Residual degeneracy from non-degenerate Landau levels of ultracold atoms in light-induced gauge potentials

We study non-degenerate Landau levels of ultracold trapped atoms in two dimensions, subject to an U(1)×U(1)U(1)×U(1) Abelian gauge field and a lateral confining potential along a specific direction. The Landau-level degeneracy is removed due to the presence of the lateral confining potential that makes the single-particle energy spectrum explicitly dependent on the transverse momentum. The effect of the finite size of the atomic cloud on the energy spectrum is to split each Landau level into a set of sub-levels, once the transverse momentum becomes quantized. We show that under appropriate conditions some energy sub-levels overlap leading to a residual degeneracy of the system. Through numerical calculations, we map the residual degeneracy as a function of the effective magnetic field strength. Finally, we briefly discuss future studies on the transport properties of this atomic system that can be considered an optically induced atomic waveguide.