Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

Physical Review Letters

Volumn 94, Issue 10, 2005, Pages

  Cozzini, M ^a   Fetter, A L ^b   Jackson, B ^a   Stringari, S ^a,c  

^a UNIVERSITY OF TRENTO   (Italy)

^b STANFORD UNIVERSITY   (United States)

^c LABORATOIRE KASTLER BROSSEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC MASS; GROSS-PITAEVSKII (GP) EQUATIONS; HARMONIC OSCILLATORS; VORTICITY;

CRYSTAL LATTICES; ELECTRON TRAPS; HARMONIC ANALYSIS; HYDRODYNAMICS; NUMERICAL ANALYSIS; OSCILLATIONS; VORTEX FLOW;

GAS CONDENSATES;

EID: 18144378437     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.100402     Document Type: Article

References (18)

1. V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, F. Chevy, and J. Dalibard, Europhys. Lett. 65, 594 (2004).
2. V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, F. Chevy, and J. Dalibard, Europhys. Lett. 65, 594 (2004).
3. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
4. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
5. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
6. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
7. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
8. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
9. A. L. Fetter, Phys. Rev. A 64, 063608 (2001); U. R. Fischer and G. Baym, Phys. Rev. Lett. 90, 140402 (2003); G. M. Kavoulakis and G. Baym, New J. Phys. 5, 51 (2003); E. Lundh, Phys. Rev. A 65, 043604 (2002); A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phys. Rev. A 69, 053619 (2004); A. Aftalion and I. Danaila, Phys. Rev. A 69, 033608 (2004); A. D. Jackson and G. M. Kavoulakis, Phys. Rev. A 70, 023601 (2004).
10. A. L. Fetter, B. Jackson, and S. Stringari, Phys. Rev. A 71, 013605 (2005).
11. M. Cozzini and S. Stringari, Phys. Rev. A 67, 041602(R) (2003).
12. The j = 0 solution is rejected due to its unphysical nature. Indeed, for the case m = 0 this solution does not conserve the particle number, while for m = 0 it gives rise to a divergent velocity field at the condensate boundaries.
13. 2, which correspond to the oscillation frequencies in an effective potential defined by the trap and the centrifugal force.
14. See for example F. Zambelli and S. Stringari, Phys. Rev. Lett. 81, 1754 (1998).
15. 2 - 2 can also be found within the hydrodynamic formalism by solving Eq. (5) perturbatively with respect to 1/ω.
16. 2〉.
17. The result for the quadrupole frequencies has been confirmed in the experiment of P. C. Haljan, I. Coddington, P. Engels, and E. A. Cornell, Phys. Rev. Lett. 87, 210403 (2001), where a harmonic trap was employed.
18. This scenario assumes that in the rotating frame only two levels (high and low lying) are excited by the operators F and F+. Numerical integration of Eq. (5) actually shows the occurrence of a very small splitting between the low-lying m = ±2 modes, which however barely affects the main results of the present analysis.