Correlations between interacting Rydberg atoms

This paper is a short introduction to Rydberg physics and quantum nonlinear optics using Rydberg atoms. It has been prepared as a compliment to a series of lectures delivered during the Latin American School of Physics “Marcos Moshinsky” 2017. We provide a short introduction to the properties of individual Rydberg atoms and discuss in detail how the interaction potential between Rydberg atom pairs is calculated. We then discuss how this interaction gives rise to the Rydberg blockade mechanism. With the aid of hallmark experiments in the field applications of the blockade for creating correlated quantum systems are discussed. Our aim is to give an overview of this exciting and rapidly evolving field. The interested reader is referred to original work and more comprehensive reviews and tutorials for further details on these subjects.