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.
Similar content being viewed by others
Notes
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
L. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).
E. P. Gross, Nuovo Cim. 20, 454 (1961).
N. Bogolyubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 77 (1947).
V. L. Ginzburg and L. P. Pitaevskii, Sov. Phys. JETP 7, 858 (1958).
R. J. Donnelly, Quantized Vortices in Helium II (Cambridge Univ. Press, Cambridge, 1991).
F. Dalfovo, Phys. Rev. B 46, 5482 (1992).
G. Ortiz and D. M. Ceperley, Phys. Rev. Lett. 75, 4642 (1995).
S. A. Vitiello, L. Reatto, G. V. Chester, and M. H. Kalos, Phys. Rev. B 54, 1205 (1996).
S. Giorgini, J. Boronat, and J. Casulleras, Phys. Rev. Lett. 77, 2754 (1996).
D. E. Galli, L. Reatto, and M. Rossi, Phys. Rev. B 89, 224516 (2014).
E. J. Yarmchuk, M. J. V. Gordon, and R. E. Packard, Phys. Rev. Lett. 43, 214 (1979).
E. J. Yarmchuk and R. E. Packard, J. Low Temp. Phys. 46, 479 (1982).
W. Guo, D. Jin, G. M. Seidel, and H. J. Maris, Phys. Rev. B 79, 054515 (2009).
D. D. Jin and H. Maris, J. Low Temp. Phys. 162, 329 (2011).
G. P. Bewley, D. P. Lathrop, and K. R. Sreenivasan, Nature (London, U.K.) 441, 588 (2006).
G. Bewley, M. Paoletti, K. Sreenivasan, and D. Lathrop, Proc. Natl. Acad. Sci. (U.S.A.) 105, 13707 (2008).
M. Paoletti, M. E. Fisher, and D. Lathrop, Phys. D (Amsterdam, Neth.) 239, 1367 (2010).
M. S. Paoletti and D. P. Lathrop, Ann. Rev. Condens. Matter Phys. 2, 213 (2011).
E. Fonda, D. P. Meichle, N. T. Ouellette, S. Hormoz, and D. P. Lathrop, Proc. Natl. Acad. Sci. (U.S.A.) 111, 4707 (2014).
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).
C. F. Barenghi and Y. A. Sergeev, Phys. Rev. B 80, 024514 (2009).
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
L. Pitaevskii and S. Stringari, Bose–Einstein Condensation and Superfluidity (Oxford Univ. Press, Oxford, 2016).
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).
K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000).
B. P. Anderson, P. C. Haljan, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 85, 2857 (2000).
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).
P. C. Haljan, B. P. Anderson, I. Coddington, and E. A. Cornell, Phys. Rev. Lett. 86, 2922 (2001).
J. Abo-Shaeer, C. Raman, J. Vogels, and W. Ketterle, Science (Washington, DC, U. S.) 292, 476 (2001).
E. Hodby, G. Hechenblaikner, S. A. Hopkins, O. M. Marago, and C. J. Foot, Phys. Rev. Lett. 88, 010405 (2001).
A. Fetter, Rev. Mod. Phys. 81, 647 (2009).
E. Lundh, C. J. Pethick, and H. Smith, Phys. Rev. A 58, 4816 (1998).
F. Dalfovo and M. Modugno, Phys. Rev. A 61, 023605 (2000).
O. Hosten, P. Vignolo, A. Minguzzi, B. Tanatar, and M. P. Tosi, J. Phys. B 36, 2455 (2003).
R. P. Teles, F. E. A. dos Santos, M. A. Caracanhas, and V. S. Bagnato, Phys. Rev. A 87, 033622 (2013).
S. W. Seo, J.-Y. Choi, and Y.-I. Shin, J. Korean Phys. Soc. 64, 53 (2013).
A. Aftalion and T. Riviere, Phys. Rev. A 64, 043611 (2001).
J. J. Garcia-Ripoll and V. M. Perez-Garcia, Phys. Rev. A 64, 053611 (2001).
A. Aftalion and I. Danaila, Phys. Rev. A 68, 023603 (2003).
M. Modugno, L. Pricoupenko, and Y. Castin, Eur. Phys. J. D 22, 235 (2003).
C. Raman, J. R. Abo-Shaeer, J. M. Vogels, K. Xu, and W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001).
P. Rosenbusch, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002).
V. Bretin, P. Rosenbusch, F. Chevy, G. V. Shlyapnikov, and J. Dalibard, Phys. Rev. Lett. 90, 100403 (2003).
S. Donadello, S. Serafini, M. Tylutki, L. P. Pitaevskii, F. Dalfovo, G. Lamporesi, and G. Ferrari, Phys. Rev. Lett. 113, 065302 (2014).
G. Lamporesi, S. Donadello, S. Serafini, F. Dalfovo, and G. Ferrari, Nat. Phys. 9, 656 (2013).
S. Donadello, S. Serafini, T. Bienaime, F. Dalfovo, G. Lamporesi, and G. Ferrari, Phys. Rev. A 94, 023628 (2016).
J. Brand and W. P. Reinhardt, Phys. Rev. A 65, 043612 (2002).
S. Komineas and N. Papanicolaou, Phys. Rev. A 68, 043617 (2003).
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).
M. Tylutki, S. Donadello, S. Serafini, L. P. Pitaevskii, F. Dalfovo, G. Lamporesi, and G. Ferrari, Eur. Phys. J. Spec. Top. 224, 577 (2015).
F. Dalfovo, L. Pitaevskii, and S. Stringari, Phys. Rev. A 54, 4213 (1996).
Y. Castin and R. Dum, Phys. Rev. Lett. 77, 5315 (1996).
Y. Kagan, E. L. Surkov, and G. V. Shlyapnikov, Phys. Rev. A 54, R1753 (1996).
F. Dalfovo, C. Minniti, S. Stringari, and L. Pitaevskii, Phys. Lett. A 227, 259 (1997).
L. P. Pitaevskii and A. Rosch, Phys. Rev. A 55, R853 (1997).
R. N. Bisset, S. Serafini, E. Iseni, M. Barbiero, T. Bienaime, G. Lamporesi, G. Ferrari, and F. Dalfovo, Phys. Rev. A 96, 053605 (2017).
I. Coddington, P. C. Haljan, P. Engels, V. Schweikhard, S. Tung, and E. A. Cornell, Phys. Rev. A 70, 063607 (2004).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday
The article is published in the original.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776118110018