Related papers: Four-Dimensional Quantum Hall Effect with Ultracol…

In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…

We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent $\nu\approx 1.2$ of…

We demonstrate a novel experimental arrangement which rotates a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated…

We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass,…

Realization of strong synthetic magnetic fields in driven optical lattices has enabled implementation of topological bands in cold-atom setups. A milestone has been reached by a recent measurement of a finite Chern number based on the…

We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate…

Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to…

We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain…

Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers…

In the recent years, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a way to realize 2nd Chern number…

A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably…

We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in both directions. When the difference between the two tilted fields is large, Bloch…

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…

The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…

Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in various engineered set-ups. In this paper, we propose a new type of 4D topological system that, unlike other 2D and 4D QH models, does not…

The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…

A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded…

We recently proposed quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions [Phys. Rev. Lett. 125, 030504 (2020)]. Conceptually, the scheme is based on the idea that aphysical monolayer optical…

We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…

Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which…