PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result which can be tested experimentally.

http://arxiv.org/abs/1307.0149

Optics (physics.optics); Quantum Physics (quant-ph)

A lattice of optical ring resonators can exhibit a topological insulator phase, with the direction of rotation in the resonators playing the role of spin. This occurs when the inter-resonator coupling is sufficiently large, and the synthetic magnetic vector potential set up by the couplers is zero. Using the transfer matrix method, we derive the band structure, phase diagram, and the projected band diagram showing the existence of spin-polarized edge states. When PT (parity/time-reversal) symmetric gain and loss are introduced, the system functions as an optical diode which does not require optical nonlinearities.

http://arxiv.org/abs/1212.5034
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)