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

Quantum simulators using Rydberg atoms have recently attracted much attention [1]. So far, for the Hamiltonian of a spin system represented by the Rydberg state, pulses have been applied periodically in time, and the XYZ model [2] and the XY interaction and the mono-axial Dzyaloshinskii-Moriya (DM) interaction [3] have been implemented by using Floquet engineering. Indeed, the XYZ model has been realized experimentally [2]. We focus on the method proposed in Ref. [3], which combines global and local pulses and is irradiated periodically. We extend this technique with an optical tweezers array of Rydberg atoms on a two-dimensional square lattice and use Floquet engineering to construct a Hamiltonian with the Heisenberg interaction and a DM interaction that depends on the bond direction [4]. The advantage of this method is that the strength of the interaction can be tuned by changing the time interval of the pulses, making it possible to realize parameter regimes where the DM interaction is stronger than the exchange interaction, which is difficult to achieve in real solids. In this talk, we will present a method for constructing Hamiltonians with Heisenberg interactions and bond direction-dependent DM interactions in a system of Rydberg atoms on a two-dimensional square lattice with an optical tweezers array.

[1] A. Browaeys and T. Lahaye, Nature Phys. 16, 132 (2020).

[2] S. Geier, et al., Science 374, 1149 (2021).

[3] N. Nishad, et al., Phys. Rev. A 108, 053318 (2023).

[4] H. Kuji, et al., arXiv:2408.04160 (2024).