Hermitian four-well potential as a realization of a PT-symmetric system

Abstract

A PT-symmetric Bose-Einstein condensate can be theoretically described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents of a two-well system are implemented by coupling two additional wells to the system, which act as particle reservoirs. In terms of a simple four-mode model we derive conditions under which the two middle wells of the Hermitian four-well system behave exactly as the two wells of the PT-symmetric system. We apply these conditions to calculate stationary solutions and oscillatory dynamics. By means of frozen Gaussian wave packets we relate the Gross-Pitaevskii equation to the four-mode model and give parameters required for the external potential, which provides approximate conditions for a realistic experimental setup.

5 pages, 4 figures, Figures 3 and 4 modified

References in corpus (12)

• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• PT-Symmetric Electronics
• 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
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Bypassing the bandwidth theorem with PT symmetry
• Realization of a single Josephson junction for Bose-Einstein condensates
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate

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• The Dissipative Bose-Hubbard Model. Methods and Examples
• Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials
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• Balanced gain and loss in Bose-Einstein condensates without PT symmetry
• Photonic currents in driven and dissipative resonator lattices
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
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• Spin Josephson effects of spin-orbit-coupled Bose-Einstein condensates in a non-Hermitian double well
• Stability of Bose-Einstein condensates in a $\mathcal{P}\mathcal{T}$ symmetric double-$\delta$ potential close to branch points
• Time-dependent spectral renormalization method
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• PT-Symmetric potential impact on the scattering of a Bose-Einstein condensate from a Gaussian Obstacle
• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Perpetual emulation threshold of PT-symmetric Hamiltonians
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Purity oscillations in coupled Bose-Einstein condensates