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.

Abstract. We explore the prospects for confining alkaline-earth Rydberg atoms in an optical lattice via optical dressing of the secondary core valence electron. Focussing on the particular case of strontium, we identify experimentally accessible magic wavelengths for simultaneous trapping of ground and Rydberg states. A detailed analysis of relevant loss mechanisms shows that the overall lifetime of such a system is limited only by the spontaneous decay of the Rydberg state, and is not significantly affected by photoionization or autoionization. The van der Waals C 6 coefficients for the Sr(5sns 1 S 0 ) Rydberg series are calculated, and we find that the interactions are attractive. Finally we show that the combination of magic-wavelength lattices and attractive interactions could be exploited to generate many-body Greenberger-HorneZeilinger (GHZ) states.

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We derive and investigate the microscopic model of the quantum magnet BiCu2PO6 using band structure calculations, magnetic susceptibility and high-field magnetization measurements, as well as Exact Diagonalization (ED) and Density-Matrix Renormalization Group (DMRG) techniques. The resulting quasi-one-dimensional spin model is a two-leg antiferromagnetic ladder with frustrating next-nearest-neighbor couplings along the legs. The individual couplings are estimated from band structure calculations and by fitting the magnetic susceptibility with theoretical predictions, obtained using full diagonalizations. The nearest-neighbor leg coupling J1, the rung coupling J4, and one of the next-nearest-neighbor couplings J2 amount to 120 − 150 K, while the second nextnearest-neighbor coupling is J ′ 2 ≃ J2/2. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions J2 and J ′ 2 have very similar superexchange pathways, they differ substantially in magnitude due to a tiny difference in the O-O distances and in the arrangement of non-magnetic PO4 tetrahedra. An extensive ED study of the proposed model provides the low-energy excitation spectrum and shows that the system is in the strong rung coupling regime. The strong frustration by the next-nearest-neighbor couplings leads to a triplon branch with an incommensurate minimum. This is further corroborated by a strong-coupling expansion up to second order in the inter-rung coupling. Based on high-field magnetization measurements, we estimate the spin gap of ∆ ≃ 32 K and suggest the likely presence of antisymmetric DzyaloshinskiiMoriya anisotropy and inter-ladder coupling J3. We also provide a tentative description of the physics of BiCu2PO6 in magnetic field, in the light of the low-energy excitation spectra and numerical calculations based on ED and DMRG. In particular, we raise the possibility for a rich interplay between one-and two-component Luttinger liquid phases and a magnetization plateau at 1/2 of the saturation value.

We report magnetization and specific heat measurements on polycrystalline samples of BaCdVO(PO4)2 and show that this compound is a S = 1/2 frustrated square lattice with ferromagnetic nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) interactions. The coupling constants J1 ≃ −3.6 K and J2 ≃ 3.2 K are determined from a fitting of the susceptibility data and confirmed by an analysis of the saturation field (µ0Hs = 4.2 T), the specific heat, and the magnetic entropy. BaCdVO(PO4)2 undergoes magnetic ordering at about 1 K, likely towards a columnar antiferromagnetic state. We find that BaCdVO(PO4)2 with the frustration ratio α = J2/J1 ≃ −0.9 is closer to a critical (quantum spin liquid) region of the frustrated square lattice than any of the previously reported compounds. Positive curvature of the magnetization curve is observed in agreement with recent theoretical predictions for high-field properties of the frustrated square lattice close to the critical regime.

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