Stability of Bose-Einstein condensates in a $\mathcal{P}\mathcal{T}$ symmetric double-$\delta$ potential close to branch points

Abstract

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 $\mathcal{P}\mathcal{T}$ symmetric external potential. If the strength of the in- and outcoupling is increased two $\mathcal{P}\mathcal{T}$ broken states bifurcate from the $\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ symmetric double-$\delta$ 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.

6 pages, 4 figures

References in corpus (11)

• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Stable dark solitons in PT-symmetric dual-core waveguides
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation

Cited by in corpus (6)

• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• Dipolar Bose-Einstein condensates in a PT-symmetric double-well potential
• A model of three coupled wave guides and third order exceptional points
• Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
• Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{P}\mathcal{T}$-symmetric double-delta trap
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates