Sharp transition between ballistic and diffusive transport in PT-symmetric media

In this work, we show theoretically and experimentally that in certain parity-time (PT) symmetric systems both transport regimes coexist, however on different time scales. Our study was based on a PT-symmetric optical waveguide array exhibiting an alternating loss profile with homogeneous coupling between neighbouring waveguides, as indicated in Fig.1(a). Mathematically, the dynamics of such a structure can be described by a set of coupled equations, which read -i∂_za_n = αa_n + κb_n-1 + κb_n and -i∂_tb_n = βb_n+κa_n+1 +κa_n. Here, a_n and b_n represent the field amplitudes inside the lattice site, κ is the coupling coefficient, and z is the longitudinal propagation direction. The waveguides exhibit alternating, complex propagation constants which are denoted by the respective values of α and β.