Towards the simulation of a 1-D and 2-D transverse Ising model with a Rydberg-dressed atom array

We propose novel applications for quantum simulation utilizing an array of tweezer-trapped Rydberg atoms within an optical cavity. A programmable array of Rydberg atoms combined with cavity-mediated interactions is a versatile platform for quantum simulation of mesoscopic systems.

Within quantum simulation, a particular region of interest in condensed matter and AMO physics is the observation of quantum phase transitions in single atoms. With our Rydberg-cavity system, we can perform quantum simulation of the transverse field Ising model by encoding spins as Rydberg-dressed hyperfine ground states. The long coherence time of the Rydberg-dressed state enables us to achieve real-time observation of the phase transition from paramagnet to ferromagnet using cavity-based weak measurement. Additionally, the use of single atoms allows for detailed exploration of the dynamics within both a 1-D and 2-D Ising model, while the reconfigurable geometry of the tweezer array enables the investigation of phenomena such as a frustration.

Alternatively, we can leverage the cavity to realize all-to-all interactions in tandem with Rydberg nearest-neighbor interactions. From these effects, we can generate a transverse Ising chain coupled to a photonic field to study the rich physics of the Dicke-Ising model.