Cavity QED models of non-Abelian gauge theories

Gauge theories are central to the study of fundamental interactions in particle physics and have applications across condensed matter and quantum information theory. While quantum devices have successfully simulated Abelian gauge theories, the implementation of non-Abelian systems remains a major challenge. In this work, we propose and analyze a simplified model of the pure-gauge Yang-Mills theory, implemented in a cavity QED setting. Expanding the gauge fields in cavity eigenmodes, the non-Abelian structure induces a non-linear interaction between the low-frequency modes. This approach maps the gauge fields onto interacting bosonic excitations in a chain of coupled cavities, leading to an effective model reminiscent of the Bose-Hubbard Hamiltonian. We show analytically that the ground-state energy is minimized for even excitation numbers within a cavity. In particular, two-boson states form bound composite particles, which we identify as SU(2) "glueballs". We further investigate the dynamics of these glueballs using degenerate perturbation theory, revealing conditions under which they propagate as stable bound states along the cavity chain. Finally, we propose a circuit QED analog implementation of this model, demonstrating that current superconducting quantum hardware can provide a versatile platform to explore non-Abelian many-body phenomena.