We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides.We show that although the total norm of the system is not conserved in parity-time symmetric phase, the dark state intensity remains constant. However, in broken phase the eliminated waveguide loses its darkness, i.e., its field amplitude starts increasing. In both exact and broken phases, the effective Hamiltonian derived from the adiabatic elimination condition describes the dynamics of all states except the dark state. Specifically, it cannot predict the amplification in the intensity of the dark state. Our results can strengthen the control of the dynamics in cavities with active elements and improve the design of controllable absorbers.
Sharaf, Rahman; Dehghani, Mojgan; and Ramezani, Hamidrez, "Effect of non-Hermiticity on adiabatic elimination in coupled waveguides" (2018). Physics and Astronomy Faculty Publications and Presentations. 283.
Physical Review A