## PT-symmetry breaking with divergent potentials: lattice and continuum cases

Yogesh N. Joglekar, Derek D. Scott, Avadh Saxena

We investigate the parity- and time-reversal (PT)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, PT-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile PT threshold for an open finite lattice, we show that continuum loss-gain potentials $$V_a(x)\sim i|x|^a{\rm sign}(x)$$ have a positive PT-breaking threshold for $$\alpha>−2$$, and a zero threshold for α≤−2. When α<0 localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of PT-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the PT-symmetry broken region.

http://arxiv.org/abs/1403.4204
Quantum Physics (quant-ph); Optics (physics.optics)