Photonic Landau levels in a high-dimensional frequency-degenerate cavity

Topological orders emerge in both microscopic quantum dynamics and macroscopic materials as a fundamental principle to characterize intricate properties in nature with vital significance, for instance, the Landau levels of electron systems in magnetic field. Whilst, recent advances of synthetic photonic systems enable generalized concepts of Landau levels across fermionic and bosonic systems, extending the modern physical frontier. However, the controls of Landau levels of photons were only confined in complex artificial metamaterials or multifolded cavities. Here, we exploit advanced structured light laser technology and propose the theory of high-dimensional frequency-degeneracy, which enables photonic Landau level control in a linear open laser cavity with simple displacement tuning of intracavity elements. This work not only create novel structured light with new topological effects but also provides broad prospects for Bose-analogue quantum Hall effects and topological physics.