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Topological quantum matter in synthetic dimensions

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 realization 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 set-ups, we discuss future prospects in many-body physics, applications and topological effects in three or more spatial dimensions.

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Acknowledgements

T.O. was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI grant number JP18H05857, the RIKEN Incentive Research Project and the Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) program at RIKEN. H.M.P. was supported by funding from the Royal Society.

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The authors declare no competing interests.

Correspondence to Tomoki Ozawa.

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Fig. 1: The concept of synthetic dimension.
Fig. 2: Main experimental set-ups used to realize synthetic dimension for atomic gases.
Fig. 3: Different approaches towards synthetic dimensions in photonics.
Fig. 4: Prospects of synthetic dimensions.