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arXiv:2408.04160 · Physical Review A

Proposal for realizing quantum-spin systems on a two-dimensional square lattice with Dzyaloshinskii-Moriya interaction by Floquet engineering using Rydberg atoms

Hiroki Kuji, Masaya Kunimi, Tetsuro Nikuni

Published Jul 28, 2025• 3 citations
arXivHTMLPDF

Abstract

We theoretically propose a method for implementing a Hamiltonian incorporating Heisenberg and Dzyaloshinskii-Moriya (DM) interactions within Rydberg atoms arranged in a two-dimensional square lattice, utilizing Floquet engineering. In our scheme, we use both global and local operations of the spins. The global operations can be realized by applying microwave pulses, and the local operations can be realized by locally addressing atoms with off-resonant lasers, which induce the site-dependent ac-Stark shift. Since our engineered Hamiltonian contains bond-dependent DM interactions, we expect the emergence of quantum skyrmions in the ground state.

DOI
10.1103/5sh7-cgyr

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We theoretically propose a method for implementing a Hamiltonian incorporating Heisenberg and Dzyaloshinskii-Moriya (DM) interactions within Rydberg atoms arranged in a two-dimensional square lattice, utilizing Floquet engineering. In our scheme, we use both global and local operations of the spins. The global operations can be realized by applying microwave pulses, and the local operations can be realized by locally addressing atoms with off-resonant lasers, which induce the site-dependent ac-Stark shift. Since our engineered Hamiltonian contains bond-dependent DM interactions, we expect the emergence of quantum skyrmions in the ground state.
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 have developed a method to simulate quantum spin models with the Dzyaloshinskii-Moriya interaction (DMI) using Rydberg atom quantum simulators. Our approach involves a two-photon Raman transition and a transformation to the spin-rotating frame, both of which are feasible with current experimental techniques. As a model that can be simulated in our setup but not in solid-state systems, we consider an S=12S=\frac{1}{2}S=21​ spin chain with a Hamiltonian consisting of the DMI and Zeeman energy. We study the magnetization curve in the ground state of this model and quench dynamics. Further, we show the existence of quantum many-body scar states and asymptotic quantum many-body scar states. The observed nonergodicity in this model demonstrates the importance of the highly tunable DMI that can be realized by the proposed quantum simulator.
Quantum computation departs from the classical paradigm of deterministic, bit-based processing by exploiting inherently quantum phenomena such as superposition and entanglement. We propose a framework for qubit realization based on skyrmionic states stabilized by the Dzyaloshinskii-Moriya interaction (DMI) in two-dimensional spin lattices. The model incorporates competing exchange interactions, perpendicular magnetic anisotropy, and Zeeman coupling, solved via exact diagonalization under periodic (PBC) and open boundary conditions (OBC). A quantum skyrmionic phase emerges for PBC within a parameter space defined by DMI, exchange, field, and anisotropy, while OBC favor classical-like, topologically protected skyrmions. Quantum logic gates (Pauli X, Y, Z, Hadamard) are implemented on both skyrmion types. Energy density and entanglement entropy analyses reveal that quantum skyrmions suffer from DMI-driven decoherence and reduced gate fidelity, whereas classical-like skyrmions maintain stability. Exact simulations of qubit dynamics, including drive effects and Lindblad decoherence, demonstrate tunable anharmonic energy levels and coherent Bloch-sphere manipulation, making these skyrmionic states promising candidates for qubit implementation. Overall, the Dzyaloshinskii-Moriya interaction plays a dual role-stabilizing skyrmionic qubits while simultaneously inducing decoherence during gate operations.
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.
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.
Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter.On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize.Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian-a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics.Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade.Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs.We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations.We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.