Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates

Abstract

A PT-symmetric Bose-Einstein condensate can theoretically be 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 are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a PT-symmetric double-well if the tilt in the energy offsets of all further wells in the lattice is varied in time. We map the time-dependence of the amplitudes of a frozen Gaussian variational ansatz to a matrix model and increase the system size step by step starting with a six-well setup. In terms of this simple matrix model we derive conditions under which two wells of the Hermitian multi-well system behave exactly as the two wells of the PT-symmetric system.

13 pages, 8 figures

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Cited by in corpus (21)

• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Directed momentum current induced by the PT-symmetric driving
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Effective protection of quantum coherence by non-Hermitian driving
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• Systems that become $\mathcal{P}\mathcal{T}$ symmetric through interaction
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model
• Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential
• Broken Hermiticity phase transition in Bose-Hubbard model
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Controlling of blow-up responses by a nonlinear $\mathcal{P}\mathcal{T}$ symmetric coupling
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space
• Purity oscillations in coupled Bose-Einstein condensates
• Computing eigenfunctions and eigenvalues of boundary value problems with the orthogonal spectral renormalization method