Vortex-Core Structure in Neutral Fermion Superfluids with Population Imbalance

Quantized vortex-core structure is theoretically investigated in fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with the vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing an interesting opportunity to examine low-lying fermionic core bound states unexplored so far.

Figure 1

Order parameter profiles $|\Delta (r)|$ as a function of $r/d$ for $g/\omega d^3=-1.5$. (1) Vortex with population imbalance case $P=0.3$. (2) Vortex with population balance case $P=0$. (3) Vortex free with population balance case $P=0$. Logarithmic plot of (1) is shown in the inset to emphasize the finer scale of $|\Delta (r)|$ in the outer region.

Figure 2

Density and polarization profiles as a function of $r/d$ corresponding to curve (1) ($P=0.3,g/\omega d^3=-1.5$) in Fig. 1. $n(r)=n_{\uparrow }(r)+n_{\downarrow }(r)$: total density; $n_{\uparrow }(r)$ [$n_{\downarrow }(r)$]: up [down] spin density; and $m(r)$: magnetization.

Figure 3

Density maps of (a) $n_{\uparrow }(r)$, (b) $n_{\downarrow }(r)$, and (c) $n(r)$, corresponding to Fig. 2. (d) $n(r)$ for $P=0$ and $g/\omega d^3=-1.5$. By comparing (c) the imbalance case and (d) the balance case, the core in (d) is clearly seen as a small but sharp dot at the center. The field of view is $14.0\times 14.0$ in units of $d$.

Figure 4

Density profiles of the total number $n(r)$ for various polarizations: $P=0$, 0.11, 0.35, 0.43, and 0.52 from top to bottom. The inset shows the filling factor $F=n(0)/n_{\max }$ defined by the ratio between the maximum value $n_{\max }$ and $n(r=0)$ for various couplings ($g/\omega d^3=-1.5$, $-1.4$, $-1.3$, $-1.2$, and $-1.1$ from bottom to top).

Figure 5

Spectral evolutions for the majority species (up-spin atoms) $N_{\uparrow }(r,E)$ with $q_z=0$. (a) Stereographic view and (b) density map. $P=0.3$ and $g/\omega d^3=-1.5$. The labels show the angular momentum $l$ for each CdGM bound state. In (b), the order parameter $\pm \Delta (r)$ is overlaid. Energy is normalized by the harmonic frequency $\omega$. $E_F$ is the Fermi level position.