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arXiv:2507.22461 · Physical Review A

Proposal for realizing Heisenberg-type quantum-spin models in Rydberg-atom quantum simulators

Masaya Kunimi, Takafumi Tomita

Published Oct 9, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|nS_{1/2}, m_J\rangle$ and $|(n+1)S_{1/2}, m_J\rangle$. 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.

DOI
10.1103/c97b-my2w

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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.
We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, 88{}^{88}88Sr and 174{}^{174}174Yb. Considering the pair of Rydberg states ∣ns,3S1,mJ⟩|ns,{}^3S_1,m_J\rangle∣ns,3S1​,mJ​⟩ and ∣(n+1)s,3S1,mJ⟩|(n+1)s,{}^3S_1,m_J\rangle∣(n+1)s,3S1​,mJ​⟩, we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for 174{}^{174}174Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in 174{}^{174}174Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in 174{}^{174}174Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.
A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.
We report the observation of electron spin interactions between Rydberg atoms, which are driven by spin-orbit coupling through second-order dipole perturbation and exhibit a spatial anisotropy governed by the atomic configuration. Specifically, we observe coherent electron spin exchange dynamics, with the measured coupling strength agreeing well with both numerical calculations and theoretical models. Furthermore, we show that global microwave dressing enables active engineering and dynamical freezing of the spin exchange by introducing a differential AC Stark shift between the participating states. Additionally, we achieve tunability of the interaction by applying a stronger magnetic field, which effectively modifies the energy contributions of the underlying spin-orbit coupling channels. Finally, measuring spin dynamics in one-dimensional multi-atom chains aligned parallel or perpendicular to the magnetic field provides a self-consistent validation of the anisotropic XXZ framework. This electron spin interaction natively features spin-position coupling and enables a natural mapping onto the Heisenberg-Kitaev model. Our findings reveal a new class of electron spin-spin interactions among Rydberg atoms, expanding the scope of quantum simulation with Rydberg atom arrays.
We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic external microwave field to engineer XXZ spin Hamiltonians with tunable anisotropies.The atoms are placed in one-dimensional (1D) and two-dimensional (2D) arrays of optical tweezers.As illustrations, we apply this engineering to two iconic situations in spin physics: the Heisenberg model in square arrays and spin transport in 1D.We first benchmark the Hamiltonian engineering for two atoms and then demonstrate the freezing of the magnetization on an initially magnetized 2D array.Finally, we explore the dynamics of 1D domain-wall systems with both periodic and open boundary conditions.We systematically compare our data with numerical simulations and assess the residual limitations of the technique as well as routes for improvement.The geometrical versatility of the platform, combined with the flexibility of the simulated Hamiltonians, opens up exciting prospects in the fields of quantum simulation, quantum information processing, and quantum sensing.
Strong interactions between sss-orbital Rydberg atoms underpin atom-array-based quantum computation and quantum simulation. Typically, the spin dependence of these interactions is negligible and plays no practical role. In this Letter, we uncover that a strong electron-spin-dependent Rydberg interaction can emerge when the principal quantum numbers of the two sss-orbital atoms differ by a sweet-spot value. This interaction originates from the fine-structure splitting of nearby ppp orbitals, which endows it with distinct symmetry properties such that the electron spins are coupled to the relative position of the two atoms, featuring a spatially defined anisotropy. We further demonstrate that this interaction admits a universal form, independent of the principal quantum numbers, and highlight its fundamental distinction from conventional magnetic dipolar interactions, establishing it as a new type of native magnetic interaction in nature. Our findings introduce a new element to the Rydberg quantum simulation toolbox. As a concrete application, we propose a native realization of the Kitaev-Heisenberg model, which hosts an unusual stripe phase as a quantum many-body manifestation of spin-space locking.
Strong mutual interaction which correlates elementary excitations of quantum matter plays a key role in a range of emergent phenomena, from binding and condensation to quantum thermalization and many-body localization. Here, we employ a Rydberg quantum simulator to experimentally demonstrate strongly correlated spin transport in anisotropic Heisenberg magnets, where the magnon-magnon interaction can be tuned 2 orders of magnitude larger than the magnon hopping strength. In our approach, the motion of magnons is controlled by an induced spin-exchange interaction through far off-resonant driving, which enables coherent transport of a single Rydberg excitation across a chain of ground-state atoms. As the most prominent signature of a giant anisotropy, we show that nearby Rydberg excitations form distinct types of magnon-bound states, where a tightly bound pair exhibits frozen dynamics in a fragmented Hilbert space, while a loosely bound pair propagates and establishes correlations beyond a single lattice site. Our scheme complements studies using resonant dipole-dipole interactions between Rydberg states and opens the door to exploring quantum thermodynamics with ultrastrong interactions and kinetic constraints. Published by the American Physical Society 2024