Probing Fractional Quantum Hall states in weakly interacting Fermi gases

Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to achieve in practice. We point out that for weakly interacting Fermi gases, this rapid-rotation limit is not needed to access the LLL: As a direct consequence of first-order perturbation theory, many-body wave functions of states in the LLL remain unchanged at any rotation, and only their energies shift. This implies that even in the absence of rotations or for moderate rotations frequencies, LLL states are present as excited states at finite angular momentum. For fermions with contact interactions, these states are exact eigenstates of a paradigmatic model of Fractional Quantum Hall (FQH) states described by a single Haldane pseudopotential ($V_1$ for spin-polarized and $V_0$ for spinful systems), which realizes exact Laughlin and Haldane wave functions. We suggest that recently developed excitation and imaging techniques for rotating few-fermion systems allow for a detailed experimental investigation of FQH wave functions and to study the crossover to large particle number. We illustrate this for $N = 6$ spin-balanced fermions