Spectral singularities in PT-symmetric Bose-Einstein condensates

Abstract

We consider the model of a PT-symmetric Bose-Einstein condensate in a delta-functions double-well potential. We demonstrate that analytic continuation of the primarily non-analytic term |psi|^2 psi - occurring in the underlying Gross-Pitaevskii equation - yields new branch points where three levels coalesce. We show numerically that the new branch points exhibit the behaviour of exceptional points of second and third order. A matrix model which confirms the numerical findings in analytic terms is given.

15 pages, 9 figures, modifications in Figs. 1 and 2, additions in the text, to be published in J. Phys. A

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• Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
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• On the integrability of PT-symmetric dimers
• 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
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Asymmetric lasing at spectral singularities
• Wave emission and absorption at spectral singularities
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Dissipation-facilitated molecules in a Fermi gas with non-Hermitian spin-orbit coupling
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
• Metastable two-component solitons near an exceptional point
• Stability of Bose-Einstein condensates in a $\mathcal{P}\mathcal{T}$ symmetric double-$\delta$ potential close to branch points
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Bloch oscillations in a Bose-Hubbard chain with single-particle losses