We have so far spoken almost exclusively of photons and linear-optical elements, and seen just how powerful those two components can be for information processing. They provide unbreakable cryptographic tools, and allow for efficient quantum computing. However, many more possibilities become available when we allow photons to interact with atoms and solid matter in a quantum mechanical way. In particular, a quantum memory, the principal difficulty for linear-optical quantum computing, can be created. In this chapter we will take the first steps towards a full understanding of a photon's interaction with atoms. We will show how to describe the interactions within a system consisting of photons and few-level atoms and show how this interaction can be manipulated and exploited to provide quantum information processors based on both atomic and photonic qubits. We will also show that photon emission from atoms can degrade the quantum information contained within atoms, and we will present a formalism to model this effect. We begin with a general discussion of atom-photon interactions.

Atomic systems as qubits

Let us first consider an electron in an isolated atom. It is bound there by the Coulomb force due to the charge distribution of all the other electrons and the nucleus. The potential that describes this coupling is given by V(r).