Localized breathing oscillations of Bose-Einstein condensates in periodic traps

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 3, 2002, Pages 336101-336106

  Carretero Gonzalez R ^a   Promislow, K ^b  

^a SAN DIEGO STATE UNIVERSITY   (United States)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; CONDENSATION; CRYSTAL LATTICES; HARMONIC GENERATION; INTEGRATION; LOW TEMPERATURE EFFECTS; NONLINEAR EQUATIONS; OSCILLATIONS; PERTURBATION TECHNIQUES; POTENTIAL ENERGY; SOLITONS; WAVE EQUATIONS;

BOSE EINSTEIN CONDENSATES (BEC); PERIODIC TRAPS;

ATOMIC PHYSICS;

EID: 0036757462     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.66.033610     Document Type: Article

References (45)

1. B.P. Anderson and M.A. Kasevich, Science 282, 1686 (1998); D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998).
2. B.P. Anderson and M.A. Kasevich, Science 282, 1686 (1998); D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998).
3. K. Berg-Sørensen and K. Mølmer, Phys. Rev. A 58, 1480 (1998).
4. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001).
5. P.S. Jessen and I.H. Deutsch, Adv. At., Mol., Opt. Phys. 37, 95 (1996); K.I. Petsas et al., Phys. Rev. A 50, 5173 (1994).
6. P.S. Jessen and I.H. Deutsch, Adv. At., Mol., Opt. Phys. 37, 95 (1996); K.I. Petsas et al., Phys. Rev. A 50, 5173 (1994).
7. J. Javanainen, Phys. Rev. A 60, 4902 (1999).
8. M.L. Chiofalo and M.P. Tosi, Phys. Lett. A 268, 406 (2000).
9. F. Kh. Abdullaev et al., Phys. Rev. A 64, 043606 (2001).
10. E.P. Gross, Nuovo Cimento 20, 454 (1961); L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).
11. E.P. Gross, Nuovo Cimento 20, 454 (1961); L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).
12. F. Dalfovo et al., Rev. Mod. Phys. 71, 463 (1999).
13. A.D. Jackson et al., Phys. Rev. A 58, 2417 (1998); V. Pérez-García et al., ibid. 57, 3837 (1998); M. Key et al., Phys. Rev. Lett. 84, 1371 (2000); N.H. Dekker et al., ibid. 84, 1124 (2000).
14. A.D. Jackson et al., Phys. Rev. A 58, 2417 (1998); V. Pérez-García et al., ibid. 57, 3837 (1998); M. Key et al., Phys. Rev. Lett. 84, 1371 (2000); N.H. Dekker et al., ibid. 84, 1124 (2000).
15. A.D. Jackson et al., Phys. Rev. A 58, 2417 (1998); V. Pérez-García et al., ibid. 57, 3837 (1998); M. Key et al., Phys. Rev. Lett. 84, 1371 (2000); N.H. Dekker et al., ibid. 84, 1124 (2000).
16. A.D. Jackson et al., Phys. Rev. A 58, 2417 (1998); V. Pérez-García et al., ibid. 57, 3837 (1998); M. Key et al., Phys. Rev. Lett. 84, 1371 (2000); N.H. Dekker et al., ibid. 84, 1124 (2000).
17. P.A. Ruprecht et al., Phys. Rev. A 51, 4704 (1995).
18. J. Reichel et al., Phys. Rev. Lett. 83, 3398 (1999); W. Hänsel et al., ibid. 86, 608 (2001); J. Reichel et al., Appl. Phys. B: Lasers Opt. B72, 81 (2000).
19. J. Reichel et al., Phys. Rev. Lett. 83, 3398 (1999); W. Hänsel et al., ibid. 86, 608 (2001); J. Reichel et al., Appl. Phys. B: Lasers Opt. B72, 81 (2000).
20. J. Reichel et al., Phys. Rev. Lett. 83, 3398 (1999); W. Hänsel et al., ibid. 86, 608 (2001); J. Reichel et al., Appl. Phys. B: Lasers Opt. B72, 81 (2000).
21. Th. Busch and J.R. Anglin, Phys. Rev. Lett. 84, 2298 (2000); S. Burger et al., ibid. 83, 5198 (2000).
22. Th. Busch and J.R. Anglin, Phys. Rev. Lett. 84, 2298 (2000); S. Burger et al., ibid. 83, 5198 (2000).
23. B. Deconinck et al., e-print cond-mat/0106231.
24. M. Schiffer et al., Appl. Phys. B: Lasers Opt. B67, 705 (1998); E.M. Wright et al., Phys. Rev. A 63, 013608 (2001).
25. M. Schiffer et al., Appl. Phys. B: Lasers Opt. B67, 705 (1998); E.M. Wright et al., Phys. Rev. A 63, 013608 (2001).
26. Collapse for attractive BECs is identified with the collapse of the NLS in dimensions D 2. Since the NLS does not blow up in 1D, designing a trap that confines the BEC to an almost perfect 1D profile (a very thin cigar shape) could arrest, or at least delay, the collapse.
27. C.C. Bradley et al., Phys. Rev. Lett. 78, 985 (1997).
28. J.C. Bronski, L.D. Carr, R. Carretero-González, B. Deconinck, J.N. Kutz, and K. Promislow, Phys. Rev. E 64, 056615 (2001).
29. V.I. Karpman and V. Solov'ev, Physica D 3, 142 (1981).
30. R. Scharf and A.R. Bishop, Phys. Rev. E 47, 1375 (1993); V. Pérez-García et al., Phys. Rev. Lett. 77, 5320 (1996).
31. R. Scharf and A.R. Bishop, Phys. Rev. E 47, 1375 (1993); V. Pérez-García et al., Phys. Rev. Lett. 77, 5320 (1996).
32. V.S. Gerdjikov et al., Phys. Rev. E 55, 6039 (1997); J.M. Arnold, ibid. 60, 979 (1999).
33. V.S. Gerdjikov et al., Phys. Rev. E 55, 6039 (1997); J.M. Arnold, ibid. 60, 979 (1999).
34. R. Carretero-González and K. Promislow, Discrete Contin. Dyn. Syst. Ser. B (to be published).
35. M. Toda, Theory of Nonlinear Lattices (Springer, New York, 1989).
36. J. Denschlag et al., Science 287, 97 (2000).
37. Y.S. Kivshar, Phys. Rev. E 48, R43 (1993); S. Flach and C.R. Willis, Phys. Rep. 295, 181 (1998); T. Bountis et al., Phys. Lett. A 268, 50 (2000).
38. Y.S. Kivshar, Phys. Rev. E 48, R43 (1993); S. Flach and C.R. Willis, Phys. Rep. 295, 181 (1998); T. Bountis et al., Phys. Lett. A 268, 50 (2000).
39. Y.S. Kivshar, Phys. Rev. E 48, R43 (1993); S. Flach and C.R. Willis, Phys. Rep. 295, 181 (1998); T. Bountis et al., Phys. Lett. A 268, 50 (2000).
40. The remaining intersections, the even ones, also give rise to a homoclinic orbit with a central portion consisting of two identical amplitudes [22].
41. R.S. MacKay and S. Aubry, Nonlinearity 7, 1623 (1994); S. Flach, Phys. Rev. E 51, 1503 (1995).
42. R.S. MacKay and S. Aubry, Nonlinearity 7, 1623 (1994); S. Flach, Phys. Rev. E 51, 1503 (1995).
43. S. Aubry, Physica D 71, 196 (1994).
44. D. Chen et al., Phys. Rev. Lett. 77, 4776 (1996).
45. I.H. Deutsch et al., Fortschr. Phys. 48, 923 (2000).