Topological Quantization of Berry Phases in the Space of Exceptional Points

Non-Hermitian Hamiltonians may be employed to describe the dynamics of a subsystem. Striking differences to Hermitian dynamics have been observed and associated to exceptional points--parameters at which not only the eigenvalues of a Hamiltonian but also its eigenvectors coalesce. While most previous research has explored the neighborhood of exceptional points, we jump right onto them.

In fact, under full parametric control, exceptional points form high-dimensional, connected but not simply-connected spaces, over which adiabatic transport may be performed. We find that the associated Berry phases are topologically quantized to multiples of 2π/n for a general nxn non-Hermitian Hamiltonian. A topological Berry phase of π may be implemented with a single dissipative qubit coupled to radiation.