Resolving the topology of encircling multiple exceptional points

• Published in: Nature communications Vol. 15; no. 1; p. 1369
• Main Authors: Guria, Chitres, Zhong, Qi, Ozdemir, Sahin Kaya, Patil, Yogesh S. S., El-Ganainy, Ramy, Harris, Jack Gwynne Emmet
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 14.02.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/1130/2800; 639/766/119/2792; Control systems; Coupled modes; Eigenvalues; Euclidean space; Humanities and Social Sciences; Hybrid systems; Knots; Mechanical systems; multidisciplinary; Parameters; Physics; Science; Science (multidisciplinary); Topology
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-024-45530-6

Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling of exceptional points (EPs). To date, most work has focused on systems consisting of two modes that are tuned by two control parameters and have isolated EPs. While these systems exhibit exotic features related to EP encircling, it has been shown that richer behavior occurs in systems with more than two modes. Such systems can be tuned by more than two control parameters, and contain EPs that form a knot-like structure. Control loops that encircle this structure cause the system’s eigenvalues to trace out non-commutative braids. Here we consider a hybrid scenario: a three-mode system with just two control parameters. We describe the relationship between control loops and their topology in the full and two-dimensional parameter space. We demonstrate this relationship experimentally using a three-mode mechanical system in which the control parameters are provided by optomechanical interaction with a high-finesse optical cavity. When multiple oscillators are tuned, degeneracies occur on a knot-shaped region in the space of tuning parameters. This knot influences how such systems can be tuned. Here, the authors reconcile two common means for visualizing this influence.