Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well

Abstract

The observation of PT symmetry in a coupled optical wave guide system that involves a complex refractive index has been demonstrated impressively in the experiment by Rüter el al. (Nat. Phys. 6, 192, 2010). This is, however, only an optical analogue of a quantum system, and it would be highly desirable to observe the manifestation of PT symmetry and the resulting properties also in a real, experimentally accessible, quantum system. Following a suggestion by Klaiman et al. (Phys. Rev. Lett. 101, 080402, 2008), we investigate a PT symmetric arrangement of a Bose-Einstein condensate in a double well potential, where in one well cold atoms are injected while in the other particles are extracted from the condensate. We investigate, in particular, the effects of the nonlinearity in the Gross-Pitaevskii equation on the PT properties of the condensate. To study these effects we analyze a simple one-dimensional model system in which the condensate is placed into two PT symmetric delta-function traps. The analysis will serve as a useful guide for studies of the behaviour of Bose-Einstein condensates in realistic PT symmetric double wells.

5 pages, 3 figures (one redundant figure removed), minor changes in the discussion

References in corpus (18)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• The physics of dipolar bosonic quantum gases
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity
• Solitons in PT-symmetric nonlinear lattices
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• 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
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
• Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
• Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate
• Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices
• Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice
• The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
• An explicitly solvable model of the spontaneous PT-symmetry breaking

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