We consider a two-dimensional (2D) atomic array coupled to different photonic environments, focusing on the half-filled excitation subspace, where strong photon interactions can give rise to complex many-body states. In particular, we demonstrate that the least radiant state in this sector is well described by a coherent superposition of all possible quantum dimer coverings: a resonating valence bond liquid state. We discuss possible strategies to probe this exotic state, along with their limitations and challenges. Finally, we show that such a quantum dimer covering can also emerge as the ground state of the coherent Hamiltonian describing a 2D atomic array coupled to a photonic band-gap material.

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• Quantum optics
• Quantum simulation
• Quantum many-body systems
• Waveguides
• Exact diagonalization
• Exact solutions for many-body systems
• Quantum master equation
• Two-level models