Synthetic dimensions for topological and quantum phases: Perspective

TL;DR

This perspective reviews recent advances in synthetic dimensions, highlighting their applications in quantum simulation, topological phases, and mimicking complex physical systems across atomic physics, quantum optics, and photonics.

Contribution

It provides a comprehensive overview of how synthetic dimensions are utilized to design quantum simulators and explore complex physical phenomena.

Findings

Synthetic dimensions enable simulation of curved spaces and gauge fields.

Applications include mimicking lattice gauge theories and twistronics.

Progress demonstrates potential for quantum technologies and fundamental physics.

Abstract

In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Pozna\'n (UAM), Krak\'ow (UJ), and Allahabad (HRI). The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more.