Probing Quantum Floating Phases in Rydberg Atom Arrays*

Quantum floating phases, long proposed in commensurate-incommensurate transitions, have lacked experimental confirmation. In this study, we experimentally observe a quantum floating phase using Rydberg arrays with ladder geometries, employing up to 92 qubits. Our analysis reveals that 1+1 dimensions with rectangular arrays of Rydberg atoms have an extended region in the phase diagram where the floating phase appears. Through meticulous comparisons of measurements across phases and system sizes, incommensurate order within the floating phase is observed Unique bitstring distributions characterize each phase, emphasizing the critical state's distinctive nature. Our findings hint at potential applications of ladder-shaped atom arrays in quantum simulation research, advancing our understanding of quantum phases and paving the way for further exploration in Rydberg dynamics using neutral atom arrays.