The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the simulation of gauge fields and give access to exotic topological states. We review here recent advances in the field and discuss future perspectives for interacting systems.
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the simulation of gauge fields and give access to exotic topological states. We review here recent advances in the field and discuss future perspectives for interacting systems.
Synthetic dimension approach has emerged as a versatile and powerful technique in cold-atom toolbox for quantum simulation, serving as a complementary alternative to conventional optical lattice platforms. By mapping internal or external atomic states into discrete lattice sites, this method provides precise control over local tunneling amplitudes, phases, and on-site potentials, enabling flexible engineering of tight-binding Hamiltonians. Such capabilities have facilitated the experimental exploration of topology, synthetic gauge fields, disorder-induced phenomena, and exotic time-dependent dynamics across a range of platforms, including hyperfine and Rydberg states, momentum lattices, and harmonic-trap modes. In this review, we summarize the underlying principles of the key experimental synthetic dimension platforms, and their recent advances in quantum simulation. We also discuss the advantages and current limitations of the synthetic method, and provide a perspective on future directions, including hybrid-dimensional architectures and the study of high-dimensional many-body physics.
Abstract 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. 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), Poznan (UAM), Kraków (UJ), and Allahabad (HRI). 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.
Abstract The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.
Owing to rapid recent progress, ultracold atomic lattice systems for simulating topological phases are now at a pivotal stage, evolving from established paradigms into increasingly versatile and programmable quantum simulators. In this review, we survey recent experimental advances across four major classes of platforms: optical lattices, including optical lattices with laser-assisted tunneling and optical Raman lattices; synthetic lattices in momentum or internal-state space; Floquet-engineered lattices; and optical tweezer arrays, all of which offer distinct capabilities for realizing and probing topological matter. For each class, we highlight representative experimental breakthroughs, the topological models that have been realized, and the advanced detection and characterization techniques employed, emphasizing how these complementary approaches collectively expand the frontier of quantum simulation. We also discuss emerging directions in strongly correlated and nonequilibrium topological phases, and conclude with an outlook on future prospects.
This proceedings presents recent advancements in the realization of topological states of matter using ultracold atomic gases. We focus on the simulation of the quantum Hall effect, originally discovered in two-dimensional electron gases subjected to a magnetic field. Given that ultracold atoms are neutral, simulating the effect of a magnetic field requires an ad-hoc technique. We review various methods developed for this purpose, highlighting their respective advantages and limitations. Furthermore, we explore the extension of these techniques to interacting quantum gases within topological bands, aiming to create analogs of fractional quantum Hall states. These many-body states are distinguished by their topological order, which is characterized by long-range entanglement among particles and the emergence of low-lying excitations exhibiting fractional quantum statistics. The discussion will encompass the current state of research and potential future directions in the field.