The dynamics of many-body systems, such as large arrays of interacting spin-1/2 particles, remains one of the most challenging problems. Quantum simulation, emulating the evolution of a real system, is a promising approach to overcome this difficulty. Recent advances using low-angular-momentum Rydberg atoms trapped in optical tweezers have demonstrated simulation of systems with up to 100 spins. However, despite the long lifetime of Rydberg states on the order of 100s of microseconds, the collective lifetime of large arrays of particles reduces significantly, thereby restricting the accessible simulation time. 

Our approach uses atoms in circular Rydberg (cRy) states characterized by maximal orbital and magnetic quantum numbers. They exhibit dramatically longer lifetimes on the order of tens of milliseconds. Moreover, they decay spontaneously only via a single microwave transition to the next lower cRy state. By placing these atoms between capacitor plates spaced by a few millimeters, we can inhibit this microwave emission. It gives us an exceptionally long lifetime of the order of minutes, which is crucial for exploring longer dynamics in many-body systems. 

We are currently developing an experimental setup to prepare and trap chains of cRy atoms inside such an inhibition capacitor, operating at cryogenic temperatures near 4K. In this talk, I will present the underlying physical principles and share our latest experimental progress.