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Supersymmetric Model of a Bose-Einstein Condensate in a 𝓟𝓣-Symmetric Double-delta Trap

Nikolas Abt, Holger Cartarius, Günter Wunner

arXiv:1410.7718International Journal of Theoretical PhysicsJan 29, 201515 citations

Bose-einstein condensation in a finite one-dimensional system due to an attractive delta potential

Mirabeau Dias, A. N. Chaba

Revista brasileira de fisicaJan 1, 19800 citations

Bose-Einstein condensation of spinor S=1 bosons

Longxiang Liu, Youjin Deng, Anatoly B. Kuklov

Bulletin of the American Physical SocietyMar 7, 20180 citations

Peakons in spinor F=1 Bose–Einstein condensates with PT-symmetric δ-function potentials

Lao, Jun-Yi, Qin, Zi-Yang, Zhang, Jia-Rui +1 more

By introducing PT-symmetric δ-function potentials into three-component Gross–Pitaevskii equations that describe spinor F=1 Bose–Einstein condensates, we obtain stable and unstable analytical peakon solutions which enable us to explore the patterns of mean-field and spin-exchange interaction in relation to variations in energy of nonlinear modes. Furthermore, using iterative algorithms, we generate a series of numerical solutions and represent several families of peakon solutions in the form of energy curves, examining the impact of parameters on energy. Additionally, we observe a closed-loop structure in the family of peakons, with P0 and μ0 serving as the coordinate axes. On this curve, we discover stable peakons exhibiting periodic oscillatory properties, which can be regarded as a form of internal energy transfer within the coupled system. This research could contribute to a more comprehensive understanding of coupled nonlinear systems and serve as a reference for future experiments in this domain.By introducing PT-symmetric δ-function potentials into three-component Gross–Pitaevskii equations that describe spinor F=1 Bose–Einstein condensates, we obtain stable and unstable analytical peakon solutions which enable us to explore the patterns of mean-field and spin-exchange interaction in relation to variations in energy of nonlinear modes. Furthermore, using iterative algorithms, we generate a series of numerical solutions and represent several families of peakon solutions in the form of energy curves, examining the impact of parameters on energy. Additionally, we observe a closed-loop structure in the family of peakons, with P0 and μ0 serving as the coordinate axes. On this curve, we discover stable peakons exhibiting periodic oscillatory properties, which can be regarded as a form of internal energy transfer within the coupled system. This research could contribute to a more comprehensive understanding of coupled nonlinear systems and serve as a reference for future experiments in this domain.

Jan 1, 20240 citations

On ground state of spinor Bose–Einstein condensates

Daomin Cao, I‐Liang Chern, Juncheng Wei

Nonlinear Differential Equations and Applications NoDEAFeb 7, 201143 citations

STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS

Andreas Löhle, Holger Cartarius, Daniel Haag +3 more

A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a PT symmetric external potential. If the strength of the in- and outcoupling is increased two PT broken states bifurcate from the PT symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a PT symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a PT symmetric external potential. If the strength of the in- and outcoupling is increased two PT broken states bifurcate from the PT symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a PT symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.

arXiv:1401.2354Acta PolytechnicaApr 30, 20147 citations

Peakons in spinor F=1 Bose–Einstein condensates with PT -symmetric δ -function potentials

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Peakons in spinor F=1 Bose–Einstein condensates with PT -symmetric δ -function potentials

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