Geometric Structure and Topological Characteristics of High Order Exceptional Points

Project: Research project

Project Details


Hermitian Hamiltonians are commonly used to describe physical systems, thanks to their entirely real-valued eigenvalues and eigenvectors, which are suitable for representing steady states. However, recent theoretical developments on non-Hermitian Hamiltonians have inspired physicists to rethink the formalism and to use non-Hermitian Hamiltonians to study systems that incorporate loss and/or gain. Such systems are particularly commonplace in optics and classical waves. Unprecedented phenomena enabled by non-Hermiticity, including single-mode lasing, asymmetric absorption, etc., can lead to important applications in laser, energy transfer, and sensor technologies. Therefore, classical waves, such as light and acoustic waves, are quickly becoming the next hotspot for the research in non-Hermitian physics.

An exceptional point (EP) emerges when two or more states coalesce at a certain parametric point of a non-Hermitian system. The critical behaviours of non-Hermitian systems in the vicinity of an EP have attracted tremendous academic attention. A particularly intriguing characteristic is the evolution of eigenvalues near an EP as the system is tuned. Typically, the complex eigenvalues form a self-intersecting Riemann surface in the parameter space, which gives the EP some peculiar properties such as unconventional topological structures. A variety of unconventional phenomena associated with these properties have been discovered, such as asymmetric guiding mode switching and topological energy transfer. Additionally, it has been shown that three or more interacting states can simultaneously coalesce to form a high order EP, which dwells on an even more exotic Riemann surface. However, the rich behaviours in the proximity of a high order EP remain unexplored. Here, we propose to study the geometric structure and topological characteristics of high order EPs. We will use tight-binding theory to identify the conditions for high order EPs to arise from 3×3 and 4×4 non-Hermitian Hamiltonians. We plan to realise these high order EPs in acoustic experiments, which have proven to be a versatile platform for studying non-Hermitian physics. EPs with specific geometric properties, such as an anisotropic high order EPs, will be designed and realised. Our acoustic wave systems will also enable the fine-tuning of relevant parameters, including coupling, loss, and detuning, and allow us to drive the systems around the EP to uncover the topological structures
Effective start/end date1/07/1930/06/22


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