Abstract
The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.
Highlights
Exceptional points (EPs) are degeneracies in nonHermitian systems [1,2,3,4]
This fact implies that when the state approaches the end point, it would be on the lowerloss Riemann sheet, and the details of the previous dynamical process such as the injected mode and the number of nonadiabatic transitions (NATs) would all be forgotten by the system
Determining the delay time in realistic non-Hermitian systems remains a very complicated issue that needs further investigation. We have shown both numerically and experimentally that a pair of ferromagnetic waveguides applied with nonuniform bias magnetic fields serves as a good platform to study dynamical processes in nonHermitian systems
Summary
Exceptional points (EPs) are degeneracies in nonHermitian systems [1,2,3,4]. Unlike degeneracies in Hermitian systems such as diabolic points (DPs) [5,6], whose eigenvalues but not eigenvectors coalesce, at EPs, both the eigenvalues and the eigenvectors coalesce, leading to various counterintuitive phenomena and fascinating applications such as loss-induced transmission enhancement [7], lasing effects [8,9,10,11], unusual beam dynamics [12,13], enhanced sensing [14,15,16], robust wireless power transfer [17], and others [18,19,20,21,22,23]. The so-called state flip achieved by adiabatically encircling an EP is made possible by the degeneracy-induced intersection of complex Riemann sheets [24,25] This phenomenon has been demonstrated experimentally in microwave cavities [26], exciton-polariton systems [27] and acoustic systems [28], where static measurements of the spectra and eigenmodes successfully revealed the topological structure of EPs. the outcome is completely different if an EP is encircled in a dynamical process. The topological structure of the system can be designed by choosing appropriate system parameters, allowing us to dynamically encircle different numbers of EPs (e.g., zero, one, or even two) without changing or moving the sample, and to study the dependence of the dynamics on the starting/end point of the encircling loop. A theoretical model was used to investigate the underlying physics and reveal the role of the starting point
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