Nonlinear quantum dynamics in a PT-symmetric double well

Abstract

We investigate the mean-field dynamics of a Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii equation (GPE) in a double-well potential with particle gain and loss, rendering the system PT-symmetric. The stationary solutions of the system show a change from elliptically stable behavior to hyperbolically unstable behavior caused by the appearance of PT-broken solutions of the GPE and influenced by the nonlinear interaction. The dynamical behavior is visualized using the Bloch sphere formalism. However, the dynamics is not restricted to the surface of the sphere due to the nonlinear and non-Hermitian nature of the system.

10 pages, 9 figures, additions in the text, two figures added

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• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
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• Stationary states in the many-particle description of Bose-Einstein condensates with balanced gain and loss
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model
• PT-symmetric gain and loss in a rotating Bose-Einstein condensate
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates
• Acute entanglement and Photon/Phonons statistics in a balanced/unbalanced PT-symmetry systems
• Non-Hermitian interaction of a discrete state with a continuum
• Hybrid Breathers in Nonlinear $\mathcal{P}\mathcal{T}$-Symmetric Metamaterials