Comparing theoretical approaches to modelling cold atoms in disordered optical lattices

This project explores how disorder effects the non-equilibrium steady state of an array of coupled cavities.

While the basic laws of quantum mechanics, and the interactions between electrons in a crystal have been well known for over a century, it still remains difficult to start from these laws and predict the behaviour of complex systems with many interacting parts. Even at what might seem the simplest level -- predicting the properties of various solids still proves a challenging, i.e. knowing from its chemical composition whether a given material is a superconductor or a magnet, or transparent. Following a suggestion of Richard Feynman over 20 years ago, an alternate approach to this problem has been proposed, that of "quantum simulation" --- producing controllable systems that can be made to emulate the behaviour of a given material, and thus understand how slightly changing the properties of the material might change its behaviour.

Very recently, possible quantum simulators using strong coupling between light and matter have been produced. These are very promising in that they can be made relatively large. However they differ from the ideal system in that light may leak out. The aim of this project is to understand one specific consequence of the effect of these losses, and to ask whether these systems can really emulate the behaviour of real materials which invariably include disorder (i.e. dirt --- impurity atoms or atoms in the wrong place).

We found that the behaviour of a disordered system of strongly coupled matter and light can be studied using a computational method known as "stochastic mean field theory", but that the computational effort involved is greater than might initially be expected. Using this, we found a more striking result: the behaviour of disordered quantum simulators made of light is dramatically different from quantum simulators using e.g. ultracold atoms. The fact that light can leak out of the system, when combined with disorder, means that other, more damaging kinds of disorder can arise, and that disorder may dramatically shift the properties of such quantum emulators.