A strongly coupled cavity-quantum-electrodynamics (CQED) system can serve as a powerful platform for quantum optics and quantum information processing; however, the excitation of high-order optical modes can lead to linewidth broadening and diminished mode-matching efficiency, constraining the system’s performance. A degenerate optical cavity, in which all supported modes resonate at the same frequency, provides a means to break through these limitations, facilitating unified interactions between high-order modes and atoms. In this work, we theoretically and experimentally investigate the coupling between high-order optical orbital angular momentum modes and atoms in a degenerate cavity. The cavity consists of a $4f$ system, which possesses a stable self-imaging property that effectively suppresses atom-induced cross-mode coupling. The mode volume of the degenerate cavity and the coupling strength are analytically calculated. The interaction strength between high-order modes and atoms is measured using mode-splitting spectroscopy. The results demonstrate that the collective coupling strength $g\sqrt{N}$ of the atomic ensemble remains independent of the transverse mode distribution. This study establishes a foundation for further exploration of multimode light-matter interactions in CQED systems.

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• Angular momentum of light
• Atoms, ions, & molecules in cavities
• Cavity quantum electrodynamics
• Quantum information with atoms & light
• Quantum optics
• Quantum simulation
• Atomic ensemble
• Atomic gases