Cold atoms meet lattice gauge theory.

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.

Bell Correlations at Ising Quantum Critical Points.

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a nonlocal behavior. Focusing on the Ising model in a transverse field with power-law (1/r^{α}) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions (α=0), namely, when interactions and correlations are themselves permutationally invariant.

Quantum chaos and entanglement in ergodic and nonergodic systems.

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and nonergodic systems. In particular we look at the quantum kicked top and kicked rotor as multispin systems and investigate the single-spin EE which characterizes bipartite entanglement of this spin with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems and local chaos in nonergodic systems. In particular, we show that EE can be maximized even when systems are highly nonergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analog of Kolmogorov-Arnol'd-Moser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.