A first encounter with exceptional points in a quantum model

Abstract

An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their vicinity. Here we consider perhaps the simplest quantum model which exhibits an exceptional point and which allows for an analytical treatment. In particular, we re-examine a two-level atom driven by a laser and suffering from losses. The same exceptional point arises in several non-Hermitian matrices which determine various aspects of the dynamics of the system. There are consequences for some important observables, for example the spectrum evolves from being a Lorentzian-like singlet to a Mollow triplet upon passing through the exceptional point. Our analysis supports the perspective that viewing certain quantum systems through the lens of exceptional points offers some desirable explanatory advantages.