Abstract
We consider a Bose-Einstein condensate with an attractive particle interaction in a symmetric double well potential. It is known that in the mean field description a symmetric solution for the condensate wavefunction becomes unstable when the interactions are stronger than some critical value. We analyze the system around the critical point applying the number conserving Bogoliubov theory and exact diagonalization of the two mode hamiltonian. It allows for estimation of the density fluctuations in the system. Fluctuations of the order parameter, which is defined in the mean field description, turn out to be maximal at the critical point.
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S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Phys. Rev. A 59, 620 (1999); E. A. Ostrovskaya, Y.S. Kivshar, M. Lisak, B. Hall, F. Cattani, and D. Anderson Phys. Rev. A 61, 031601 (R) (2000).
K. W. Mahmud, J. N. Kutz, and W. P. Reinhardt, Phys. Rev. A 66, 063607 (2002); P. Zin, E. Infeld, M. Matuszewski, G. Rowlands, and M. Trippenbach, Phys. Rev. A 73, 022105 (2006); E. Infeld, P. Zin, J. Gocalek, and M. Trippenbach, Phys. Rev. E 74, 026610 (2006).
J. I. Cirac, M. Lewenstein, K. Mølmer, and P. Zoller, Phys. Rev. A 57, 1208 (1998); J. Ruostekoski, M. J. Collett, R. Graham, and D. F. Walls, Phys. Rev. A 57, 511 (1998); D. Gordon and C. M. Savage, Phys. Rev. A 59, 4623 (1999); D. A. R. Dalvit, J. Dziarmaga, and W. H. Zurek, Phys. Rev. A 62, 013607 (2000); A. Micheli, D. Jaksch, J. I. Cirac, and P. Zoller, Phys. Rev. A 67, 013607 (2003).
Z. P. Karkuszewski, K. Sacha, and A. Smerzi, Eur. Phys. J. D 21, 251 (2002); B. Wu, R. B. Diener, and Q. Niu, Phys. Rev. A 65, 025601 (2002); D. Witthaut, E. M. Graefe, and J. Korsch, Phys. Rev. A 73, 063609 (2006).
L. Pitaevskii and S. Stringari, Phys. Rev. Lett. 87, 180402 (2001).
M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. 95, 110405 (2005); R. Gati, B. Hemmerling, J. Fölling, M. Albiez, and M. K. Oberthaler, Phys. Rev. Lett. 96, 130404 (2006).
For a topical review see R. Gati and M. Oberthaler, J. Phys. B 40, R61 (2007) and references therein.
R. Kanamoto, H. Saito, and M. Ueda, Phys. Rev. A 73, 033611 (2006).
G. J. Milbum, J. Corney, E. M. Wright, and D. P. Walls, Phys. Rev. A 55, 4318 (1997).
R. Botet and R. Jullien, Phys. Rev. B 28, 3955 (1983).
P. Ziń, J. Chwedeńczuk, B. Oleś, K. Sacha, and M. Trippenbach, EPL 83, 64007 (2008).
M. D. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959); C. W. Gardiner, Phys. Rev. A 56, 1414 (1997); M. D. Girardeau, Phys. Rev. A 58, 775 (1998).
Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998); Y. Castin, in Les Houches Session, LXXII, Coherent Atomic Matter Waves 1999, Ed. by R. Kaiser, C. Westbrook, and F. David (Springer, Berlin, Heilderberg, New York, 2001).
A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
J. Dziarmaga and K. Sacha, Phys. Rev. A 67, 033608 (2003); J. Dziarmaga and K. Sacha, J. Phys. B 39, 57 (2006).
B. Oleś and K. Sacha, J. Phys. A 41, 145005 (2008).
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Oleś, B., Ziń, P., Chwedeńczuk, J. et al. Bose-Einstein condensate in a double well potential in the vicinity of a critical point. Laser Phys. 20, 671–677 (2010). https://doi.org/10.1134/S1054660X10050130
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DOI: https://doi.org/10.1134/S1054660X10050130