Spin Fluctuations, Susceptibility, and the Dipole Oscillation of a Nearly Ferromagnetic Fermi Gas

We discuss the spin fluctuations and the role played by the magnetic susceptibility in an atomic Fermi gas interacting with a positive scattering length. Both thermal and zero-temperature quantum fluctuations are considered. Using a sum rule approach and recent ab initio Monte Carlo results for the magnetic susceptibility of uniform matter, we provide explicit predictions for the frequency of the spin dipole oscillation of a gas trapped by a harmonic potential and discuss the deviations from the ideal gas behavior when the system approaches the ferromagnetic transition. The role of the Landau’s parameters in the characterization of the magnetic properties is also discussed.

Figure 1

Inverse spin susceptibility for an homogeneous Fermi gas as a function of the interaction parameter $k_{F}a$. Points: Monte Carlo data from Ref. 8. Dashed (green) line: Fit to the Monte Carlo data. The dot-dashed (blue) and the continuous (red) lines are the first- and second-order expansion, respectively [see Eq. (8)].

Figure 2

Main panel: Spin dipole frequency as a function of the interaction parameter $k_F^{0}a$ (see the text). The dashed line is the first-order expansion Eq. (13). The dash-dotted horizontal line is the position at which the susceptibility should diverge at the center of the cloud. Inset: The value of the interaction parameter $k_{F}a$ in the trap as a function of $k_F^{0}a$. $k_F$ is the Fermi momentum of the interacting cloud calculated at the center of the trap.