PT-symmetry breaking and universal chirality in a PT-symmetric ring

Abstract

We investigate the properties of an $N$-site tight-binding lattice with periodic boundary condition (PBC) in the presence of a pair of gain and loss impurities $\pm i\gamma$, and two tunneling amplitudes $t_0,t_b$ that are constant along the two paths that connect them. We show that the parity and time-reversal ($\mP\mT$)-symmetric phase of the lattice with PBC is robust, insensitive to the distance between the impurities, and that the critical impurity strength for PT-symmetry breaking is given by ${\gamma }_{PT}=|t_0-t_b|$. We study the time-evolution of a typical wave packet, initially localized on a single site, across the PT-symmetric phase boundary. We find that it acquires chirality with increasing $\gamma$, and the chirality reaches a universal maximum value at the threshold, $\gamma ={\gamma }_{PT}$, irrespective of the initial location of the wave packet or the lattice parameters. Our results imply that PT-symmetry breaking on a lattice with PBC has consequences that have no counterpart in open chains.

5 pages, 3 figures

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Cited by in corpus (4)

• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring