Annihilation of exceptional points from different Dirac valleys in a 2D photonic system

TL;DR

This paper demonstrates the experimental annihilation of second order exceptional points from different Dirac valleys in a 2D photonic system, revealing new non-Hermitian topological transitions and valley-physics.

Contribution

It reports the first observation of annihilation of EPs from different valleys in a 2D photonic system, linking non-Hermitian topology with valley physics.

Findings

EPs of opposite charges from different valleys can meet and annihilate.

Displacement of EPs in reciprocal space can be controlled by non-Hermiticity.

The annihilation occurs only in a topologically trivial Hermitian phase.

Abstract

Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or surfaces. They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point. The annihilation of 2D Dirac points carrying opposite charges has been experimentally reported. It remained elusive for Weyl points and second order EPs terminating different Fermi arcs. Here, we observe the annihilation of second order EPs issued from different Dirac points forming distinct valleys. We study a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Two neighboring modes can be described by a two-band Hermitian Hamiltonian showing two topological phases with either two same-sign or four opposite-sign Dirac points (valleys). Non-Hermiticity is provided by polarization-dependent losses, which split Dirac points into pairs of EPs, connected by Fermi arcs. We measure their topological charges and control their displacement in reciprocal space by increasing the non-Hermiticity degree. EPs of opposite charges from different valleys meet and annihilate, connecting in a closed line the different Fermi arcs. This non-Hermitian topological transition occurs only when the Hermitian part of the Hamiltonian is topologically trivial (with four valleys), but is distinct from the Hermitian transition. Our results offer new perspectives of versatile manipulation of EPs, opening the new field of non-Hermitian valley-physics.