Abstract.
Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices have been studied. For a weak lattice potential, the perturbed correction to the heteroclinic orbit in a repulsive system is constructed. We find the boundedness conditions of the perturbed correction contain the Melnikov chaotic criterion predicting the onset of Smale-horseshoe chaos. The effect of the chemical potential on the spatiotemporal dynamics is numerically investigated. It is revealed that the variance of the chemical potential can lead the systems into chaos. Regulating the intensity of the lattice potential can efficiently suppress the chaos resulting from the variance of the chemical potential. And then the effect of the phenomenological dissipation is considered. Numerical calculation reveals that the chaos in the dissipative system can be suppressed by adjusting the chemical potential and the intensity of the lattice potential.
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References
M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)
K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)
N.K. Efremidis, S. Sears, D.N. Christodoulides, J.W. Fleischer, M. Segev, Phys. Rev. E 66, 046602 (2002)
M. BenDahan, E. Peik, J. Reichel, Y. Castin, C. Salomon, Phys. Rev. Lett. 76, 4508 (1996)
B.P. Anderson, M.A. Kasevich, Science 282, 1686 (1998)
S. Liu, H. Xiong, Z. Xu, G. Huang, J. Phys. B 36, 2083 (2003)
J.K. Pachos, P.L. Knight, Phys. Rev. Lett. 91, 107902 (2003)
R. Ionicioiu, P. Zanardi, Phys. Rev. A 66, 050301(R) (2002)
O. Morsch, J.H. Muller, M. Cristiani, D. Ciampini, E. Arimondo, Phys. Rev. Lett. 87, 140402 (2001)
D.I. Choi, Q. Niu, Phys. Rev. Lett. 82, 2022 (1999)
B. Wu, Q. Niu, Phys. Rev. A 64, 061603(R) (2001)
M. Cristiani, O. Morsch, J.H. Müller, D. Ciampini, E. Arimondo, Phys. Rev. A 65, 063612 (2002)
J. Liu et al., Phys. Rev. A 66, 023404 (2002)
D.I. Choi, Q. Niu, Phys. Lett. A 318, 558 (2003)
A. Trombettoni, A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001)
K. Berg-Sørensen, K. Mølmer, Phys. Rev. A 58, 1480 (1998)
M. Holthaus, J. Opt. B: Quant. Semiclass. Opt. 2, 589 (2000)
M.M. Cerimele, M.L. Chiofalo, F. Pistella, S. Succi, M.P. Tosi, Phys. Rev. E 62, 1382 (2000)
R.G. Scott, A.M. Martin, T.M. Fromhold, S. Bujkiewicz, F.W. Sheard, M. Leadbeater, Phys. Rev. Lett. 90, 110404 (2003)
G. Chong, W. Hai, Q. Xie, Chaos 14, 217 (2004)
G. Chong, W. Hai, Q. Xie, Phys. Rev. E 71, 016202 (2005)
P.A. Ruprecht, M. Edwards, K. Burnett, C.W. Clark, Phys. Rev. A 54, 4178 (1996)
J.H. Denschlag et al., J. Phys. B 35, 3095 (2002)
A.S. Mellish, G. Duffy, C. McKenzie, R. Geursen, A.C. Wilson, Phys. Rev. A 68, 051601(R) (2003)
L. Fallani, F.S. Cataliotti, J. Catani, C. Fort, M. Modugno, M. Zawada, M. Inguscio, Phys. Rev. Lett. 91, 240405 (2003)
W. Hai, C. Lee, G. Chong, L. Shi, Phys. Rev. E 66, 026202 (2002)
N.G. Parker, N.P. Proukakis, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 92, 160403 (2004); N.G. Parker, N.P. Proukakis, C.F. Barenghi, C.S. Adams, J. Phys. B 37, S175 (2004)
N.P. Proukakis, N.G. Parker, C.F. Barenghi, C.S. Adams, Phys. Rev. Lett. 93, 130408 (2004)
Y. Kagan, E.L. Surkov, G.V. Shlyapnikov, Phys. Rev. Lett. 79, 2604 (1997); S.L. Cornish, N.R. Claussen, J.L. Roberts, E.A. Cornell, C.E. Wieman, Phys. Rev. Lett. 85, 1795 (2000)
M. Machholm, C.J. Pethick, H. Smith, Phys. Rev. A 67, 053613 (2003)
E.V. Goldstein, P. Meystre, Phys. Rev. A 59, 1509 (1999)
E.V. Goldstein, P. Meystre, Phys. Rev. A 59, 3896 (1999)
H.Y. Ling, Phys. Rev. A 65, 013608 (2001)
Q. Xie, W. Hai, G. Chong, Chaos 13, 801 (2003); G. Chong, W. Hai, Q. Xie, Chaos 14, 217 (2004)
F. Li, W. Hai, Acta Phys. Sin. 53, 1309 (2004); F. Li, W. Hai, G. Chong, Q. Xie, Commun. Theor. Phys. 42, 599 (2004)
F. Li, W. Hai, Z. Ren, W. Shu, Phys. Lett. A 355, 104 (2006)
W. Hai, Y. Duan, X. Zhu, X. Luo, L. Shi, J. Phys. A 31, 2991 (1998)
S. Inouye et al., Nature 392, 151 (1998)
S.T. Vohra et al., Phys. Rev. Lett. 75, 65 (1995); K. Taniguchi, Y. Kawai, Phys. Rev. Lett. 83, 548 (1999); C.U. Choe et al., Phys. Rev. E 72, 036206 (2005)
E. Ott, C. Grebogi, J. Yorke, Phys. Rev. Lett. 64, 1196 (1990)
Y. Braiman, I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); R. Chacón, J.D. Bejarano, Phys. Rev. Lett. 71, 3103 (1993)
P.O. Fedichev et al., Phys. Rev. A 60, 3220 (1999)
A. Muryshev et al., Phys. Rev. Lett. 89, 110401 (2002)
S. Choi, S.A. Morgan, K. Burnett, Phys. Rev. A 57, 4057 (1998)
K. Kasamatsu, M. Tsubota, M. Ueda, Phys. Rev. A 67, 033610 (2003)
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Li, F., Shu, W., Jiang, J. et al. Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices. Eur. Phys. J. D 41, 355–361 (2007). https://doi.org/10.1140/epjd/e2006-00247-3
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DOI: https://doi.org/10.1140/epjd/e2006-00247-3
PACS.
- 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations
- 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow
- 05.45.Ac Low-dimensional chaos
- 05.45.Gg Control of chaos, applications of chaos