PT symmetry and spontaneous symmetry breaking in a microwave billiard

TL;DR

This paper experimentally demonstrates PT symmetry and spontaneous symmetry breaking in a dissipative microwave billiard system near an exceptional point, revealing real and complex conjugate eigenvalues depending on system parameters.

Contribution

It provides the first experimental realization of PT symmetry and symmetry breaking in a microwave billiard, with detailed analysis of eigenvalues near an exceptional point.

Findings

Eigenvalues are real or complex conjugate depending on parameters.

PT symmetry is revealed through basis transformation.

Spontaneous symmetry breaking occurs at the exceptional point.

Abstract

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.