Degenerate Landau levels for tripod-type cold atoms in U(2) Abelian gauge field

We propose a laser configuration to create degenerate Landau levels for tripod-type cold atoms in the presence of an optically induced gauge field. In previous works with cold atoms in tripod configuration, the gauge field has a non-Abelian term that makes the Landau levels nondegenerate and changes the structure of the energy spectrum. Here, the synthetic gauge field is purely Abelian and leads to degenerate Landau levels with an energy spectrum having a similar structure as those for standard changed particle system. We present the appropriate conditions to that the lowest Landau level regime have been reached.