Quantum Spin-Ice and Dimer Models with Rydberg Atoms

Abstract

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.

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Plain Language Summary

Ice has always played a paradigmatic role in our understanding of statistical mechanics. The melting of an ice cube in a glass of water is one of the most familiar instances of a phase transition. In the realm of quantum mechanics, ice is just as fascinating, and it plays an archetypical role in the context of systems with competing interactions, also known as quantum frustrated systems. Such systems display many types of surprising collective behavior. In this context, quantum ice has proven to be ideally suited to exhibit how the physics of many spins and electrons can be remarkably connected to the physics of the subatomic world, in particular, electromagnetism. While “synthetic” classical ice dynamics has already been demonstrated in different solid-state platforms, realizing quantum ice is an outstanding challenge. We propose a realization of quantum-ice dynamics in a system of ultracold atoms trapped in two-dimensional optical lattice potentials. Our goal is to realize dynamical gauge fields in a synthetic system, a common theoretical tool in the description of both strongly correlated spin systems and particle physics.

Fundamentally, the dynamics of quantum ice models has to respect a set of constraints, known as ice rules, which play very much the same role as Gauss’s law in electromagnetism—they do not allow a charge (appropriately defined) to appear unless an anticharge is also closely created alongside it. Specifically, these ice rules require that, at each vertex of the lattice, the number of incoming and outgoing flux lines (of the synthetic gauge field) are equal, thus imposing net charge neutrality. We show how this set of constraints can be faithfully implemented using the properties of laser-excited Rydberg states (i.e., states with large principal quantum numbers) of rubidium atoms. These highly excited atomic states display interactions that are orders of magnitude larger than the interactions of ground-state atoms. This feature, combined with the anisotropic nature of the interparticle potentials, provides a large energy scale on which to constrain the system dynamics.

The very same route can be pursued on many lattice geometries, including kagome and honeycomb lattices.

Our detailed analysis of the many-body effects of realistic van der Waals interaction potentials shows how the exotic states of quantum ice can be experimentally accessed.