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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.

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.

The transport measurements of an interacting fermionic quantum gas in an optical lattice provide a direct experimental realization of the Hubbard model—one of the central models for interacting electrons in solids—and give insights into the transport properties of many-body phases in condensed-matter physics.

A single two-dimensional array of atoms trapped in an optical lattice shows a tunable cooperative subradiant optical response, acting as a single-monolayer optical mirror with controllable reflectivity.

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.

By implementing a 2D topological charge pump using ultracold bosonic atoms, the theoretically predicted 4D integer quantum Hall effect is confirmed experimentally.

Many-body localization, which exhibits a fascinating interplay between disorder and interactions, can be studied using ultracold atoms in a quasiperiodic chain. Adding periodic driving makes things even more interesting.

No limit to the speed of information propagation exists in non-relativistic quantum field theory, but finite-velocity transport of correlations is now found in a system of ultracold atoms in an optical lattice, aiding fundamental understanding of closed quantum systems far from equilibrium.

In 2002, an experiment with ultracold atoms emulated a textbook condensed-matter physics phenomenon: the phase transition from a superfluid to a Mott insulator. Two decades later, Immanuel Bloch and Markus Greiner ponder how far quantum simulation with ultracold atoms has come.

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.

The realization of efficient light–matter interfaces is important for many quantum technologies. An experiment now shows how to coherently switch the collective optical properties of an array of quantum emitters by driving a single ancilla atom to a Rydberg state.

A ‘Higgs’ mode, signifying the breaking of a continuous symmetry in a model with emergent Lorentz invariance, is found close to the transition to the Mott insulating phase in a two-dimensional neutral superfluid.

Proposals for skyrmion-based high-density memory devices require an understanding of the formation and shape of skyrmions in confined geometries. Here, the authors use electron holography to image magnetic textures in FeGe nanostripes and explore the parameters governing skyrmion morphology.

Ultracold atoms in optical lattices provide a versatile tool to investigate fundamental properties of quantum many-body systems. This paper demonstrates control at the most fundamental level, using a laser beam and microwave field to flip the spin of individual atoms at specific sites of an optical lattice. The technique should enable studies of entropy transport and the quantum dynamics of spin impurities, the implementation of novel cooling schemes, engineering of quantum many-body phases and various quantum information processing applications.

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.

A ladder-like arrangement of an ultracold gas of lithium atoms trapped in an optical lattice enables the observation of a symmetry-protected topological phase.

The trend towards using ultracold atomic gases to explore emergent phenomena in many-body systems continues to gain momentum. This time around, they have been used to explore novel pairing mechanisms in one dimension. See Letter p.567

Using quantum gas microscopy, Hilbert space fragmentation and fractonic excitations are observed in a two-dimensional tilted Bose–Hubbard model.

Observations of the formation of individual stripes in a mixed-dimensional cold-atom Fermi–Hubbard quantum simulator are described, enhancing understanding of the phase diagram of high-temperature superconducting materials and the relationship between charge pairs and stripes.

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.

Ultracold polyatomic molecules can be created by electroassociation in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance.

The control of long-range interactions is an essential ingredient for the study of exotic phases of matter using atoms in optical lattices. Such control is demonstrated using Rydberg dressing: the coupling of ground state atoms to Rydberg states.

Interactions between microscopic particles are usually described as two-body interactions, although it has been shown that higher-order multi-body interactions could give rise to new quantum phases with intriguing properties. Here, effective six-body interactions are demonstrated in a system of ultracold bosonic atoms in a three-dimensional optical lattice.

High-resolution, in situ imaging of Rydberg atoms in a Mott insulator reveals the emergence of spatially ordered excitation patterns with random orientation but well-defined geometry.

Tuning interspecies interactions in atomic Bose–Fermi mixtures is shown to drive the system through a quantum phase transition. This enables the generation of heteronuclear molecules in the quantum-degenerate regime.

The direct observation of hole pairing in a doped Hubbard model is demonstrated using ultracold atoms in a quantum gas microscope setting by engineering mixed-dimensional fermionic ladders.

A type of universal scattering resonance between ultracold microwave-dressed polar molecules associated with field-linked tetramer bound states in the long-range potential well is observed, providing a general strategy for resonant scattering between ultracold polar molecules.

The simulation of strongly correlated quantum phases using ultracold atoms in optical lattices was first proposed 20 years ago. In the wake of that pioneering idea, quantum simulations are now widely pursued in experiments across the world.

A general and efficient approach to evaporatively cool ultracold polar molecules through elastic collisions to create a degenerate quantum gas in three dimensions is demonstrated using microwave shielding.

Studies of unconventional pairing mechanisms in cold atoms require ultralow temperatures. Large-scale numerics show that certain bilayer models allow for deeply bound and highly mobile pairs of charges at more accessible temperatures.

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.

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.

The Landau–Zener model of a two-state system is a standard method for studying quantum dynamics. This textbook example of single-particle dynamics has now been generalized to a many-body system represented by two coupled ultracold Bose liquids.

Understanding the propagation of spin excitations is a difficult problem in quantum magnetism. Using site-resolved imaging in a one-dimensional atomic gas, it is possible to track the dynamics of a moving spin impurity through the Mott-insulator and superfluid regimes.

Bound states of elementary spin waves (magnons) have been predicted to occur in one-dimensional quantum magnets; the observation of two-magnon bound states in a system of ultracold bosonic atoms in an optical lattice is now reported.

Experiments with ultracold quantum gases provide a platform for creating many-body systems that can be well controlled and whose parameters can be tuned over a wide range. These properties put these systems in an ideal position for simulating problems that are out of reach for classical computers. This review surveys key advances in this field and discusses the possibilities offered by this approach to quantum simulation.

Magnetic polarons are imaged with single-site spin and density resolution in the low-doping regime of the atomic Fermi–Hubbard model, showing that mobile delocalized doublons are necessary for polaron formation.

Direct observation of incommensurate spin correlations in doped and spin-imbalanced Hubbard chains confirms two fundamental predictions for Luttinger liquids and shows that such correlations are suppressed by interchain coupling.

For several years, researchers have aspired to record in situ images of a quantum fluid in which each underlying quantum particle is detected. This goal has now been achieved: here, fluorescence imaging is reported of strongly interacting bosonic Mott insulators in an optical lattice, with single-atom and single-site resolution. The approach opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice.

The current status and future perspectives for quantum simulation are overviewed, and the potential for practical quantum computational advantage is analysed by comparing classical numerical methods with analogue and digital quantum simulators.

The interplay of kinetic and spin degrees of freedom in strongly correlated materials leads to interesting emergent many-body phases, but their microscopic origin is still unclear. Here, a theoretical study quantifies the effect of hole motion in driving an antiferromagnetic spin background into a highly frustrated magnetic system.

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.