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The quantum simulation of driven, strongly correlated phases at large scales is challenging, primarily due to detrimental heating effects. Now, a large-scale interacting Mott–Meissner phase has been realized in a neutral atom quantum simulator.

In the band theory of solids, the topological properties of Bloch bands are characterized by geometric phases. For cold atoms moving in a one-dimensional optical potential the geometric phase can be measured directly using Bloch oscillations and Ramsey interferometry.

Laser-assisted tunnelling allows quantum gases in optical lattices to be exposed to tunable artificial magnetic fields. Using such fields to confine a bosonic gas to an array of one-dimensional ladders, a low-dimensional equivalent of the Meissner effect has been observed.

The observation of edge modes in topological systems is challenging because precise control over the sample and occupied states is required. An experiment with atoms in a driven lattice now shows how edge modes with programmable potentials can be realized.

Chern numbers characterize the quantum Hall effect conductance—non-zero values are associated with topological phases. Previously only spotted in electronic systems, they have now been measured in ultracold atoms subject to artificial gauge fields.

Standard topological invariants commonly used in static systems are not enough to fully capture the topological properties of Floquet systems. In a periodically driven quantum gas, chiral edge modes emerge despite all Chern numbers being equal to zero.

It was predicted that complex thermalizing behaviour can arise in many-body systems in the absence of disorder. Here, the authors observe non-ergodic dynamics in a tilted optical lattice that is distinct from previously studied regimes, and propose a microscopic mechanism that is due to emergent kinetic constrains.

An effective Hamiltonian exhibiting \({\Bbb Z}_2\) symmetry has been engineered by implementing a Floquet-based method on ultracold bosons in an optical lattice, providing a first step towards quantum simulation of \({\Bbb Z}_2\) lattice gauge theories with ultracold matter.

Fluctuating hydrodynamics posits that thermalization in non-equilibrium systems depends on equilibrium transport coefficients. This hypothesis is now tested by exploring the emergence of fluctuations in non-equilibrium dynamics of ultracold atoms.

Large-scale quantum simulations of gauge theories are relevant to high-energy and condensed matter physics. This Review covers recent developments in simulating lattice gauge theories using cold atoms.

Thouless pumping is a dynamical quantum effect that results in a quantized response of a many-body system. It stems from the topological properties of the band structure that emerge under a periodic drive in the adiabatic limit. This Review addresses the robustness of topology in adiabatically driven systems exploring fundamental issues regarding the roles of interactions, disorder and higher dimensions in quantum transport.

Quantum gas microscopy is an in-situ imaging technique used to investigate many-body phenomena in cold-atom quantum simulators and can provide resolution at the single-particle level; however, limiting factors, such as short lattice constants and finite signal-to-noise ratios, weaken image resolution. Here, the authors develop an algorithm based on unsupervised deep learning that can reconstruct the occupation of an optical lattice of Cs atoms from fluorescence images with high fidelity.