Beam dynamics induced by the quantum metric of exceptional rings

Topological physics has broadened its scope from the study of topological insulating phases to include nodal phases containing band structure singularities. The geometry of the corresponding quantum states is described by the quantum metric which provides a theoretical framework for explaining phenomena that conventional approaches fail to address. The field has become even broader by encompassing non-Hermitian singularities: in addition to Dirac, Weyl nodes, or nodal lines, it is now common to encounter exceptional points, exceptional or Weyl rings, and even Weyl spheres. They give access to fascinating effects that cannot be reached within the Hermitian picture. However, the quantum geometry of non-Hermitian singularities is not a straightforward extension of the Hermitian one, remaining far less understood. Here, we study experimentally and theoretically the dynamics of wave packets at exceptional rings stemming from Dirac points in a photonic honeycomb lattice. First, we demonstrate a transition between conical diffraction and non-Hermitian broadening in real space. Next, we predict and demonstrate a new non-Hermitian effect in the reciprocal space, induced by the non-orthogonality of the eigenstates. We call it transverse non-Hermitian drift, and its description requires biorthogonal quantum metric. The non-Hermitian drift can be used for applications in beam steering.