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arXiv:2306.07041 · Physical Review A

Quantum simulation of generic spin-exchange models in Floquet-engineered Rydberg-atom arrays

Naveen Nishad, Anna Keselman, Thierry Lahaye, Antoine Browaeys, Shai Tsesses

Published Nov 21, 2023• 28 citations
arXivHTMLPDF

Abstract

Although quantum simulation can give insight into elusive or intractable physical phenomena, many quantum simulators are unavoidably limited in the models they mimic. Such is also the case for atom arrays interacting via Rydberg states, a platform potentially capable of simulating any kind of spin exchange model, albeit with currently unattainable experimental capabilities. Here, we propose a route towards simulating generic spin-exchange Hamiltonians in atom arrays, using Floquet engineering with both global and local control. To demonstrate the versatility and applicability of our approach, we numerically investigate the generation of several spin-exchange models which have yet to be realized in atom arrays, using only previously demonstrated experimental capabilities. Our proposed scheme can be readily explored in many existing setups, providing a path to investigate a large class of exotic quantum spin models.

DOI
10.1103/physreva.108.053318

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Although quantum simulation can give insight into elusive or intractable physical phenomena, many quantum simulators are unavoidably limited in the models they mimic. Such is also the case for atom arrays interacting via Rydberg states, a platform potentially capable of simulating any kind of spin exchange model, albeit with currently unattainable experimental capabilities. Here, we propose a route towards simulating generic spin-exchange Hamiltonians in atom arrays, using Floquet engineering with both global and local control. To demonstrate the versatility and applicability of our approach, we numerically investigate the generation of several spin-exchange models which have yet to be realized in atom arrays, using only previously demonstrated experimental capabilities. Our proposed scheme can be readily explored in many existing setups, providing a path to investigate a large class of exotic quantum spin models.
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.
Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.
Many-body cages have very recently emerged as a general route for nonergodic behaviour in quantum matter. Here, we show that new types of many-body cages can be engineered in Floquet circuits with the potential to realize novel nonequilibrium quantum states. For that purpose, we first identify an explicit, general construction of Floquet circuits capable of hosting many-body cages. We then present a generic strategy to engineer and structure Floquet many-body cages. We demonstrate the developed scheme for the quantum hard disk model as a generic constrained model system, realizable for instance in Rydberg atom arrays. We construct Floquet circuits yielding Floquet many-body cages with topological properties and πππ-quasienergy modes, implying `time crystalline' spatiotemporal order. Our results can be directly extended to general quantum circuits, thus providing a new tool to engineer nonequilibrium behaviour in driven systems.
A frontier challenge in quantum science and technology is the construction of scalable quantum systems which can operate in regimes beyond classical simulatability. Such systems can be used as tools for simulating and exploring complex phenomena in quantum physics; they can also be used to benchmark and test quantum algorithms. Several experimental platforms, based on a variety of quantum mechanical building blocks, are currently being pursued with these goals in mind, with state-of-the-art systems capable of controlling up to around fifty particles. In this thesis, we present the development of a new platform based on individually controlled neutral atoms. In this approach, hundreds of individual atoms are trapped in an array of optical tweezers, and they are sorted in real-time into programmable geometries in one and two dimensions. After initialization of an array, atom interactions are switched on by coherent excitation to highly excited Rydberg states, resulting in a rich spin Hamiltonian. We experimentally advance several key aspects of this platform, developing new tools for controlling strongly interacting atom arrays and probing novel quantum phases and non-equilibrium dynamics. We additionally utilize Rydberg interactions to entangle atoms, demonstrating high fidelity universal quantum logic gates as well as the preparation of fully entangled Schrödinger cat states. This work highlights the prospects for scalable quantum simulation and quantum information processing beyond the limit of classical computation using neutral atom arrays.
We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, ∣nS1/2,mJ⟩|nS_{1/2}, m_J\rangle∣nS1/2​,mJ​⟩ and ∣(n+1)S1/2,mJ⟩|(n+1)S_{1/2}, m_J\rangle∣(n+1)S1/2​,mJ​⟩. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it XXZ} model can be tuned by applying a magnetic field and, in particular, that it changes drastically near the Förster resonance points. Based on this result, we propose experimental realizations of spin-1/2 and spin-1 Heisenberg-type quantum spin models in Rydberg atom quantum simulators, without relying on Floquet engineering. Our results provide guidance for future experiments of Rydberg atom quantum simulators and offer insight into quantum many-body phenomena emerging in the Heisenberg model.