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.

arXiv comment13 pages, 4 figures

References in corpus (28)

• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• PT-Symmetric Quantum Mechanics
• Visualization of Branch Points in PT-Symmetric Waveguides
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Spontaneous rotating vortex lattices in a pumped decaying condensate
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• 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
• PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Time evolution of non-Hermitian Hamiltonian systems
• Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure
• Complex Correspondence Principle
• Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
• Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer
• Wave packet evolution in non-Hermitian quantum systems
• Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
• Complex scaling approach to the decay of Bose-Einstein condensates
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• Barrier transmission for the one-dimensional nonlinear Schrödinger equation: resonances and transmission profiles
• Hamiltonian Quantum Dynamics With Separability Constraints
• Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential
• PT-symmetry breaking in complex nonlinear wave equations and their deformations

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