Vortex lattice in spin-imbalanced unitary Fermi gas

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory, we provide insight into states that emerge from a competition between Abrikosov lattice formation, spatial phase separation, and the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In the case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a boxlike trap reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and the emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.

Figure 1

(a) Simulated densities $n(x,y,z=0)$ for a nonrotating system, trapped in a harmonic potential, separately for the majority $|\uparrow \rangle$ and minority $|\downarrow \rangle$ components and different population imbalances $\delta$. (b) Comparison between the experimental absorption images (exp) and the simulated densities $n(x,y,z=0)$ (sim) for a rotating system trapped in a harmonic potential, separately for the majority $|\uparrow \rangle$ and minority $|\downarrow \rangle$ components and different population imbalances $\delta$. Experimental figures taken from Ref. [20] and reprinted with permission from AAAS. (c) Simulated densities $n(x,y,z=0)$ for a rotating system, trapped in a box potential, separately for the majority $|\uparrow \rangle$ and minority $|\downarrow \rangle$ components and different population imbalances $\delta$. The dashed line sets (on the right side of it) the cases with the superfluid phase apart from the ones (on the left) without it. In panel (b), we can see the discrepancy in the position of this line as the experimental absorption image was taken for $\frac{1}{k_{F}a}=0.2$ (i.e., slightly on the BEC side).

Figure 2

Real part of the order parameter $\mathrm{\Delta }$ as a function of the distance from the system center for different population imbalances [dashed (red) line]. Fit to Eq. (9) is shown by solid (blue) line.

Figure 3

(a) Polarization $p(x,y,z=0)$ (top left part of each subplot), densities $n_{\sigma }(x,y,z=0)$ of the majority (top right part of each subplot), and the minority components (bottom right part of each subplot), as well as the indication of the superfluid region (bottom left part of each subplot). (b) Pairing gap absolute value $\left|\mathrm{\Delta }\right(x,y,z=0\left)\right|$ (left column) and its phase $arg\mathrm{\Delta }(x,y,z=0)$ (right column). The rows correspond to $\delta =10\%$ (top) and $50\%$ (bottom).

Figure 4

Probability current (total ${\mathit{j}}^{\prime }={\mathit{j}}_{\uparrow }^{\prime }+{\mathit{j}}_{\downarrow }^{\prime }$ for $\delta =0\%,18\%,62\%$, minority component ${\mathit{j}}_{\downarrow }^{\prime }$ for $\delta =50\%$) in a rotating frame. Only the surroundings of selected vortices are presented. The reversed flow is visible for $\delta =50\%$ and $62\%$.

Figure 5

Polarization $p(x,y,z=0)$ (top left part of each subplot), densities $n_{\sigma }(x,y,z=0)$ of the majority (top right part of each subplot), and the minority components (bottom right part of each subplot), as well as the indication of the superfluid part (bottom left part of each subplot).

Figure 6

Velocity profiles of the majority $|\uparrow \rangle$ (solid blue line) and minority $|\downarrow \rangle$ (dashed-dotted red line) components as functions of the distance from the system center $r$. Spin imbalance $\delta =39\%$. Trapping potential: (a) the harmonic oscillator and (b) the tube. The dashed black line corresponds to the solid-body rotation.

Figure 7

Normalized number of vortices ${\tilde{N}}_v/N_{v,\max }$ as a function of population imbalance $\delta$. Comparison between the experimental results (exp) for the Fermi gas on the BEC side ($\frac{1}{k_{F}a}=0.2$), the BCS side ($\frac{1}{k_{F}a}=-0.15$) near the unitary regime, and the simulation results (sim). Experimental points are taken from [20].