Topological quantum matter in synthetic dimensions

TL;DR

Synthetic dimensions in quantum systems allow emulation of higher-dimensional topological phases by coupling internal states, enabling exploration of complex condensed matter phenomena in lower-dimensional platforms.

Contribution

This paper reviews recent advances in studying topological matter using synthetic dimensions, highlighting new methods and future directions in many-body physics and higher-dimensional topological effects.

Findings

Successful realization of topological phases in synthetic dimensions

Proposal for exploring many-body physics in higher dimensions

Potential applications in quantum simulation and topological quantum computing

Abstract

In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of `synthetic dimensions' has recently emerged as a powerful way to emulate phenomena such as topological phases of matter, which are now of great interest across many areas of physics. The main idea of a synthetic dimension is to couple together suitable degrees of freedom, such as a set of internal atomic states, in order to mimic the motion of a particle along an extra spatial dimension. This approach provides a way to engineer lattice Hamiltonians and enables the realisation of higher-dimensional topological models in platforms with lower dimensionality. We give an overview of the recent progress in studying topological matter in synthetic dimensions. After reviewing proposals and realizations in various setups, we discuss future prospects in many-body physics, applications, and topological effects in three or more spatial dimensions.