Fano-Feshbach resonances in two-channel scattering around exceptional points

Abstract

It is well known that in open quantum systems resonances can coalesce at an exceptional point, where both the energies {\em and} the wave functions coincide. In contrast to the usual behaviour of the scattering amplitude at one resonance, the coalescence of two resonances invokes a pole of second order in the Green's function, in addition to the usual first order pole. We show that the interference due to the two pole terms of different order gives rise to patterns in the scattering cross section which closely resemble Fano-Feshbach resonances. We demonstrate this by extending previous work on the analogy of Fano-Feshbach resonances to classical resonances in a system of two driven coupled damped harmonic oscillators.

arXiv comment8 pages, 5 figures, submitted to J. Phys. A

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• Enhanced response of non-Hermitian photonic systems near exceptional points
• Fano resonances in scattering: an alternative perspective
• Experimental observation of the avoided crossing of two $S$-matrix resonance poles in an ultracold atom collider
• A unified approach to $\Lambda$-, $\Xi$- and $V$-type systems with one continuum
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