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The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with a high degree of controllability. Recently, an atomic $\nu =1/2$Laughlin state has been realized experimentally for a small system of two particles on $4\times 4$sites [Léonard , ]. The next challenge concerns the preparation of Laughlin states in extended systems, ultimately giving access to anyonic braiding statistics or gapless chiral edge-states in systems with open boundaries. Here, we propose and analyze an experimentally feasible scheme to grow larger Laughlin states by connecting multiple copies of the already-existing $4\times 4$system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended $8\times 4$system with four particles. Then, we analyze different preparation schemes, setting the focus on two shapes for the extended system, and discuss their respective advantages: While growing striplike lattices could give experimental access to the central charge, squarelike geometries are advantageous for creating quasihole excitations in view of braiding protocols. We highlight the robust quantization of the fractional quasihole charge upon using our preparation protocol. We benchmark the performance of our patchwork preparation scheme by comparing it to a protocol based on coupling one-dimensional chains. We find that the patchwork approach consistently gives higher target-state fidelities, especially for elongated systems. The results presented here pave the way towards near-term implementations of extended Laughlin states in quantum gas microscopes and the subsequent exploration of exotic properties of topologically ordered systems in experiments. Published by the American Physical Society2024 

Abstract Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν  = 1. We reveal the nature of the low energy spin-singlet states around ν  ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- T c superconductivity. 

Abstract We investigate the formation of magnetic Bose polaron, an impurity atom dressed by spin-wave excitations, in a one-dimensional spinor Bose gas. Within an effective potential model, the impurity is strongly confined by the host excitations which can even overcome the impurity-medium repulsion leading to a self-localized quasi-particle state. The phase diagram of the attractive and self-bound repulsive magnetic polaron, repulsive non-magnetic (Fröhlich-type) polaron and impurity-medium phase-separation regimes is explored with respect to the Rabi-coupling between the spin components, spin–spin interactions and impurity-medium coupling. The residue of such magnetic polarons decreases substantially in both strong attractive and repulsive branches with strong impurity-spin interactions, illustrating significant dressing of the impurity. The impurity can be used to probe and maneuver the spin polarization of the magnetic medium while suppressing ferromagnetic spin–spin correlations. It is shown that mean-field theory fails as the spinor gas approaches immiscibility since the generated spin-wave excitations are prominent. Our findings illustrate that impurities can be utilized to generate controllable spin–spin correlations and magnetic polaron states which can be realized with current cold atom setups. 

The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement1. Although these phases were discovered in a solid-state setting2,3, recent innovations in systems of ultracold neutral atoms—uncharged atoms that do not naturally experience a Lorentz force—allow the synthesis of artificial magnetic, or gauge, fields4,5,6,7,8,9,10. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems11,12. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states4,13,14,15,16,17. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper–Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field18. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.