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arXiv:2402.10651 · Physical Review Research

Quantum dimer models with Rydberg gadgets

Zhongda Zeng, Giuliano Giudici, Hannes Pichler

Published Jan 9, 2025• 13 citations
arXivHTMLPDF

Abstract

The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic nature of the blockade effect, however, restricts the range of natively accessible models and quantum states. In this work, we propose a method to systematically overcome this limitation, by developing gadgets, i.e., specific arrangements of atoms, that transform the underlying Rydberg blockade into more general constraints. We apply this technique to realize dimer models on square and triangular geometries. In these setups, we study the role of the quantum fluctuations induced by a coherent drive of the atoms and find signatures of U ( 1 ) and Z 2 quantum spin liquid states in the respective ground states. Finally, we show that these states can be dynamically prepared with high fidelity, paving the way for the quantum simulation of a broader class of constrained models and topological matter in experiments with Rydberg atom arrays.

DOI
10.1103/physrevresearch.7.l012006

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The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic nature of the blockade effect, however, restricts the range of natively accessible models and quantum states. In this work, we propose a method to systematically overcome this limitation, by developing gadgets, i.e., specific arrangements of atoms, that transform the underlying Rydberg blockade into more general constraints. We apply this technique to realize dimer models on square and triangular geometries. In these setups, we study the role of the quantum fluctuations induced by a coherent drive of the atoms and find signatures of U ( 1 ) and Z 2 quantum spin liquid states in the respective ground states. Finally, we show that these states can be dynamically prepared with high fidelity, paving the way for the quantum simulation of a broader class of constrained models and topological matter in experiments with Rydberg atom arrays.
Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.
The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
We theoretically analyze recent experiments [Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.
Programmable arrays of neutral Rydberg atoms are one of the leading platforms today for scalable quantum simulation and computation. In these systems, the dipole-dipole interactions between the individual atoms, or qubits, typically result in binary -- i.e., two-body -- couplings. In this work, we develop an experimentally accessible scheme for engineering three-body interactions in Rydberg lattices. Such strong three-body couplings can fundamentally modify the underlying physics compared to systems with only two-body interactions: we demonstrate this, in particular, by systematically investigating the effective many-body Hamiltonian and its emergent quantum phases. This capability paves the way for the quantum simulation of a broader class of correlated models of condensed matter and high-energy physics.
Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z 2 topological order [G. Semeghini , ], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.
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.