This study investigates the quantum phases in ladder arrays of Rydberg atoms, focusing on the emergence of the quantum floating phase. The researchers experimentally observe and analyze the formation of domain walls within the commensurate ordered phase, which subsequently give rise to the floating phase with incommensurate quasi-long-range order. By analyzing the site-resolved Rydberg state densities and state occurrences, they reveal that the floating phase exhibits a continuous distribution of wave vectors that are incommensurate with the lattice. As the system size increases, these wave vectors approach a continuum of values. The study provides numerical support for the full phase diagram of the ladder system and demonstrates the experimental measurement of various phase regimes. The findings highlight the potential of Rydberg atom arrays as highly programmable quantum simulators, facilitating the exploration of critical phenomena and quantum many-body phases.This study investigates the quantum phases in ladder arrays of Rydberg atoms, focusing on the emergence of the quantum floating phase. The researchers experimentally observe and analyze the formation of domain walls within the commensurate ordered phase, which subsequently give rise to the floating phase with incommensurate quasi-long-range order. By analyzing the site-resolved Rydberg state densities and state occurrences, they reveal that the floating phase exhibits a continuous distribution of wave vectors that are incommensurate with the lattice. As the system size increases, these wave vectors approach a continuum of values. The study provides numerical support for the full phase diagram of the ladder system and demonstrates the experimental measurement of various phase regimes. The findings highlight the potential of Rydberg atom arrays as highly programmable quantum simulators, facilitating the exploration of critical phenomena and quantum many-body phases.