Investigations of many-body physics in an AMO context often employ a static optical lattice to create a periodic potential. Such systems, while capable of exploring, e.g., the Hubbard model, lack the fully emergent crystalline order found in solid state systems whose stiffness is not imposed externally, but arises dynamically. We will discuss our multimode cavity QED experiment to explore the spontaneous continuous symmetry breaking observed in compliant crystallization, providing an environment to observe effects pertinent to soft condensed matter systems including frustration and liquid crystalline topological defects concomitant with superfluidity. Associative memory and spin-glasses also may form due to cavity-mediated long-range, oscillatory, and frustrated spin-spin interactions.
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