Derek D. Scott, Yogesh N. Joglekar

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 PT-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.

http://arxiv.org/abs/1203.1345

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)