Quantum Simulation with Synthetic Dimensions

Topological phases of matter exhibit fascinating phenomena, such as the robust quantization of conductance in the 2D quantum Hall effect that was first discovered for electrons moving in a magnetic field. In cold atoms or photonics, however, it can be experimentally challenging to explore such topological effects, as atoms and photons are neutral particles and so require the engineering of artificial gauge fields. In this context, synthetic dimensions have emerged as a powerful and general experimental concept. The main idea of this approach is to couple together suitable degrees of freedom to mimic the motion of a particle along an extra spatial dimension, providing a way to engineer controllable lattice models. In this talk I will give an overview of this topic, and present recent works from my group based on synthetic dimensions in cold atoms and photonics. I will also discuss how synthetic dimensions can be used to go beyond what is possible in traditional materials to experimentally explore phenomena that only emerge in four spatial dimensions.