Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well

Abstract

We show how non-Hermitian potentials used to describe probability gain and loss in effective theories of open quantum systems can be achieved by a coupling of the system to an environment. We do this by coupling a Bose-Einstein condensate (BEC) trapped in an attractive double-delta potential to a condensate fraction outside the double well. We investigate which requirements have to be imposed on possible environments with a linear coupling to the system. This information is used to determine an environment required for stationary states of the BEC. To investigate the stability of the system we use fully numerical simulations of the dynamics. It turns out that the approach is viable and possible setups for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a BEC are accessible. Vulnerabilities of the whole system to small perturbations can be adhered to the singular character of the simplified delta-shaped potential used in our model.

9 pages, 6 figures, minor changes in the text, correction of two references

References in corpus (13)

• Visualization of Branch Points in PT-Symmetric Waveguides
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
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• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
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Cited by in corpus (9)

• Magnetic suppression of non-Hermitian skin effects
• Quantum master equation with balanced gain and loss
• Giant Non-reciprocity Near Exceptional Point Degeneracies
• Balanced gain and loss in Bose-Einstein condensates without PT symmetry
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• 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
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations