Abstract
We have studied the dynamic evolution of the collective excitations in Bose-Einstein condensates in a deep optical lattice with tunable three-body interactions. Their dynamics is governed by a high order discrete nonlinear Schrödinger equation (DNLSE). The dynamical phase diagram of the system is obtained using the variational method. The dynamical evolution shows very interesting features. The discrete breather phase totally disappears in the regime where the three-body interaction completely dominates over the two-body interaction. The soliton phase in this particular regime exists only when the soliton line approaches the critical line in the phase diagram. When weak two-body interactions are reintroduced into this regime, the discrete breather solutions reappear, but occupies a very small domain in the phase space. Likewise, in this regime, the soliton as well as the discrete breather phases completely disappear if the signs of the two-and three-body interactions are opposite. We have analysed the causes of this unusual dynamical evolution of the collective excitations of the Bose-Einstein condensate with tunable interactions. We have also performed direct numerical simulations of the governing DNLS equation to show the existence of the discrete soliton solution as predicted by the variational calculations, and also to check the long term stability of the soliton solution.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Kraemer et al., Nature 440, 315 (2006)
V. Efimov, Phys. Lett. B 33, 563 (1970)
B. Huang et al., Phys. Rev. Lett. 112, 190401 (2014)
S. Will et al., Nature 465, 09036 (2010)
A. Safavi-Naini et al., Phys. Rev. Lett. 109, 135302 (2012)
F. Ferlaino, R. Grimm, Physics 3, 9 (2010)
T. Lompe et al., Science 330, 940 (2010)
A.J. Daley, J. Simon, Phys. Rev. A 89, 053619 (2014)
L. Pitaevskii, S. Stringari Bose-Einstein Condensation (Oxford University Press, Oxford, 2003)
B. Eiermann et al., Phys. Rev. Lett. 92, 230401 (2004)
R. Sarkar, B. Dey, Phys. Rev. E 76, 016605 (2007) and references therein
M. Bartenstein et al., Phys. Rev. Lett. 92, 203201 (2004)
Y. Wen-Mei et al., Commun. Theor. Phys. 51, 433 (2009)
L. Guan-Qiang et al., Phys. Rev. A 74, 055601 (2006)
L. Guan-Qiang et al., Commun. Theor. Phys. 50, 1129 (2008)
H. Ji-Xuan, Phys. Lett. A 368, 366 (2007)
L. Hao-Cai et al., Chin. Phys. Lett. 27, 030304 (2010)
P. Ping, L. Guan-Qiang, Chin. Phys. B 18, 3221 (2009)
E.B. Kolomeisky, T.J. Newman, J.P. Straley, X. Qi, Phys. Rev. Lett. 85, 1146 (2000)
E.H. Lieb, R. Seiringer, J. Yngvason, Phys. Rev. Lett. 91, 150401 (2003)
T. Kohler, Phys. Rev. Lett. 89, 210404 (2002)
C. Kittel, Introduction to Solid State Physics, 7th edn. (John Wiley and Sons Ltd., Singapore, 1996)
A. Trombettoni, A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001)
A. Trombettoni, A. Smerzi, J. Phys. B 34, 4711 (2001)
F.Kh. Abdullaev et al., Phys. Rev. A 64, 043606 (2001)
G.L. Alfimov et al., Phys. Rev. E 66, 046608 (2002)
A. Maluckov, L. Hadžievski, B.A. Malomed, Phys. Rev. E 76, 046605 (2007)
C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002), Chap. 7
J.J.G. Ripoli, V.M. Perez-Garcia, Phys. Rev. A 59, 2220 (1999)
V.M. Perez-Garcia et al., Phys. Rev. A 56, 1424 (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alakhaly, G.A., Dey, B. Discrete breather and soliton-mode collective excitations in Bose-Einstein condensates in a deep optical lattice with tunable three-body interactions. Eur. Phys. J. D 69, 92 (2015). https://doi.org/10.1140/epjd/e2015-50464-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2015-50464-6