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Quantum Magnetism in Dipolar Rydberg Atom Arrays

Marcus Bintz

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

This thesis demonstrates that arrays of electric dipoles are good analogs for quantum magnets. We center our investigation on a recently developed experiment, in which rubidium-87 atoms are trapped in optical tweezers and then excited into two distinct electronic Rydberg states. The electric dipole-dipole interaction between these Rydberg atoms is mathematically modeled by a spin Hamiltonian with easy-plane anisotropy, and coupling strength decaying as the inverse cube of the distance. We approximately solve for the ground state of this model Hamiltonian on each of the eleven Archimedean lattices, through large-scale density matrix renormalization group calculations. For the kagome lattice, we gather extensive numerical evidence for an emergent quantum spin liquid, similar to that occurring in the canonical Heisenberg model of quantum magnetism. We predict this spin liquid to be of 𝑈(1) Dirac type, and propose new protocols for experimentally preparing and characterizing it. Our theoretical calculations support the collaborative design and analysis of experiments studying dipolar Rydberg atoms in square, circular, and kagome arrays. These respectively result in observations of continuous symmetry breaking, Tomonaga-Luttinger liquid behavior, and an atomic spin liquid candidate.

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•Oct 6, 2023•0 citations
This thesis demonstrates that arrays of electric dipoles are good analogs for quantum magnets. We center our investigation on a recently developed experiment, in which rubidium-87 atoms are trapped in optical tweezers and then excited into two distinct electronic Rydberg states. The electric dipole-dipole interaction between these Rydberg atoms is mathematically modeled by a spin Hamiltonian with easy-plane anisotropy, and coupling strength decaying as the inverse cube of the distance. We approximately solve for the ground state of this model Hamiltonian on each of the eleven Archimedean lattices, through large-scale density matrix renormalization group calculations. For the kagome lattice, we gather extensive numerical evidence for an emergent quantum spin liquid, similar to that occurring in the canonical Heisenberg model of quantum magnetism. We predict this spin liquid to be of 𝑈(1) Dirac type, and propose new protocols for experimentally preparing and characterizing it. Our theoretical calculations support the collaborative design and analysis of experiments studying dipolar Rydberg atoms in square, circular, and kagome arrays. These respectively result in observations of continuous symmetry breaking, Tomonaga-Luttinger liquid behavior, and an atomic spin liquid candidate.
We predict that the gapless U(1)U(1)U(1) Dirac spin liquid naturally emerges in a two-dimensional array of quantum dipoles. In particular, we demonstrate that the dipolar XY model$\unicode{x2014}$realized in both Rydberg atom arrays and ultracold polar molecules$\unicode{x2014}$hosts a quantum spin liquid ground state on the kagome lattice. Large-scale density matrix renormalization group calculations indicate that this spin liquid exhibits signatures of gapless, linearly-dispersing spinons, consistent with the U(1)U(1)U(1) Dirac spin liquid. We identify a route to adiabatic preparation via staggered on-site fields and demonstrate that this approach can prepare cold spin liquids within experimentally realistic time-scales. Finally, we propose a number of novel signatures of the Dirac spin liquid tailored to near-term quantum simulators, including termination-dependent edge modes and the Friedel response to a local perturbation.
We experimentally investigate a frustrated spin-exchange antiferromagnet in a quantum simulator, composed of N = 114 dipolar Rydberg atoms arranged into a kagome array. Motivated by a recent theoretical proposal of a gapless U(1) Dirac spin liquid ground state, we use local addressing to adiabatically prepare low-energy states. We measure the local polarization and spin-spin correlations over this adiabatic protocol, and observe our system move from a staggered product state, through an intermediate magnetic crystal, and finally into a disordered, correlated liquid. We estimate the entropy density of this atomic liquid to be similar to that of frustrated magnetic insulators at liquid nitrogen temperatures. We compare the correlations in our liquid to those of a simple, parameter-free ansatz for the Dirac spin liquid, and find good agreement in the sign structure and spatial decay. Finally, we probe the static susceptibility of our system to a local field perturbation and to a geometrical distortion. Our results establish Rydberg atom arrays as a promising platform for the preparation and microscopic characterization of quantum spin liquid candidates.
Neutral atoms become strongly interacting when their electrons are excited to loosely bound Rydberg states. We investigate the strongly correlated quantum phases of matter that emerge in two-dimensional atom arrays where three Rydberg levels are used to encode an effective spin-1 degree of freedom. Dipolar exchange between such spin-1 Rydberg atoms naturally yields two distinct models: (i) a two-species hardcore boson model, and (ii) upon tuning near a Förster resonance, a dipolar spin-1 XY model. Through extensive, large-scale infinite density matrix renormalization group calculations, we provide a broad roadmap predicting the quantum phases that emerge from these models on a variety of lattice geometries: square, triangular, kagome, and ruby. We identify a wealth of correlated states, including lattice supersolids and simplex phases, all of which can be naturally realized in near-term experiments.
Despite long-standing theoretical interest, the chiral spin liquid, a topologically ordered phase, has yet to be observed experimentally. Here we surprisingly find its emergence in an experimentally realized dipolar XY\text{XY}XY model when Rydberg atoms are arranged in a breathing kagome lattice. Using the infinite density matrix renormalization group, we numerically calculate the ground state's chiral order parameter, spin-spin correlations, Chern number, and entanglement spectrum. Our numerical results provide strong evidence for the chiral spin liquid phase. Furthermore, we identify a quantum phase transition from a Dirac spin liquid to a chiral spin liquid as the lattice geometry is tuned from the isotropic kagome to the breathing kagome lattice.
We report numerical ground states for the dipolar XY spin model, which describes extended antiferromagnetic interactions in two-dimensional arrays of polar molecules and two-level Rydberg atoms. Carrying out large-scale density matrix renormalization group (DMRG) calculations, we compute ground state properties on nine of the eleven Archimedean lattices--tilings of the plane by regular polygons. Four of these host trivial paramagnets, while another four develop collinear Neel magnetic order, as was found previously for the square lattice. For the ordered states, we calculate the hydrodynamic parameters (magnetization, susceptibility, and stiffness) and compare to linear spin wave theory. We also investigate the triangular lattice, for which we find several competing phases including coplanar magnetism, stripe density wave order, and a possible spin liquid; their relative stability is sensitive to the long-range couplings present in our dipolar model. Finally, the Archimedean classification is completed by the kagome lattice, which we argue in a companion work is likely to be a Dirac spin liquid.
Circular Rydberg atoms, with their long lifetimes and adjustable strong dipolar interactions, are promising candidates for the implementation of quantum simulations in regimes that were previously out of reach. A new quantum simulator paradigm, based on qubits encoded in circular states, would implement an XXZ spin-1/2 Hamiltonian with dynamically adjustable parameters over a wide range of values. This thesis addresses the preliminary steps in constructing such a quantum simulator. First, we present the realization of two-dimensional arrays of optically-trapped circular Rydberg atoms with arbitrary geometries. For this purpose, we prepare arrays of ultra-cold rubidium atoms, individually trapped in optical tweezers. An additional beam with adjustable position allows us to rearrange the atoms within the array to implement the desired geometry in a deterministic manner. We then excite the atoms to the circular state with principal quantum number n=52, while trapping them in hollow beams using the ponderomotive force. These experimental capabilities allowed us to control and characterize, for the first time, the dipolar interactions between circular states, within pairs of individually trapped atoms. We showed the good agreement of these measurements with theoretical expectations and highlighted their dependence on the system's geometry. This experimental study is coupled to an investigation of the motion of the circular atoms within their traps.