Conical Intersections in Other Physical Systems

Abstract

In this chapter, we collect a few other physical scenarios where conical intersections (CIs) appear. We demonstrate the existence of CIs in an atom-cavity system, by treating the quadrature variables as slow parameters. Similar features can be found in ion trap systems, where the cavity field is replaced by the phonons associated with the trapping potential. Common to these systems are the quantum Rabi and Jaynes–Cummins models that naturally describe the interaction between the discrete energy levels of the atom or ion with the oscillator fields associated with the photons in the cavity or the phonons of the trap. We discuss how CIs may show up for classical light moving through materials with a small space-dependent refractive index and how lattice models can be emulated in such settings. These systems may realise Dirac cones by appropriately choosing the lattice structure. We finally examine the exceptional point (EP) concept for parameter-dependent non-Hermitian systems, which exhibit complex-valued energy spectra. An EP is a crossing point in parameter space between two or more energies; thus, an EP is the non-Hermitian counterpart to a CI for Hermitian system. We discuss how non-Hermitian systems can appear as effective models of open quantum systems.