Derek D. Scott, Yogesh N. Joglekar
We study the properties of an N-site tight-binding ring with parity and time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of non-Hermitian, PT-symmetric, loss and gain impurities \(\pm i\gamma\). The properties of such lattices with open boundary conditions have been intensely explored over the past two years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function \(t_\alpha(k)=[k(N-k)]^{\alpha/2}\) that, in an open lattice, leads to a strengthened PT-symmetric phase, and study the evolution of the PT-symmetric phase from the open chain to a ring. We show that, generally, periodic boundary conditions weaken the PT-symmetric phase, although for experimentally relevant lattice sizes \(N \sim 50\), it remains easily accessible. We show that the chirality, quantified by the (magnitude of the) average transverse momentum of a wave packet, shows a maximum at the PT-symmetric threshold. Our results show that although the wavepacket intensity increases monotonically across the PT-breaking threshold, the average momentum decays monotonically on both sides of the threshold.
http://arxiv.org/abs/1207.1945
Quantum Physics (quant-ph); Optics (physics.optics)