**MARIONA MORENO-CARDONER**Theoretical Quantum-Nano Photonics

ICFO-The Institute of Photonic Sciences

The ability to control interactions between light and atoms, or other quantum emitters, forms a cornerstone for fundamental physics and applications, ranging from precision measurement to quantum information processing. Photon loss — re-scattering of a photon into unwanted directions — represents a fundamental limitation in all these tasks. In typical atomic ensemble models the atoms are assumed to emit independently and in an uncorrelated fashion. This paradigm however, is expected to break down for dense and ordered atomic arrays, where interference between the emitted photons becomes relevant, and it can give rise to exciting phenomena such as the well known super-radiance and sub-radiance, for which the collective photon emission is strongly modified. In this sense, dense periodic atomic arrays offer us a novel platform that properly exploited can beat previously established bounds for applications in quantum optics.

In these lectures we aim at providing a fundamental understanding of periodic atomic arrays interacting with light, as well as discussing novel phenomena arising in these systems. In order to do this, we will introduce a novel formalism which includes in an exact way interference and re-scattering of photons while propagating through the atoms.

A more detailed outline of the lectures is as follows. The first lecture will be devoted to motivate the interest in these systems. We will review established well known models in quantum optics (such as the Jaynes-Cummings model), and then establish the connection with the novel approach to treat atom-light interactions (the quantum spin-model), which takes into account cooperative scattering of light. In the second lecture we will continue deriving the quantum spin model, and apply it to a one-dimensional regular chain of atoms, leading to surprising effects. In the third lecture we will focus on two-dimensional atomic arrays, which have the remarkable property of acting as perfect mirrors. In the last lecture we will discuss possible extensions of the model.
**
ICFO Theory Lecture, February 5, 11, 21, 28; 2019, 10:15. ICFO’s Blue Lecture Room**