Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates

Abstract

A Bose-Einstein condensate in a double-well potential features stationary solutions even for attractive contact interaction as long as the particle number and therefore the interaction strength do not exceed a certain limit. Introducing balanced gain and loss into such a system drastically changes the bifurcation scenario at which these states are created. Instead of two tangent bifurcations at which the symmetric and antisymmetric states emerge, one tangent bifurcation between two formerly independent branches arises [D. Haag et al., Phys. Rev. A 89, 023601 (2014)]. We study this transition in detail using a bicomplex formulation of the time-dependent variational principle and find that in fact there are three tangent bifurcations for very small gain-loss contributions which coalesce in a cusp bifurcation.

arXiv comment5 pages, 4 figures

References in corpus (37)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• The physics of exceptional points
• PT-Symmetric Quantum Mechanics
• Visualization of Branch Points in PT-Symmetric Waveguides
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Collapse and Bose-Einstein condensation in a trapped Bose-gas with negative scattering length
• 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
• Signatures of three coalescing eigenfunctions
• Beyond mean-field dynamics in open Bose-Hubbard chains
• Stability of Bose condensed atomic Li-7
• Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
• A pumped atom laser
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Quantum master equation with balanced gain and loss
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
• A solvable model for solitons pinned to a PT-symmetric dipole
• Complex scaling approach to the decay of Bose-Einstein condensates
• Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices
• Nonlinear quantum dynamics in a PT-symmetric double well
• Bifurcations and exceptional points in dipolar Bose-Einstein condensates
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
• Collisions of anisotropic two-dimensional bright solitons in dipolar Bose-Einstein condensates
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Finite-Dimensional Bicomplex Hilbert Spaces
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential
• Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates
• Closed system approach to open systems: Tunneling decay of interacting cold bosons in an optical lattice

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• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
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• Bloch oscillations in a Bose-Hubbard chain with single-particle losses
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
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