High-order exceptional points in supersymmetric arrays

• URL: http://arxiv.org/abs/2003.07510v1
• Date: Tue, 17 Mar 2020 03:15:43 GMT
• Title: High-order exceptional points in supersymmetric arrays
• Authors: S. M. Zhang, X. Z. Zhang, L. Jin, Z. Song
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 the 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 eigen frequency response to the perturbation $\epsilon$ acting on the resonator or waveguide couplings is $\epsilon^{1/N}$. Our findings reveal the importance of the intertwining operator technique for the spectral engineering and exemplify the practical application in non-Hermitian physics.

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