Title: Photon-photon interactions in waveguides and the physics of photon bound states

Abstract: 

Photons rarely interact. In free space photons just pass through each other without any interaction. The situation is, however, dramatically different if light is e.g. strongly coupled to individual atoms. Such systems have been realised in various experimental systems in recent years. In this case the atoms can mediate an effective interaction between the photons, and this can be exploited to realise a strongly interacting photon fluid.  

I will consider one of the conceptually simplest examples of strong photon-photon interactions: a waveguide coupled to a collection of two-level systems. Despite its simplicity I will show that this systems contains surprisingly rich and intersting physics. In particular, I will discuss the physics of photon bound states, where photons bind together similar to atoms binding together in molecules. For so-called chiral systems, where the two-level systems can only decay in one direction, such bound states for any number of photons have been known for several years but their properties have not been fully explored. I will discuss the essential physics of these bound states, i.e., what are their properties, how can one relate them to classical results for large photon numbers and how can one unambiguously detect them [1]. 

Finally I will consider non-chiral interactions. Here new types of physics appear; not only can photons bind together, they also have scattering resonances where two photons bind together for a finite time. Furthermore two photons can also undergo inelastic collisions. Understanding this few-body physics is the first towards potentially realising more complicated many-body phenomena for photons. 

[1] S. Mahmoodian, G. Calajo, D. E. Chang, K. Hammerer, and A. S. Sørensen, Phys. Rev. X 10, 031011 (2020).