One of the long standing questions in quantum physics is the reason electrical conductivity varies so widely between materials, over 16 orders of magnitude, much more than can be explained by the availability of electrons. One leading cause of insulator behaviour is Anderson localisation, which dominates in disordered systems of coherent waves.

A basic introduction to localisation is found in the above diagram. In any disordered medium, the phases acquired from a particle traversing a clockwise and anticlockwise ‘loop’ of scatterers is identical. This leads to constructive interference in the reverse direction: wave interference in a disordered medium acts to inhibit the transport.

We investigate the localisation phenomenon using ultracold atoms propagating through disordered channels, and we measure the effective ‘resistance’ of the channels to give us information about the transport properties of the medium. We do this by using high resolution imaging of a spatial light modulator, which allows us to create custom, arbitrary patterns, allowing us to control the characteristics of the disorder. We have so far succeeded in measuring a non-classical increase in resistance as we increased the amount of disorder in a channel.

Critical remaining questions that we want to answer are:

• How do interactions influence Anderson localisation?

• How does the nature of the randomness of the potential influence Anderson localisation?

• What happens if the potential depends on time?