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 (\(\mathcal{PT}\)) 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, \(\mathcal{PT}\)-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 \(\mathcal{PT}\) symmetry breaking. We discuss implications of our results to systems with specific tunneling profiles, and open or periodic boundary conditions.

http://arxiv.org/abs/1302.4314
Quantum Physics (quant-ph); Optics (physics.optics)

Recently, waveguide lattices with non-uniform tunneling have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates. Here, we investigate the dynamics, localization, and parity- and time-reversal-(PT) symmetry breaking in lattices with only localized eigenstates. We propose three families of tunneling profiles that lead to qualitatively different single-particle time evolution, and show that the effects of weak disorder contain signatures of the localized or extended nature of clean-lattice eigenstates. Our results suggest that waveguide lattices with only localized eigenstates will exhibit a wide array of phenomena that are absent in traditional systems.

http://arxiv.org/abs/1108.1402
Optics (physics.optics); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)