Complex Berry phase dynamics in PT-symmetric coupled waveguides

We show that the analog of the geometric phase for non-Hermitian coupled waveguides with PT symmetry and at least one periodically varying parameter can be purely imaginary, is hence no longer a true phase and instead a real multiplier, and will consequently result in the amplification of Floquet sidebands in the system. The sideband peaks seen in the spectrum of the system's eigenstates after evolution along the waveguides can be directly mapped to the spectrum of the derivative of the geometric function. The sidebands are magnified (becoming virtually unstable) as the exceptional point of the system is approached, and nonadiabatic effects begin to appear. Because the system cannot evolve adiabatically in the vicinity of the exceptional point, PT symmetry will be observed breaking earlier than theoretically predicted.