[Paper Review] Ferromagnetism in repulsive Fermi gases: upper branch of Feshbach resonance versus hard spheres

Soon Yong Chang, Mohit Randeria+1 more|arXiv (Cornell University)|Apr 15, 2010

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This study uses quantum Monte Carlo with backflow corrections to investigate ferromagnetic instability in repulsive Fermi gases, comparing the upper branch of a Feshbach resonance with hard-sphere interactions. It finds a critical $k_{F}a \approx 0.89$ for ferromagnetism in both systems, significantly lower than mean-field predictions, highlighting distinct short-range correlations and kinetic energy behaviors despite similar total energies.

ABSTRACT

We use quantum Monte Carlo, including backflow corrections, to investigate a two-component Fermi gas on the upper branch of a Feshbach resonance and contrast it with the hard sphere gas. We find that, in both cases, the Fermi liquid becomes unstable to ferromagnetism at a $k_F a$ smaller than the mean field result, where $k_F$ is the Fermi wavevector and $a$ the scattering length. Even though the total energies $E(k_F a)$ are similar in the two cases, their pair correlations and kinetic energies are completely different, reflecting the underlying potentials. We discuss the extent to which our calculations shed light on recent experiments.

Motivation & Objective

• To investigate the stability of repulsive Fermi gases against ferromagnetism using accurate many-body methods.
• To compare the upper branch of a Feshbach resonance with a hard-sphere model in terms of ground state properties and ferromagnetic transitions.
• To assess the validity of mean-field theory in strong-coupling repulsive Fermi systems.
• To provide a benchmark for interpreting recent ultracold atom experiments on repulsive Fermi gases.

Proposed method

• Employed continuous-time quantum Monte Carlo with backflow corrections to compute ground state energies, pair correlations, and kinetic energies.
• Used a zero-range effective interaction model with tunable scattering length $a$ to simulate both upper branch and hard-sphere cases.
• Applied the local density approximation (LDA) to map homogeneous results to harmonically trapped systems for comparison with experiments.
• Calculated the chemical potential and equation of state from QMC data to determine the onset of ferromagnetism in trapped configurations.
• Used the pair distribution function $g(r)$ and kinetic energy to probe short-range correlations and their dependence on interaction type.
• Validated results against perturbative and mean-field theories, emphasizing the limitations of the latter in strong coupling.

Experimental results

Research questions

• RQ1 Does the upper branch of a Feshbach resonance exhibit ferromagnetic instability, and at what $k_Fa$ value?
• RQ2 How does the ferromagnetic transition in the upper branch compare quantitatively and qualitatively to that in a hard-sphere Fermi gas?
• RQ3 To what extent do backflow corrections affect the stability and energy of the many-body state in these systems?
• RQ4 How do the kinetic energy and pair correlations differ between the upper branch and hard-sphere models despite similar total energies?
• RQ5 Can the equilibrium QMC results explain the observed features in recent ultracold atom experiments?

Key findings

• Ferromagnetic instability occurs at $k_Fa = 0.89(2)$ in the upper branch of the Feshbach resonance, independent of the underlying potential details in the zero-range limit.
• The critical $k_Fa$ for ferromagnetism is substantially lower than the mean-field Stoner prediction of $\pi/2 \approx 1.57$.
• Despite similar total energies, the kinetic energy and pair correlations differ significantly between the upper branch and hard-sphere systems, reflecting distinct short-range correlations.
• Backflow corrections have negligible effect on the upper branch results but are crucial for avoiding spurious ferromagnetic instabilities in other systems.
• In the harmonically trapped system, ferromagnetism is predicted to onset at the trap center when $k_F^0a \simeq 1.1$, corresponding to $k_Fa = 0.89$ in the homogeneous limit.
• The QMC results show qualitative agreement with experiment in the chemical potential trend but disagree in the kinetic energy behavior, suggesting unexplained dynamics or non-equilibrium effects in the experiment.