Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains

Abstract

The $\mathcal{P}\mathcal{T}$ symmetry breaking threshold in discrete realizations of systems with balanced gain and loss is determined by the effective coupling between the gain and loss sites. In one dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. We present numerical results and analytical arguments for this enhancement. We then consider the effects of adding neutral sites to $\mathcal{P}\mathcal{T}$ symmetric dimer and trimer configurations and show that the threshold is more than doubled, or tripled by their presence. Our results provide a surprising way to engineer the $\mathcal{P}\mathcal{T}$ threshold in experimentally accessible samples.

arXiv comment7 pages, 6 figures

References in corpus (25)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Pseudo-Hermitian Representation of Quantum Mechanics
• PT-symmetry in honeycomb photonic lattices
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Projective Hilbert space structures at exceptional points
• Physics counterpart of the PT non-hermitian tight-binding chain
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• PT spectroscopy of the Rabi problem
• PT-symmetric Rabi model: Perturbation theory
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Degrees and signatures of broken PT-symmetry in (non-uniform) lattices
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Nonlinear PT-symmetric plaquettes
• Hermitian dynamics in a class of pseudo-Hermitian networks
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Dynamics, disorder effects, and PT-symmetry breaking in waveguide lattices with localized eigenstates
• Decays of degeneracies in PT-symmetric ring-shaped lattices
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions

Cited by in corpus (3)

• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• "Striped" Rectangular Rigid Box with Hermitian and non-Hermitian $\mathcal{P}\mathcal{T}$ Symmetric Potentials