Figure 2
(a) Diabolical point (DP) of real energy spectrum of the Hermitian Hamiltonian (5) with \(\beta =0\). DP bifurcates into two EPs, shown in (b,c) for \(\beta =1\) in the real and imaginary parts of eigenspectrum, correspondingly. Naïve consideration predicts that a 4π-rotation (red trajectory) around an EP would bring the system back to its initial state (up to a phase factor). (d–f) Numerical simulations of state evolution during clockwise (purple) and anti-clockwise (green) encircling of the EP, illustrating non-adiabatic state-flip events as sharp jumps between two spectral surfaces. The system’s final state after a complete 2π-rotation depends on the encircling direction, illustrating non-reciprocity of non-Hermitian parametric driving. The non-reciprocal time evolution is shown for the cases of (d) encircling of a single EP, (e) circular trajectory in the vicinity of the EP, and (f) complete encircling of both EPs.
