High-order exceptional points in supersymmetric arrays

Abstract

We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size N. The synthesized SUSY system is equivalent to a spin (N-1)/2 under an effective magnetic field. By considering an additional imaginary magnetic field, we obtain a generalized parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of coupled resonators or waveguides under a gradient gain and loss; all the N energy levels coalesce at an exceptional point (EP), forming an isotropic high-order EP with N states coalescence (EPN). Near the EPN, the scaling exponent of phase rigidity for each eigenstate is (N-1)/2; the eigenfrequency response to the perturbation ϵ acting on the resonator or waveguide couplings is ϵ1/N. Our findings reveal the importance of the intertwining operator technique for spectral engineering and exemplify the practical application in non-Hermitian physics.