He, Journal of low temperature physics 109, 423 (1997).
  74. N. B. Kopnin, Vortex dynamics and mutual friction in superconductors and Fermi superfluids, Reports on Progress in Physics 65(11), 1633 (2002), 10.1088/0034-4885/65/11/202.
  75. E. B. Sonin, Dynamics of quantised vortices in superfluids, Cambridge University Press (2016).
  76. Y. A. Sergeev, Mutual Friction in Bosonic Superfluids: A Review, Journal of Low Temperature Physics pp. 1–55 (2023), 10.1007/s10909-023-02972-4.
  77. N.-E. Guenther, P. Massignan and A. L. Fetter, Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli, Phys. Rev. A 96, 063608 (2017), 10.1103/PhysRevA.96.063608.
  78. Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates, Phys. Rev. A 70, 043624 (2004), 10.1103/PhysRevA.70.043624.
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