Moving along an exceptional surface towards a higher-order exceptional point

Abstract

Open systems with non-Hermitian degeneracies called exceptional points show a significantly enhanced response to perturbations in terms of large energy splittings induced by a small perturbation. This reaction can be quantified by the spectral response strength of the exceptional point. We extend the underlying theory to the general case where the dimension of the Hilbert space is larger than the order of the exceptional point. This generalization allows us to demonstrate an intriguing phenomenon: The spectral response strength of an exceptional point increases considerably and may even diverge to infinity under a parameter variation that eventually increases the order of the exceptional point. This dramatic behavior is in general not accompanied by a divergence of the energy eigenvalues and is shown to be related to the well-known divergence of Petermann factors near exceptional points. Finally, an accurate and robust numerical scheme for the computation of the spectral response strength based on the general theory and residue calculus is presented.

arXiv comment11 pages, 5 figures

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Cited by in corpus (5)

• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Generalized Petermann factor of non-Hermitian systems at exceptional points
• Higher-order exceptional points in composite non-Hermitian systems
• Exceptional deficiency of non-Hermitian systems
• Adjusting exceptional points using saturable nonlinearities