Stationary states of a PT-symmetric two-mode Bose-Einstein condensate

Abstract

The understanding of nonlinear PT-symmetric quantum systems, arising for example in the theory of Bose-Einstein condensates in PT-symmetric potentials, is widely based on numerical investigations, and little is known about generic features induced by the interplay of PT-symmetry and nonlinearity. To gain deeper insights it is important to have analytically solvable toy-models at hand. In the present paper the stationary states of a simple toy-model of a PT-symmetric system are investigated. The model can be interpreted as a simple description of a Bose-Einstein condensate in a PT-symmetric double well trap in a two-mode approximation. The eigenvalues and eigenstates of the system can be explicitly calculated in a straight forward manner; the resulting structures resemble those that have recently been found numerically for a more realistic PT-symmetric double delta potential. In addition, a continuation of the system is introduced that allows an interpretation in terms of a simple linear matrix model.

13 pages, 4 figures

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• Quantum noise effects with Kerr nonlinearity enhancement in coupled gain-loss waveguides
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• Nonlinear PT-symmetric plaquettes
• Multi-stability and condensation of exciton-polaritons below threshold
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Bose-Einstein condensates with balanced gain and loss beyond mean-field theory
• Balanced gain and loss in Bose-Einstein condensates without PT symmetry
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Adjusting exceptional points using saturable nonlinearities
• Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology