Optomechanical self-organization in a mesoscopic atom array

Increasing the number of particles in a system often leads to qualitative changes in its properties, such as breaking of symmetries and the appearance of phase transitions. This renders a macroscopic system fundamentally different from its individual microscopic constituents. Lying between these extremes, mesoscopic systems exhibit microscopic fluctuations that influence behavior on longer length scales, leading to critical phenomena and dynamics. Therefore, tracing the properties of well-controlled mesoscopic systems can help bridge the gap between an exact description of few-body microscopic systems and the emergent description of many-body systems. Here, we explore mesoscopic signatures of an optomechanical self-organization phase transition using arrays of cold atoms inside an optical cavity. By precisely engineering atom-cavity interactions, we reveal how critical behavior depends on atom number, identify characteristic dynamical behaviors in the self-organized regime, and observe a finite optomechanical susceptibility at the critical point. These findings advance our understanding of particle-number- and time-resolved properties of phase transitions in mesoscopic systems.