Rapidly Rotating Fermions in an Anisotropic Trap

TL;DR

This paper studies how rotation affects the density profiles of non-interacting fermions in an anisotropic two-dimensional harmonic trap, revealing two distinct regimes with different density shapes and their crossover behavior.

Contribution

It introduces a detailed analysis of density profiles in rotating anisotropic traps, identifying two regimes and describing the crossover, including effects of temperature on these profiles.

Findings

Density profiles exhibit elliptical plateaus or Gaussian and semicircular shapes depending on anisotropy.

The crossover between regimes involves a transition from Landau level structures to Friedel oscillations.

Temperature increases wash out the density features, resulting in a Boltzmann gas profile.

Abstract

We consider a cold gas of non-interacting fermions in a two dimensional harmonic trap with two different trapping frequencies $\omega_x \leq \omega_y$, and discuss the effect of rotation on the density profile. Depending on the rotation frequency $\Omega$ and the trap anisotropy $\omega_y/\omega_x$, the density profile assumes two qualitatively different shapes. For small anisotropy ($\omega_y/\omega_x \ll \sqrt{1+4 \Omega^2/\omega_x^2}$), 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 ($\omega_y/\omega_x \gg \sqrt{1+4 \Omega^2/\omega_x^2}$), 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. Increasing the temperature causes the step structure or the Friedel oscillations to wash out leaving a Boltzmann gas density profile.