Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation

TL;DR

This paper experimentally investigates an exceptional point in a microwave billiard with broken time-reversal symmetry, revealing unique geometric phases and amplitudes associated with non-Hermitian Hamiltonians.

Contribution

It provides the first experimental characterization of an EP in a dissipative microwave system with T violation, including geometric phase and amplitude effects.

Findings

Eigenvectors acquire geometric phases when transported around the EP.

The size of T violation is determined by the eigenvector phase.

Eigenvectors gather geometric amplitudes different from unity.

Abstract

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and non-symmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.