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 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 acting on the resonator or waveguide couplings is 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. arXiv:2003.07510v1 [quant-ph]

High‐order exceptional points and enhanced sensing in subwavelength resonator arrays

“…An exceptional point with the same qualitative features as in Figure 2a was previously observed in the setting of a Hamiltonian system in Ref. 13.…”

“…These examples all follow the same pattern, whereby the gain/loss grows linearly away from the center (previously reported by Ref. 13). We expect similar behavior for even larger , which demonstrates the possibility to create asymptotic exceptional points of arbitrary order.…”

“…High‐order exceptional points have previously been observed in ‐symmetric structures, for example, by Refs. 10–13.…”

“…This approach allows us to demonstrate analogues of the exceptional points reported in, e.g., Ref. 13 and, further, reveal a rich variety of configurations and symmetries which produce high‐order exceptional points.…”

High-order exceptional point in a nanofiber cavity quantum electrodynamics system

“…In particular, high-order exceptional points can also appear in non-Hermitian systems. Obviously, three or more eigenvalues simultaneously coalesce at these points [39][40][41][42][43][44][45]. Although it is more complex than second-order EPs in theory, but it can display richer physical phenomena near these points.…”