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.

arXiv comment9 pages, 6 figures, minor changes in the text, correction of two references

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• Giant Non-reciprocity Near Exceptional Point Degeneracies
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• Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates
• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• Photonic currents in driven and dissipative resonator lattices
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• 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
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• 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
• Effects of the third-order dispersion on continuous waves in complex potentials
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Computing eigenfunctions and eigenvalues of boundary value problems with the orthogonal spectral renormalization method
• Stability band structure for periodic states in periodic potentials