Optical Visibility and Core Structure of Vortex Filaments in a Bosonic Superfluid

Abstract

We use optical images of a superfluid consisting of a weakly interacting Bose–Einstein condensate of sodium atoms to investigate the structure of quantized three-dimensional vortex filaments. We find that the measured optical contrast and the width of the vortex core quantitatively agree with the predictions of the Gross–Pitaevskii equation.

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Notes

  1. 1.

    Notice that an equation of the same form was derived in [4], within a phenomenological theory for superfluids close to the normal-superfluid phase transition; the meaning of the coefficients is however entirely different.

REFERENCES

  1. 1

    L. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).

    MathSciNet  Google Scholar 

  2. 2

    E. P. Gross, Nuovo Cim. 20, 454 (1961).

    ADS  Article  Google Scholar 

  3. 3

    N. Bogolyubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 77 (1947).

    Google Scholar 

  4. 4

    V. L. Ginzburg and L. P. Pitaevskii, Sov. Phys. JETP 7, 858 (1958).

    Google Scholar 

  5. 5

    R. J. Donnelly, Quantized Vortices in Helium II (Cambridge Univ. Press, Cambridge, 1991).

    Google Scholar 

  6. 6

    F. Dalfovo, Phys. Rev. B 46, 5482 (1992).

    ADS  Article  Google Scholar 

  7. 7

    G. Ortiz and D. M. Ceperley, Phys. Rev. Lett. 75, 4642 (1995).

    ADS  Article  Google Scholar 

  8. 8

    S. A. Vitiello, L. Reatto, G. V. Chester, and M. H. Kalos, Phys. Rev. B 54, 1205 (1996).

    ADS  Article  Google Scholar 

  9. 9

    S. Giorgini, J. Boronat, and J. Casulleras, Phys. Rev. Lett. 77, 2754 (1996).

    ADS  Article  Google Scholar 

  10. 10

    D. E. Galli, L. Reatto, and M. Rossi, Phys. Rev. B 89, 224516 (2014).

    ADS  Article  Google Scholar 

  11. 11

    E. J. Yarmchuk, M. J. V. Gordon, and R. E. Packard, Phys. Rev. Lett. 43, 214 (1979).

    ADS  Article  Google Scholar 

  12. 12

    E. J. Yarmchuk and R. E. Packard, J. Low Temp. Phys. 46, 479 (1982).

    ADS  Article  Google Scholar 

  13. 13

    W. Guo, D. Jin, G. M. Seidel, and H. J. Maris, Phys. Rev. B 79, 054515 (2009).

    ADS  Article  Google Scholar 

  14. 14

    D. D. Jin and H. Maris, J. Low Temp. Phys. 162, 329 (2011).

    ADS  Article  Google Scholar 

  15. 15

    G. P. Bewley, D. P. Lathrop, and K. R. Sreenivasan, Nature (London, U.K.) 441, 588 (2006).

    ADS  Article  Google Scholar 

  16. 16

    G. Bewley, M. Paoletti, K. Sreenivasan, and D. Lathrop, Proc. Natl. Acad. Sci. (U.S.A.) 105, 13707 (2008).

    ADS  Article  Google Scholar 

  17. 17

    M. Paoletti, M. E. Fisher, and D. Lathrop, Phys. D (Amsterdam, Neth.) 239, 1367 (2010).

  18. 18

    M. S. Paoletti and D. P. Lathrop, Ann. Rev. Condens. Matter Phys. 2, 213 (2011).

    ADS  Article  Google Scholar 

  19. 19

    E. Fonda, D. P. Meichle, N. T. Ouellette, S. Hormoz, and D. P. Lathrop, Proc. Natl. Acad. Sci. (U.S.A.) 111, 4707 (2014).

    ADS  Article  Google Scholar 

  20. 20

    D. E. Zmeev, F. Pakpour, P. M. Walmsley, A. I. Golov, W. Guo, D. N. McKinsey, G. G. Ihas, P. V. E. McClintock, S. N. Fisher, and W. F. Vinen, Phys. Rev. Lett. 110, 175303 (2013).

    ADS  Article  Google Scholar 

  21. 21

    C. F. Barenghi and Y. A. Sergeev, Phys. Rev. B 80, 024514 (2009).

    ADS  Article  Google Scholar 

  22. 22

    F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).

    ADS  Article  Google Scholar 

  23. 23

    L. Pitaevskii and S. Stringari, Bose–Einstein Condensation and Superfluidity (Oxford Univ. Press, Oxford, 2016).

    Google Scholar 

  24. 24

    M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 83, 2498 (1999).

    ADS  Article  Google Scholar 

  25. 25

    K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000).

    ADS  Article  Google Scholar 

  26. 26

    B. P. Anderson, P. C. Haljan, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 85, 2857 (2000).

    ADS  Article  Google Scholar 

  27. 27

    B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark, and E. A. Cornell, Phys. Rev. Lett. 86, 2926 (2001).

    ADS  Article  Google Scholar 

  28. 28

    P. C. Haljan, B. P. Anderson, I. Coddington, and E. A. Cornell, Phys. Rev. Lett. 86, 2922 (2001).

    ADS  Article  Google Scholar 

  29. 29

    J. Abo-Shaeer, C. Raman, J. Vogels, and W. Ketterle, Science (Washington, DC, U. S.) 292, 476 (2001).

    ADS  Article  Google Scholar 

  30. 30

    E. Hodby, G. Hechenblaikner, S. A. Hopkins, O. M. Marago, and C. J. Foot, Phys. Rev. Lett. 88, 010405 (2001).

    Article  Google Scholar 

  31. 31

    A. Fetter, Rev. Mod. Phys. 81, 647 (2009).

    ADS  Article  Google Scholar 

  32. 32

    E. Lundh, C. J. Pethick, and H. Smith, Phys. Rev. A 58, 4816 (1998).

    ADS  Article  Google Scholar 

  33. 33

    F. Dalfovo and M. Modugno, Phys. Rev. A 61, 023605 (2000).

    ADS  Article  Google Scholar 

  34. 34

    O. Hosten, P. Vignolo, A. Minguzzi, B. Tanatar, and M. P. Tosi, J. Phys. B 36, 2455 (2003).

    ADS  Article  Google Scholar 

  35. 35

    R. P. Teles, F. E. A. dos Santos, M. A. Caracanhas, and V. S. Bagnato, Phys. Rev. A 87, 033622 (2013).

    ADS  Article  Google Scholar 

  36. 36

    S. W. Seo, J.-Y. Choi, and Y.-I. Shin, J. Korean Phys. Soc. 64, 53 (2013).

    Article  Google Scholar 

  37. 37

    A. Aftalion and T. Riviere, Phys. Rev. A 64, 043611 (2001).

    ADS  Article  Google Scholar 

  38. 38

    J. J. Garcia-Ripoll and V. M. Perez-Garcia, Phys. Rev. A 64, 053611 (2001).

    ADS  Article  Google Scholar 

  39. 39

    A. Aftalion and I. Danaila, Phys. Rev. A 68, 023603 (2003).

    ADS  Article  Google Scholar 

  40. 40

    M. Modugno, L. Pricoupenko, and Y. Castin, Eur. Phys. J. D 22, 235 (2003).

    ADS  Article  Google Scholar 

  41. 41

    C. Raman, J. R. Abo-Shaeer, J. M. Vogels, K. Xu, and W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001).

    ADS  Article  Google Scholar 

  42. 42

    P. Rosenbusch, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002).

    ADS  Article  Google Scholar 

  43. 43

    V. Bretin, P. Rosenbusch, F. Chevy, G. V. Shlyapnikov, and J. Dalibard, Phys. Rev. Lett. 90, 100403 (2003).

    ADS  Article  Google Scholar 

  44. 44

    S. Donadello, S. Serafini, M. Tylutki, L. P. Pitaevskii, F. Dalfovo, G. Lamporesi, and G. Ferrari, Phys. Rev. Lett. 113, 065302 (2014).

    ADS  Article  Google Scholar 

  45. 45

    G. Lamporesi, S. Donadello, S. Serafini, F. Dalfovo, and G. Ferrari, Nat. Phys. 9, 656 (2013).

    Article  Google Scholar 

  46. 46

    S. Donadello, S. Serafini, T. Bienaime, F. Dalfovo, G. Lamporesi, and G. Ferrari, Phys. Rev. A 94, 023628 (2016).

    ADS  Article  Google Scholar 

  47. 47

    J. Brand and W. P. Reinhardt, Phys. Rev. A 65, 043612 (2002).

    ADS  Article  Google Scholar 

  48. 48

    S. Komineas and N. Papanicolaou, Phys. Rev. A 68, 043617 (2003).

    ADS  Article  Google Scholar 

  49. 49

    M. J. H. Ku, W. Ji, B. Mukherjee, E. Guardado-Sanchez, L. W. Cheuk, T. Yefsah, and M. W. Zwierlein, Phys. Rev. Lett. 113, 065301 (2014).

    ADS  Article  Google Scholar 

  50. 50

    M. Tylutki, S. Donadello, S. Serafini, L. P. Pitaevskii, F. Dalfovo, G. Lamporesi, and G. Ferrari, Eur. Phys. J. Spec. Top. 224, 577 (2015).

    Article  Google Scholar 

  51. 51

    F. Dalfovo, L. Pitaevskii, and S. Stringari, Phys. Rev. A 54, 4213 (1996).

    ADS  Article  Google Scholar 

  52. 52

    Y. Castin and R. Dum, Phys. Rev. Lett. 77, 5315 (1996).

    ADS  Article  Google Scholar 

  53. 53

    Y. Kagan, E. L. Surkov, and G. V. Shlyapnikov, Phys. Rev. A 54, R1753 (1996).

    ADS  Article  Google Scholar 

  54. 54

    F. Dalfovo, C. Minniti, S. Stringari, and L. Pitaevskii, Phys. Lett. A 227, 259 (1997).

    ADS  Article  Google Scholar 

  55. 55

    L. P. Pitaevskii and A. Rosch, Phys. Rev. A 55, R853 (1997).

    ADS  Article  Google Scholar 

  56. 56

    R. N. Bisset, S. Serafini, E. Iseni, M. Barbiero, T. Bienaime, G. Lamporesi, G. Ferrari, and F. Dalfovo, Phys. Rev. A 96, 053605 (2017).

    ADS  Article  Google Scholar 

  57. 57

    I. Coddington, P. C. Haljan, P. Engels, V. Schweikhard, S. Tung, and E. A. Cornell, Phys. Rev. A 70, 063607 (2004).

    ADS  Article  Google Scholar 

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ACKNOWLEDGMENTS

We dedicate this paper to L.P. Pitaevskii in celebration of his 85th birthday. No words can express our gratitude for the times spent working alongside him and, of course, for his pioneering contributions to physics itself. This work is supported by Provincia Autonoma di Trento and by QuantERA ERA-NET cofund project NAQUAS.

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Correspondence to F. Dalfovo.

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Contribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday

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Dalfovo, F., Bisset, R.N., Mordini, C. et al. Optical Visibility and Core Structure of Vortex Filaments in a Bosonic Superfluid. J. Exp. Theor. Phys. 127, 804–811 (2018). https://doi.org/10.1134/S1063776118110018

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