Rapidly rotating fermions in an anisotropic trap

We consider a cold gas of non-interacting fermions in a two-dimensional harmonic trap with two different trapping frequencies w_x\omega_x ≤ w_y\omega_y, and discuss the effect of rotation on the density profile. Depending on the rotation frequency Ω, and the trap anisotropy w_y\omega_y/w_x\omega_x, the density profile assumes two qualitatively different shapes. For small anisotropy, the density consists of elliptical plateaus of constant density, corresponding to Landau levels and is well described by a two-dimensional local density approximation. For large anisotropy, the density profile is Gaussian in the strong confining direction and semicircular with prominent Friedel oscillations in the weak direction. In this regime, a one-dimensional local density approximation is well suited to describe the system. The crossover between the two regimes is smooth where the step structure between the Landau level edges turn into Friedel oscillations.