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

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