# Josephson Oscillations and Self-Trapping of Superfluid Fermions in a Double-Well Potential

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## Abstract

We investigate the behaviour of a two-component Fermi superfluid in a double-well potential. We numerically solve the time dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for different potential barriers and initial conditions. In the weak link limit the results agree with a two-mode model where the relative population and the phase difference between the two wells obey coupled nonlinear Josephson equations. A more complex dynamics is predicted for large amplitude oscillations and large tunneling.

## Keywords

Josephson oscillation Self-trapping Fermi superfluids Time-dependent BdG## Notes

### Acknowledgments

We thank S. Stringari, L.P. Pitaevskii, A. Recati for fruitful discussions. P.Z is particularly indebted to R.G.Scott, whose computational expertise was of great help at the beginning of this work. Support of ERC, through the QGBE Grant, and of Provincia Autonoma di Trento is acknowledged.

## References

- 1.B.D. Josephson, Phys. Lett.
**1**, 251 (1962)CrossRefzbMATHADSGoogle Scholar - 2.A. Barone, G. Paterno,
*Physics and Applications of the Josephson Effect*(Wiley, New York, 1982)CrossRefGoogle Scholar - 3.A.J. Leggett, Rev. Mod. Phys.
**73**, 307 (2001)CrossRefADSGoogle Scholar - 4.L. Pitaevskii, S. Stringari,
*Bose–Einstein Condensation*(Oxford Science Publications, Oxford, 2003)zbMATHGoogle Scholar - 5.R. Gati, M.K. Oberthaler, J. Phys. B
**40**, R61 (2007)CrossRefADSGoogle Scholar - 6.A. Smerzi, S. Fantoni, S. Giovanazzi, S.R. Shenoy, Phys. Rev. Lett.
**79**, 4950 (1997)CrossRefADSGoogle Scholar - 7.S. Raghavan, A. Smerzi, S. Fantoni, S.R. Shenoy, Phys. Rev. A
**59**, 620 (1999)CrossRefADSGoogle Scholar - 8.E.A. Ostrovskaya, Y.S. Kivshar, M. Lisak, B. Hall, F. Cattani, D. Anderson, Phys. Rev. A
**61**, 031601R (2000)CrossRefADSGoogle Scholar - 9.D. Ananikian, T. Bergeman, Phys. Rev. A
**73**, 013604 (2006)CrossRefADSGoogle Scholar - 10.F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science
**293**, 843 (2001)CrossRefADSGoogle Scholar - 11.Th Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, M.K. Oberthaler. Phys. Rev. Lett.
**94**, 020403 (2005)Google Scholar - 12.M. Albiez, R. Gati, J. Foelling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Phys. Rev. Lett.
**95**, 010402 (2005)CrossRefADSGoogle Scholar - 13.T. Zibold, E. Nicklas, Ch. Gross, M.K. Oberthaler, Phys. Rev. Lett.
**105**, 204101 (2010)CrossRefADSGoogle Scholar - 14.S. Levy, E. Lahoud, I. Shomroni, J. Steinhauer, Nature
**449**, 579 (2007)CrossRefADSGoogle Scholar - 15.L.J. LeBlanc, A.B. Bardon, J. McKeever, M.H.T. Extavour, D. Jervis, J.H. Thywissen, F. Piazza, A. Smerzi, Phys. Rev. Lett.
**106**, 025302 (2011)CrossRefADSGoogle Scholar - 16.P. Pieri, G.C. Strinati, Phys. Rev. Lett.
**91**, 030401 (2003)CrossRefADSGoogle Scholar - 17.A. Spuntarelli, P. Pieri, G.C. Strinati, Phys. Rev. Lett.
**99**, 040401 (2007)CrossRefADSGoogle Scholar - 18.A. Spuntarelli, P. Pieri, G.C. Strinati, Phys. Rep.
**488**, 111 (2010)MathSciNetCrossRefADSGoogle Scholar - 19.F. Ancilotto, L. Salasnich, F. Toigo, Phys. Rev. A
**79**, 033627 (2009)CrossRefADSGoogle Scholar - 20.L. Salasnich, N. Manini, F. Toigo, Phys. Rev. A
**77**, 043609 (2008)CrossRefADSGoogle Scholar - 21.L. Salasnich, F. Ancilotto, N. Manini, F. Toigo, Laser Phys.
**19**, 636 (2009)CrossRefADSGoogle Scholar - 22.S.K. Adhikari, H. Lu, H. Pu, Phys. Rev. A
**80**, 063607 (2009)Google Scholar - 23.G. Watanabe, F. Dalfovo, F. Piazza, L.P. Pitaevskii, S. Stringari, Phys. Rev. A
**80**, 053602 (2009)CrossRefADSGoogle Scholar - 24.S. Giorgini, L. Pitaevskii, S. Stringari, Rev. Mod. Phys.
**80**, 1215 (2008)CrossRefADSGoogle Scholar - 25.P.G. de Gennes,
*Superconductivity of Metals and Alloys*(Benjamin, New York, 1966)zbMATHGoogle Scholar - 26.A.J. Leggett,
*Modern Trends in the Theory of Condensed Matter*, ed by A Pekalski, R, Przystawa (Springer-Verlag, Berlin, 1980)Google Scholar - 27.M. Randeria,
*Bose Einstein Condensation*, ed by A. Griffin, D. Snoke, S. Stringari (Cambridge, Cambridge, England, 1995)Google Scholar - 28.K.J. Challis, R.J. Ballagh, C.W. Gardiner, Phys. Rev. Lett.
**98**, 093002 (2007)CrossRefADSGoogle Scholar - 29.R.G. Scott, F. Dalfovo, L.P. Pitaevskii, S. Stringari, Phys. Rev. Lett.
**106**, 185301 (2011)CrossRefADSGoogle Scholar - 30.A. Bulgac, Y. Yu, Phys. Rev. Lett.
**88**, 042504 (2002)Google Scholar - 31.M. McNeil Forbes, R. Sharma, arXiv:1308.4387
- 32.R. Combescot, M.Y. Kagan, S. Stringari, Phys. Rev. A
**74**, 042717 (2006)Google Scholar - 33.M. Antezza, F. Dalfovo, L.P. Pitaevskii, S. Stringari, Phys. Rev. A
**76**, 043610 (2007)CrossRefADSGoogle Scholar - 34.R. Liao, J. Brand, Phys. Rev. A
**83**, 041604(R) (2011)CrossRefADSGoogle Scholar - 35.F. Piazza, L.A. Collins, A. Smerzi, Phys. Rev. A
**81**, 033613 (2010)CrossRefADSGoogle Scholar