We show how a broad class of lattice spin-1/2 models with angular-and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop", and "flipflip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-theart experiments.PACS numbers: 37.10. Jk, 32.80.Ee,75.10.Jm Understanding exotic forms of quantum magnetism is an outstanding challenge of condensed matter physics [1]. Cold atoms stored in optical or magnetic trap arrays provide a unique platform to realize interacting quantum spins in various lattice geometries with tunable interactions, and thus the basic ingredients of competing magnetic orders and frustrated magnetism [2]. A central experimental challenge for the observation of magnetic phases with cold atoms is given by the requirement of ultralow temperatures (and entropies), as set by the interaction scales of magnetic interactions. For spin models derived from Hubbard dynamics for atoms in optical lattices, this energy scale is set by the super-exchange processes, J ∼ t 2 H /U , with t H the hopping amplitude of atoms between lattice sites, and U the onsite interactions, resulting in (rather small) energy scales of a few-tens of Hertz (or few nK) regime [3] (see, however, Ref. [4]). Instead, we consider below laser-excited interacting Rydberg atoms [5], which provide us not only with a complete toolbox to design and realize the complex spin-1/2 models of interest, but also give rise to energy scales much larger than relevant decoherence rates. In contrast to models where a spin is encoded directly in a Rydberg state [6] we use ground state atoms weakly dressed with Rydberg states by laser light [7], which can be trapped in (large spacing) optical [8] or magnetic lattices [9] of various geometries. This provides a viable route to make phases of exotic quantum magnetism accessible to present atomic experiments.We are interested in general XY Z spin-1/2 models with both isotropic and anisotropic interactions in 2D, where S j α are spin-1/2 operators at the lattice sites r j . Our goal is to design spin-spin interaction patterns arXiv:1410.3388v2 [quant-ph] 30 Apr 2015

Quantum spin-ice represents a paradigmatic example of how the physics of frustrated magnets is related to gauge theories. In the present work, we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly laser-admixing Rydberg states to the atomic ground-states, exploiting the strong angular dependence of van der Waals interactions between Rydberg p states together with the possibility of designing steplike potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state-of-the-art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s-and p-Rydberg states in exotic geometries, e.g., on a 4-8 lattice.

There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner–Hauke–Zoller (LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a platform for quantum annealing. In LHZ an infinite-range spin-glass is mapped onto the low energy subspace of a spin-1/2 lattice gauge model with quasi-local four-body parity constraints. This spin model can be emulated in a natural way with Rubidium and Caesium atoms in a bipartite optical lattice involving laser-dressed Rydberg–Rydberg interactions, which are several orders of magnitude larger than the relevant decoherence rates. This makes the exploration of coherent quantum enhanced optimization protocols accessible with state-of-the-art atomic physics experiments.