Visualization of Vortex Bound States in Polarized Fermi Gases at Unitarity

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.

Figure 1

Density profiles of the majority ($\uparrow$ state, solid lines) and minority ($\downarrow$ state, dashed lines) components at $T=0.05T_F$ for three typical value of polarization: $p=0.12$ (a), $p=0.35$ (b), and $p=0.75$ (c). Density differences are also plotted in dot-dashed lines. All the profiles are normalized by $n_{\sigma }{,}_{\mathrm{TF}}=(1+\beta {)}^{-3/5}\sqrt{15\pi N\lambda /2}/(6{\pi }^2)(\hslash /m\omega {)}^{-3/2}$, which is the peak density for a symmetric gas at unitarity. Panel (d) shows the order parameter profiles. The small oscillations at the edge are a finite size effect.

Figure 2

Left panel: center density difference as a function of polarization at $N={10}^4$. Inset shows the dependence on the chemical potential difference. Right panel: critical polarization and critical chemical difference as a function of the number of total particles.

Figure 3

Local fermionic density of states of spin-up (solid lines) and spin-down (dashed lines) components inside the vortex core at $N={10}^4$ and $T=0.05T_F$. The thin line in (a) shows the LDOS at $p=0$. Arrows point to the position at the effective energy of the lowest bound state.

Figure 4

Vortex core size (a) and the effective energy of the lowest bound state (b) as a function of polarization at $N={10}^4$ and $T=0.05T_F$. The core size ${\xi }_{90}$ at $p=0$ is about $2.5k_F^{-1}$, where $k_F$ noninteracting Fermi wavelength at center. Solid lines are the scaling relations as described in the text. Inset shows superfluidity density profiles.