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The most intriguing properties of non-Hermitian systems are found near theexceptional points (EPs) at which the Hamiltonian matrix becomes defective. Dueto the complex topological structure of the energy Riemann surfaces close to anEP and the breakdown of the adiabatic theorem due to non-Hermiticity, the stateevolution in non-Hermitian systems is much more complex than that in Hermitiansystems. For example, recent experimental work [Doppler et al. Nature 537, 76(2016)] demonstrated that dynamically encircling an EP can lead to chiralbehaviors, i.e., encircling an EP in different directions results in differentoutput states. Here, we propose a coupled ferromagnetic waveguide system thatcarries two EPs and design an experimental setup in which the trajectory ofstate 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 theparameter space, including the size of the encircling loop and the starting/endpoint. We discovered that whether or not the dynamics is chiral actuallydepends on the starting point of the loop. In particular, dynamicallyencircling an EP with a starting point in the parity-time-broken phase resultsin non-chiral behaviors such that the output state is the same no matter whichdirection the encircling takes. The proposed system is a useful platform toexplore the topology of energy surfaces and the dynamics of state evolution innon-Hermitian systems and will likely find applications in mode switchingcontrolled with external parameters.

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point