Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall drift upon release, for a wide range of magnetic flux values, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the extracted Hall conductivity approaches a fractional value determined by the many-body Chern number, while the width of the plateau agrees with the spectral and topological properties of the prepared ground state. Besides, a direct application of Streda's formula indicates that such Hall plateaus can also be directly obtained from static density-profile measurements. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.Comment: 13 pages, 11 figures; extended version accepted for publicatio

Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice

Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such schemes are typically associated with space-dependent effective masses (tunneling amplitudes) and non-uniform flux patterns. In this work we investigate this phenomenon theoretically, by computing the effective Hamiltonians and quasienergy spectra associated with several kinds of lattice-shaking protocols. A detailed comparison with a method based on moving lattices, which are added on top of a main static optical lattice, is provided. This study allows the identification of novel shaking schemes, which simultaneously provide uniform effective mass and magnetic flux, with direct implications for cold-atom experiments and photonics.Comment: 15 pages, 10 eps figure

Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling

In this work, we explore the rich variety of topological states that arise in two-dimensional systems, by considering the competing effects of spin-orbit couplings and a perpendicular magnetic field on a honeycomb lattice. Unlike earlier approaches, we investigate minimal models in order to clarify the effects of the intrinsic and Rashba spin-orbit couplings, and also of the Zeeman splitting, on the quantum Hall states generated by the magnetic field. In this sense, our work provides an interesting path connecting quantum Hall and quantum spin Hall physics. First, we consider the properties of each term individually and we analyze their similarities and differences. Secondly, we investigate the subtle competitions that arise when these effects are combined. We finally explore the various possible experimental realizations of our model.Comment: 19 pages, 15 figure

Simulating Z_2 topological insulators with cold atoms in a one-dimensional optical lattice

We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional Z2 topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process constitutes an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.Comment: 5 pages +, 3 figures, to appear in Physical Review

Circuit improvement produces monostable multivibrator with load-carrying capability

Improved circuit provides greater reliability and load-carrying capabilities for monostable multivibrator

Efficient algorithm to compute the Berry conductivity

We propose and construct a numerical algorithm to calculate the Berry conductivityin topological band insulators. The method is applicable to cold atomsystems as well as solid state setups, both for the insulating case where the Fermienergy lies in the gap between two bulk bands as well as in the metallic regime.This method interpolates smoothly between both regimes. The algorithm isgauge-invariant by construction, efficient, and yields the Berry conductivity withknown and controllable statistical error bars. We apply the algorithm to severalparadigmatic models in the field of topological insulators, including Haldaneʼsmodel on the honeycomb lattice, the multi-band Hofstadter model, and the BHZmodel, which describes the 2D spin Hall effect observed in CdTe/HgTe/CdTequantum well heterostructures