Exponential decay and ionization thresholds in non-relativistic quantum electrodynamics

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. The latter result is derived from a new, general result on exponential decay tailor-made for our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well.