Abstract
We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).
Similar content being viewed by others
References
E. P. Gross, Nuovo Cimento 20, 454 (1961); L. P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).
F. Dalfovo et al., Rev. Mod. Phys. 71, 463 (1999).
S. Burger et al., Phys. Rev. Lett. 83, 5198 (1999); E. A. Donley et al., Nature 412, 295 (2001); B. P. Anderson et al., Phys. Rev. Lett. 86, 2926 (2001); L. Khayakovich et al., Science 296, 1290 (2002); B. Eiermann et al., Phys. Rev. Lett. 92, 230401 (2004).
J. Forthàgh et al., Phys. Rev. Lett. 81, 5310 (1998); J. Reichel, Appl. Phys. B 74, 469 (2002); R. Folman et al., Adv. At. Mol. Opt. Phys. 48, 263 (2002).
R. Grimm et al., Adv. At. Mol. Opt. Phys. 42, 95 (2000).
Author information
Authors and Affiliations
Additional information
From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 80, No. 8, 2004, pp. 609–613.
Original English Text Copyright © 2004 by Fedele, Shukla, De Nicola, M. Man’ko, V. Man’ko, Cataliotti.
This article was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Fedele, R., Shukla, P.K., De Nicola, S. et al. Controlling potential traps for filtering solitons in Bose-Einstein condensates. Jetp Lett. 80, 535–539 (2004). https://doi.org/10.1134/1.1846114
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1846114