Finding and pinpointing exceptional points of an open quantum system

An exceptional point (EP) is a point in the parameter space of an open quantum system in which the two eigenstates of the effectively non-Hermitian system coalesce and a topological effect can be observed. In this work we use the properties of the energy eigenvalues near the EP at three different points in order to find the exact EP location in the parameter space. This method does not require the two parameters of the system to be grouped as a single complex parameter, so it can easily be applied to Floquet operators. Finally, it is shown that by applying the Hellmann-Feynman theorem, the EP position can be obtained from a single point. The benefits of using the 3-point approach or the 1-point approach are discussed. These simple techniques may be of use in the search for new EPs in various physical systems. To demonstrate the utility of the method, we find an EP for an H⁺₂ molecule driven by a monochromatic laser and for a laser-driven Gaussian potential. copy; 2010 IOP Publishing Ltd.