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arXiv:2608.23694

Universal Spin-Position Coupled Rydberg Interactions

Chengshu Li, Hui Zhai

cond-mat.quant-gascond-mat.str-elphysics.atom-phquant-phSubmitted Aug 24, 2026• Announced Aug 26, 2026• 0 citations
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Abstract

Strong interactions between $s$-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 $s$-orbital atoms differ by a sweet-spot value. This interaction originates from the fine-structure splitting of nearby $p$ 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.

Comments
6 pages, 3 figures

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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.
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.
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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.
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 investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a 87Rb^{87}\mathrm{Rb}87Rb Rydberg atom the outer electron of which interacts via spin-dependent sss- and ppp-wave scattering with a polarizable 87Rb^{87}\mathrm{Rb}87Rb ground-state atom. Our model includes also the hyperfine structure of the ground-state atom as well as spin-orbit couplings of the Rydberg and ground-state atom. We focus on ddd-Rydberg states and principal quantum numbers nnn in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauss. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.