TY - JOUR

T1 - Solitons in Bose-Einstein condensates trapped in a double-well potential

AU - Shchesnovich, Valery S.

AU - Malomed, Boris A.

AU - Kraenkel, Roberto A.

N1 - Funding Information:
The research by VS was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil. BAM appreciates hospitality of Instituto de Fisica Teórica at Universidade Estadual Paulista (São Paulo, Brazil).

PY - 2004/2/1

Y1 - 2004/2/1

N2 - We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrödinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves ("radiation"). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system.

AB - We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrödinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves ("radiation"). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system.

KW - Coupled nonlinear Schrödinger equations

KW - Soliton stability

KW - Solitons in Bose-Einstein condensates

UR - http://www.scopus.com/inward/record.url?scp=0347758754&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2003.07.010

DO - 10.1016/j.physd.2003.07.010

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AN - SCOPUS:0347758754

SN - 0167-2789

VL - 188

SP - 213

EP - 240

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -