Measuring the knot of non-Hermitian degeneracies and non-commuting braids.

Autor: Patil YSS; Department of Physics, Yale University, New Haven, CT, USA. yogesh.patil@yale.edu., Höller J; Department of Physics, Yale University, New Haven, CT, USA.; Howard Hughes Medical Institute, Janelia Research Campus, Ashburn, VA, USA., Henry PA; Department of Applied Physics, Yale University, New Haven, CT, USA., Guria C; Department of Physics, Yale University, New Haven, CT, USA., Zhang Y; Department of Physics, Yale University, New Haven, CT, USA., Jiang L; Department of Physics, Yale University, New Haven, CT, USA., Kralj N; Department of Physics, Yale University, New Haven, CT, USA.; Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark., Read N; Department of Physics, Yale University, New Haven, CT, USA.; Department of Applied Physics, Yale University, New Haven, CT, USA.; Yale Quantum Institute, Yale University, New Haven, CT, USA., Harris JGE; Department of Physics, Yale University, New Haven, CT, USA. jack.harris@yale.edu.; Department of Applied Physics, Yale University, New Haven, CT, USA. jack.harris@yale.edu.; Yale Quantum Institute, Yale University, New Haven, CT, USA. jack.harris@yale.edu.
Jazyk: angličtina
Zdroj: Nature [Nature] 2022 Jul; Vol. 607 (7918), pp. 271-275. Date of Electronic Publication: 2022 Jul 13.
DOI: 10.1038/s41586-022-04796-w
Abstrakt: Any system of coupled oscillators may be characterized by its spectrum of resonance frequencies (or eigenfrequencies), which can be tuned by varying the system's parameters. The relationship between control parameters and the eigenfrequency spectrum is central to a range of applications 1-3 . However, fundamental aspects of this relationship remain poorly understood. For example, if the controls are varied along a path that returns to its starting point (that is, around a 'loop'), the system's spectrum must return to itself. In systems that are Hermitian (that is, lossless and reciprocal), this process is trivial and each resonance frequency returns to its original value. However, in non-Hermitian systems, where the eigenfrequencies are complex, the spectrum may return to itself in a topologically non-trivial manner, a phenomenon known as spectral flow. The spectral flow is determined by how the control loop encircles degeneracies, and this relationship is well understood for [Formula: see text] (where [Formula: see text] is the number of oscillators in the system) 4,5 . Here we extend this description to arbitrary [Formula: see text]. We show that control loops generically produce braids of eigenfrequencies, and for [Formula: see text] these braids form a non-Abelian group that reflects the non-trivial geometry of the space of degeneracies. We demonstrate these features experimentally for [Formula: see text] using a cavity optomechanical system.
(© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)
Databáze: MEDLINE
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