Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization

Abstract

Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena, such as level crossings in nuclear and condensed matter physics, and unusual phenomena in optics, such as loss-induced lasing and unidirectional transmission, can be understood by considering a simple 2×2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge, and as the system parameters vary, these EPs can collide and merge, leading to higher-order singularities and topological characteristics much richer than those seen in two-state systems. The new physics obtained is not limited to the acoustic systems demonstrated here. It also applies to other systems as well, such as coupled photonic cavities and waveguides.

Alternate abstract:

Plain Language Summary

Researchers have often focused on “closed” systems, but real-life systems are almost always “open,” given that interactions with the environment are inevitable. It is known that two-state open systems have exceptional points, which are transitions at which eigenstates coalesce. Recently, such points have been actively pursued in various fields of physics. However, many realistic open systems have multiple states, and therefore the physics of such multiple-state systems is worth investigating. Here, we investigate exceptional points in an ensemble of coupled acoustic cavities subject to losses.

We show both theoretically and experimentally that multiple exceptional points can collide in phase space, leading to new higher-order singularities that do not occur in two-state problems. In a four-state system of coupled stainless-steel cavities held at room temperature, we propagate acoustic waves and discover the existence of multiple exceptional points and their collisions when we insert sponges into the cavities to induce losses. These collision points, which are associated with frequencies of roughly 3000 Hz, are able to form new higher-order singularities with new topological properties in their eigenmodes. We successfully experimentally realize the different topological classes using this coupled acoustic cavity system, and we emphasize that the experimental realization of exceptional point physics is generally very difficult even for a two-state system. These new singularities and their associated topological properties will likely serve as platforms for realizing new phenomena that apply to other forms of waves such as electromagnetic and matter waves.

We anticipate that our results will motivate future studies of exceptional points in a wide variety of multiple-state setups.