Ferromagnetic spin correlations in a few-fermion system

We study the spin correlations of a few fermions in a quasi-one-dimensional trap. Exact diagonalization calculations demonstrate that repulsive interactions between the two species drives ferromagnetic correlations. The ejection probability of an atom provides an experimental probe of the spin correlations. With more than five atoms trapped, the system approaches the itinerant Stoner limit. Losses to Feshbach molecules are suppressed by the discretization of energy levels when fewer than seven atoms are trapped.

Figure 1

Left: The green solid line is the trapping potential $V\left(z\right)$ that is lowered to the green dashed line to allow an atom to escape. The energy levels for up-spin (red) and down-spin (blue) atoms within the potential are shown in brown, with the putative escape of the highest energy up-spin atom. Right: The ejection probability of a down-spin atom into a state fully polarized along the quantization axis. The gray region is excluded due to atom losses for differing initial numbers of atoms.

Figure 2

(a)–(d) The energy of the (two–five)-atom states calculated with exact diagonalization. The red, magenta, and blue lines highlight open channels with $\S$ signifying identical states with larger $S_{\text{z}}$, and gray lines indicating all other states. The green line shows the final bound molecular state that crosses the low-spin open channel, and the green dashed line the bound state with the COM motion excited into the $n_{\text{x},\text{y}}=2$ orbital examined in Ref. [13]. The points show QMC results whose uncertainty is the point size. (e) Density profile of the state $|1/2,2,1\rangle$ for two majority species atoms with a pinned minority atom. (f) Difference in energy from the polaron in an infinite system [45] with number of trapped atoms. (g) Pair correlation function at the confinement-induced resonance around a down-spin pinned at $z=0$ normalized by the noninteracting density profile.

Figure 3

(a) The energy bands, following Fig. 2 conventions. (b) The map of crossing events for the $n_{\text{band}}$-th excited molecular state with $N_{\uparrow }{N}_{\downarrow }$. Blue denotes a single crossing, and red a double crossing. (c) The minimum interaction strength to avoid the band crossing region.