PT symmetric lattices with a local degree of freedom

Abstract

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{P}\mathcal{T}$) operations. Here, we model and investigate the effects of a local, two-state, quantum degree of freedom, called a pseudospin, on a one-dimensional tight-binding lattice with position-dependent tunneling amplitudes and a single pair of non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric impurities. We show that if the resulting Hamiltonian is invariant under exchange of two pseudospin labels, the system can be decomposed into two uncoupled systems with tunable threshold for $\mathcal{P}\mathcal{T}$ symmetry breaking. We discuss implications of our results to systems with specific tunneling profiles, and open or periodic boundary conditions.

4 pages. 3 figures

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• Observation of PT phase transition in a simple mechanical system
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• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Gegenbauer-solvable quantum chain model
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Cited by in corpus (5)

• Convective and absolute PT symmetry breaking in tight-binding lattices
• Revisiting the optical $PT$-symmetric dimer
• An introduction to arrays of coupled waveguides
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Parity-time symmetry under magnetic flux