Arrays of Rydberg atoms interacting via dipole-dipole interactions offer a powerful platform for probing quantum many-body physics. However, these intrinsic interactions also determine and constrain the models-and parameter regimes thereof-for quantum simulation. Here, we propose a systematic framework to engineer arbitrary desired long-range interactions in Rydberg-atom lattices, enabling the realization of fully tunable J_{1}-J_{2}-J_{3} Heisenberg models. Using site-resolved periodic modulation of Rydberg states, we develop an experimentally feasible protocol to precisely control the interaction ratios J_{2}/J_{1} and J_{3}/J_{1} in a kagome lattice. This control can increase the effective range of interactions and drive transitions between competing spin-ordered and spin-liquid phases. To generalize this approach beyond the kagome lattice, we reformulate the design of modulation patterns through a graph-theoretic approach, demonstrating the universality of our method across all 11 planar Archimedean lattices. Our strategy overcomes the inherent constraints of power-law-decaying dipolar interactions, providing a versatile toolbox for exploring frustrated magnetism, emergent topological phases, and quantum correlations in systems with long-range interactions.
Arrays of Rydberg atoms interacting via dipole-dipole interactions offer a powerful platform for probing quantum many-body physics. However, these intrinsic interactions also determine and constrain the models-and parameter regimes thereof-for quantum simulation. Here, we propose a systematic framework to engineer arbitrary desired long-range interactions in Rydberg-atom lattices, enabling the realization of fully tunable J_{1}-J_{2}-J_{3} Heisenberg models. Using site-resolved periodic modulation of Rydberg states, we develop an experimentally feasible protocol to precisely control the interaction ratios J_{2}/J_{1} and J_{3}/J_{1} in a kagome lattice. This control can increase the effective range of interactions and drive transitions between competing spin-ordered and spin-liquid phases. To generalize this approach beyond the kagome lattice, we reformulate the design of modulation patterns through a graph-theoretic approach, demonstrating the universality of our method across all 11 planar Archimedean lattices. Our strategy overcomes the inherent constraints of power-law-decaying dipolar interactions, providing a versatile toolbox for exploring frustrated magnetism, emergent topological phases, and quantum correlations in systems with long-range interactions.
Long-range interactions are important to complex physical systems. Specifically in quantum mechanical many-body systems, long-range interactions promote spatial structures, give rise to quantum frustration, and generate quantum entanglement. Nevertheless, quantum simulations of lattice systems have largely not been able to realize long-range interactions. Many efforts are underway to explore long-range interacting lattice systems using polar molecules, Rydberg atoms, and magnetic atoms. In this thesis, I present the realization of long-range interacting itinerant systems using magnetic erbium atoms. I start by discussing the construction of the Erbium quantum gas microscope, including the installation of an in-vacuum high-numerical-aperture objective, various optical lattices, and potential projection through the objective. Then, I present emerging quantum phases with half-filling and directly probe the spatial structures of dipolar quantum solids using site-resolved imaging. A kaleidoscope of phases emerges as we tune the dipolar interaction, demonstrating the great tunability of this experimental platform. The dipolar interactions can be tuned slowly to study first-order quantum phase transitions between different solids. Next, I discuss topological phases that emerge with unity filling. With a zoo of Fano-Feshbach resonances, erbium atoms are gifted with the flexibility of widely tunable on-site interaction, allowing continuous probing of the quantum phase transitions between topologically trivial and non-trivial phases. We explore average symmetry protected topological phases as an instance of the mixed state quantum order. Finally, I briefly discuss the observation of spin squeezing with itinerant systems and super- and sub-radiance in a sub-wavelength optical lattice.
Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.
Analog quantum simulations with Rydberg atoms in optical tweezers have emerged as a powerful tool for exploring strongly correlated many-body physics. However, the range of accessible phenomena remains limited by constraints in controlling many-body interactions in these systems. Here, we propose an alternative approach to realizing tunable interactions using Rydberg dressing on Aquila, a 256-atom quantum simulator based on optical tweezer arrays. By weakly admixing a Rydberg state via off-resonant laser coupling, we generate long-range interactions with temporal control. In combination with programmable atom geometries and site-selective control, this dressing protocol enables simulation of quantum spin models with state preparation and measurement in arbitrary basis. These capabilities enable access to exciting regimes of quantum simulation, including Quantum spin liquids, XYZ lattice models and broader application of quantum reservoir computing. Our approach establish Rydberg dressing as a practical and scalable tool for expanding the class of many-body systems accessible to analog quantum simulation and provides a critical stepping stone toward quantum machine learning and hybrid analog-digital quantum simulation with neutral atoms.
Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting frontier in quantum science. Programmable quantum simulators based on neutral atom arrays are a promising approach to achieve this goal, since strong Rydberg blockade interactions can be used to naturally create low energy subspaces that can encode local gauge constraints. However, realizing regimes of LGTs where both matter and gauge fields exhibit significant dynamics requires the presence of tunable multi-body interactions such as those associated with ring exchange, which are challenging to realize directly. Here, we develop a method for generating such interactions based on time-periodic driving. Our approach utilizes controlled deviations from time-reversed trajectories, which are accessible in constrained PXP-type models via the application of frequency modulated global pulses. We show that such driving gives rise to a family of effective Hamiltonians with multi-body interactions whose strength is non-perturbative in their respective operator weight. We apply this approach to a two-dimensional U(1) LGT on the Kagome lattice, where we engineer strong six-body magnetic plaquette terms that are tunable relative to the kinetic energy of matter excitations, demonstrating access to previously unexplored dynamical regimes. Potential generalizations and prospects for experimental implementations are discussed.
Quantum phases with topological order, such as quantum spin liquids, have been the focus of explorations for several decades. Such phases feature a number of remarkable properties including long-range quantum entanglement. Moreover, they can be potentially exploited for the realization of robust quantum computation, as exemplified by the paradigmatic toric code model. While some indications that such phases may be present in frustrated condensed matter systems have been previously reported, so far quantum spin liquids have eluded direct experimental detection. In this talk, I will show how a programmable quantum simulator based on Rydberg atom arrays can be used to realize and probe quantum spin liquid states. In our approach, atoms are placed on the links of a kagome lattice and coherent evolution under Rydberg blockade enables the transition into frustrated quantum states with no local order. We detect the onset of a quantum spin liquid phase of the toric code type by measuring topological string operators in two complementary bases. The properties of this state are further revealed using a lattice with non-trivial topology, representing a step towards the realization of a topological qubit. Our observations open the door to the controlled experimental exploration of topological quantum matter, and could enable the investigation of new methods for topologically protected quantum information processing.
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.