Floquet transverse-field Ising dynamics in a Rydberg-dressed optical tweezer array

The transverse-field Ising model (TFIM) is a paradigmatic model of quantum magnetism with broader applications in quantum control and computation. With time-dependent control of its two noncommuting terms — the interactions and the transverse field — it becomes a powerful tool for optimal control of entanglement, quantum optimization algorithms, emulating more complex spin models, or exploring driven quantum systems with no equilibrium analog. The transverse-field Ising model may be naturally implemented for cold atoms by periodically alternating between pulses of Rydberg dressing to induce interactions and microwave rotations to emulate the transverse field. In previous experimental work in a bulk gas of cesium atoms, we demonstrated such a Floquet implementation of the transverse-field Ising model, observing dynamical signatures of a mean-field paramagnet-ferromagnet phase transition. By optimizing the Rydberg dressing pulse sequence, we extended the coherence time of the interactions to generate squeezed spin states for quantum-enhanced sensing. In this poster, we present experimental upgrades to an array of single atoms in optical tweezers and discuss three directions enabled by the optical control of Ising interactions afforded by Rydberg dressing: (a) Realization of Floquet symmetry-protected topological phases, (b) simulation of emergent black hole dynamics based on a Floquet conformal field theory, and (c) optimal control of entanglement for quantum metrology.