Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Abstract

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

Theory of complex-coordinate transformation acoustics for non-Hermitian metamaterials

“…[34][35][36][37][38][39][40][41][42][43][44][45][46] Recently, as another striking property of non-Hermitian systems, 𝒜𝒫𝒯 symmetry has been proved, defined by {𝒫𝒯 , H} = 0, which may facilitate the experiments since it requires either gain or loss. [47][48][49] With the help of the positive and negative refractive index materials, many intriguing effects can beachieved, such as chiral mode transfer, [50] quantum squeezing and sensing, [51] and shift of EPs. [52] However, the artificial modulation of the imaginary part of wave vector in non-conservative systems, which is crucial for the amplification and attenuation of acoustic waves and the design of non-Hermitian acoustic metamaterials, would require the transformation acoustic method to adapt to complex spatial coordinate space and map complex coordinates.…”

“…Furthermore, it can reduce the complexity of material parameters in comparison with traditional realcoordinate transformation, which may inspire the experimental implementation of a perfect cloak which has not been realized before. [33,50] 2. Jacobian matrix for 𝒫𝒯 and 𝒜𝒫𝒯 symmetries…”