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Journal of Experimental and Theoretical Physics

, Volume 127, Issue 5, pp 865–876 | Cite as

Drag Force and Superfluidity in the Supersolid Stripe Phase of a Spin–Orbit-Coupled Bose–Einstein Condensate

  • G. I. MartoneEmail author
  • G. V. Shlyapnikov
Article
  • 12 Downloads

Abstract

The phase diagram of a spin–orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin–orbit coupling. This phase has been recently found experimentally [31]. In the present work, we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed. Moreover, due to the spin–orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity. Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities, the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.

REFERENCES

  1. 1.
    M. Boninsegni and N. V. Prokof’ev, Rev. Mod. Phys. 84, 759 (2012).ADSCrossRefGoogle Scholar
  2. 2.
    E. P. Gross, Phys Rev. 106, 161 (1957).ADSCrossRefGoogle Scholar
  3. 3.
    E. P. Gross, Ann. Phys. (N.Y.) 4, 57 (1958).ADSCrossRefGoogle Scholar
  4. 4.
    A. F. Andreev and I. M. Lifshitz, Sov. Phys. JETP 29, 1107 (1969).ADSGoogle Scholar
  5. 5.
    A. J. Leggett, Phys. Rev. Lett. 25, 1543 (1970).ADSCrossRefGoogle Scholar
  6. 6.
    G. V. Chester, Phys. Rev. A 2, 256 (1970).ADSCrossRefGoogle Scholar
  7. 7.
    D. A. Kirzhnits and Yu. A. Nepomnyashchii, Sov. Phys. JETP 32, 1191 (1971).ADSGoogle Scholar
  8. 8.
    L. P. Pitaevskii, JETP Lett. 39, 511 (1984).ADSGoogle Scholar
  9. 9.
    S. Balibar, Nature (London, U.K.) 464, 176 (2010).ADSCrossRefGoogle Scholar
  10. 10.
    Y. Pomeau and S. Rica, Phys. Rev. Lett. 72, 2426 (1994).ADSCrossRefGoogle Scholar
  11. 11.
    N. Henkel, R. Nath, and T. Pohl, Phys. Rev. Lett. 104, 195302 (2010).ADSCrossRefGoogle Scholar
  12. 12.
    F. Cinti, P. Jain, M. Boninsegni, A. Micheli, P. Zoller, and G. Pupillo, Phys. Rev. Lett. 105, 135301 (2010).ADSCrossRefGoogle Scholar
  13. 13.
    S. Saccani, S. Moroni, and M. Boninsegni, Phys. Rev. B 83, 092506 (2011).ADSCrossRefGoogle Scholar
  14. 14.
    H. P. Buchler, E. Demler, M. Lukin, A. Micheli, N. Prokof’ev, G. Pupillo, and P. Zoller, Phys. Rev. Lett. 98, 060404 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    G. E. Astrakharchik, J. Boronat, I. L. Kurbakov, and Yu. E. Lozovik, Phys. Rev. Lett. 98, 060405 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    I. L. Kurbakov, Yu. E. Lozovik, G. E. Astrakharchik, and J. Boronat, Phys. Rev. B 82, 014508 (2010).ADSCrossRefGoogle Scholar
  17. 17.
    Z.-K. Lu, Y. Li, D. S. Petrov, and G. V. Shlyapnikov, Phys. Rev. Lett. 115, 075303 (2015).ADSCrossRefGoogle Scholar
  18. 18.
    C. Wang, C. Gao, C.-M. Jian, and H. Zhai, Phys. Rev. Lett. 105, 160403 (2010).ADSCrossRefGoogle Scholar
  19. 19.
    T.-L. Ho and S. Zhang, Phys. Rev. Lett. 107, 150403 (2011).ADSCrossRefGoogle Scholar
  20. 20.
    C.-J. Wu, I. Mondragon-Shem, and X.-F. Zhou, Chin. Phys. Lett. 28, 097102 (2011).ADSCrossRefGoogle Scholar
  21. 21.
    Y. Li, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 108, 225301 (2012).ADSCrossRefGoogle Scholar
  22. 22.
    V. Galitski and I. B. Spielman, Nature (London, U.K.) 494, 49 (2013).ADSCrossRefGoogle Scholar
  23. 23.
    X. Zhou, Y. Li, Z. Cai, and C. Wu, J. Phys. B 46, 134001 (2013).ADSCrossRefGoogle Scholar
  24. 24.
    H. Zhai, Rep. Progr. Phys. 78, 026001 (2015).ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Y. Li, G. I. Martone, and S. Stringari, in Annual Review of Cold Atoms and Molecules, Ed. by K. W. Madison, K. Bongs, L. D. Carr, A. M. Rey, and H. Zhai (World Scientific, Singapore, 2015), Vol. 3, Chap. 5, p. 201.Google Scholar
  26. 26.
    Y. Zhang, M. E. Mossman, T. Busch, P. Engels, and C. Zhang, Front. Phys. 11, 118103 (2016).CrossRefGoogle Scholar
  27. 27.
    Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature (London, U.K.) 471, 83 (2011).ADSCrossRefGoogle Scholar
  28. 28.
    J. Li, W. Huang, B. Shteynas, S. Burchesky, F. C. Top, E. Su, J. Lee, A. O. Jamison, and W. Ketterle, Phys. Rev. Lett. 117, 185301 (2016).ADSCrossRefGoogle Scholar
  29. 29.
    G. I. Martone, Y. Li, and S. Stringari, Phys. Rev. A 90, 041604 (2014).ADSCrossRefGoogle Scholar
  30. 30.
    G. I. Martone, Eur. Phys. J. Spec. Top. 224, 553 (2015).CrossRefGoogle Scholar
  31. 31.
    J. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. C. Top, A. O. Jamison, and W. Ketterle, Nature (London, U.K.) 543, 91 (2017).ADSCrossRefGoogle Scholar
  32. 32.
    J. Léonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Nature (London, U.K.) 543, 87 (2017).ADSCrossRefGoogle Scholar
  33. 33.
    Y. Li, G. I. Martone, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 110, 235302 (2013).ADSCrossRefGoogle Scholar
  34. 34.
    G. E. Astrakharchik and L. P. Pitaevskii, Phys. Rev. A 70, 013608 (2004).ADSCrossRefGoogle Scholar
  35. 35.
    Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).ADSCrossRefGoogle Scholar
  36. 36.
    G. Dresselhaus, Phys. Rev. 100, 580 (1955).ADSCrossRefGoogle Scholar
  37. 37.
    L. P. Pitaevskii and S. Stringari, Bose–Einstein Condensation and Superfluidity (Oxford Univ. Press, Oxford, 2016).CrossRefzbMATHGoogle Scholar
  38. 38.
    C. J. Pethick and H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, Cambridge, 2008).CrossRefGoogle Scholar
  39. 39.
    S. Saccani, S. Moroni, and M. Boninsegni, Phys. Rev. Lett. 108, 175301 (2012).ADSCrossRefGoogle Scholar
  40. 40.
    M. Kunimi and Y. Kato, Phys. Rev. B 86, 060510(R) (2012).Google Scholar
  41. 41.
    T. Macri, F. Maucher, F. Cinti, and T. Pohl, Phys. Rev. A 87, 061602(R) (2013).Google Scholar
  42. 42.
    R. Liao, Phys. Rev. Lett. 120, 140403 (2018).ADSCrossRefGoogle Scholar
  43. 43.
    T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106, 1135 (1957).ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Z.-Q. Yu, Phys. Rev. A 95, 033618 (2017).ADSCrossRefGoogle Scholar
  45. 45.
    P.-S. He, Y.-H. Zhu, and W.-M. Liu, Phys. Rev. A 89, 053615 (2014).ADSCrossRefGoogle Scholar
  46. 46.
    R. Liao, O. Fialko, J. Brand, and U. Zu[umlaut]licke, Phys. Rev. A 93, 023625 (2016).ADSCrossRefGoogle Scholar
  47. 47.
    M. Kato, X.-F. Zhang, and H. Saito, Phys. Rev. A 96, 033613 (2017).ADSCrossRefGoogle Scholar
  48. 48.
    G. I. Martone, Y. Li, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 86, 063621 (2012).ADSCrossRefGoogle Scholar
  49. 49.
    M. A. Khamehchi, Y. Zhang, C. Hamner, T. Busch, and P. Engels, Phys. Rev. A 90, 063624 (2014).ADSCrossRefGoogle Scholar
  50. 50.
    S.-C. Ji, L. Zhang, X.-T. Xu, Z. Wu, Y. Deng, S. Chen, and J.-W. Pan, Phys. Rev. Lett. 114, 105301 (2015).ADSCrossRefGoogle Scholar
  51. 51.
    Q. Zhu, C. Zhang, and B. Wu, Europhys. Lett. 100, 50003 (2012).ADSCrossRefGoogle Scholar
  52. 52.
    T. Ozawa, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 87, 063610 (2013).ADSCrossRefGoogle Scholar
  53. 53.
    W. Zheng, Z.-Q. Yu, X. Cui, and H. Zhai, J. Phys. B 46, 134007 (2013).ADSCrossRefGoogle Scholar
  54. 54.
    X.-L. Chen, J. Wang, Y. Li, X.-J. Liu, and H. Hu, Phys. Rev. A 98, 013614 (2018).Google Scholar
  55. 55.
    G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. A 66, 023603 (2002).ADSCrossRefGoogle Scholar
  56. 56.
    K. Sun, C. Qu, Y. Xu, Y. Zhang, and C. Zhang, Phys. Rev. A 93, 023615 (2016).ADSCrossRefGoogle Scholar
  57. 57.
    Z.-Q. Yu, Phys. Rev. A 93, 033648 (2016).ADSCrossRefGoogle Scholar
  58. 58.
    G. I. Martone, F. V. Pepe, P. Facchi, S. Pascazio, and S. Stringari, Phys. Rev. Lett. 117, 125301 (2016).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.LPTMS, CNRS, Univ. Paris-Sud, Université Paris-SaclayOrsayFrance
  2. 2.Russian Quantum CenterSkolkovoMoscowRussia
  3. 3.SPEC, CEA, CNRS, Université Paris-Saclay, CEA SaclayGif sur YvetteFrance
  4. 4.Van der Waals–Zeeman Institute, Institute of Physics, University of AmsterdamAmsterdamNetherlands
  5. 5.Wuhan Institute of Physics and Mathematics, Chinese Academy of SciencesWuhanChina
  6. 6.Russian Quantum Center, National University of Science and Technology MISISMoscowRussia

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