Angular Fulde-Ferrell-Larkin-Ovchinnikov state in cold fermion gases in a toroidal trap

We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases near the BCS-BEC crossover. We investigate the superfluid gases at low temperatures on the basis of the Bogoliubov–de Gennes equation and examine the stability against thermal fluctuations using the $T$-matrix approach beyond the local-density approximation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap but not in the harmonic trap. The angular FFLO state is stable near the BCS-BEC crossover owing to the formation of pseudogap. Spatial dependences of number density and local population imbalance are shown for an experimental test.

Figure 1

(Color online) The phase diagram for the imbalance $P$ and the reduced temperature $T/{\epsilon }_{\text{F}}$. Phase boundaries obtained by the BdG equations are shown by circles, triangles, and diamonds. The BCS state, R-FFLO state, and A-FFLO state are shown in the figure. The phase diagram determined by the RSTA is shown by the squares and (purple) thin solid line. The A-FFLO state is stable above the thin solid line, while the R-FFLO or BCS state is stable below it. We fix the particle density $N/N_{\text{L}}=0.1$ in all figures.

Figure 2

(Color online) Spatial dependence of superfluid order parameter $\Delta \left(\vec{r}\right)$ at $T/{\epsilon }_{\text{F}}=0.00062$. (a) $P=0$, (b) 0.21, (c) 0.39, (d) 0.44, (e) 0.49, and (f) 0.69, respectively.

Figure 3

(Color online) Spatial dependence of local population imbalance $n_1\left(\vec{r}\right)-n_2\left(\vec{r}\right)$. We assume $P=0.1$ in (a). The other parameters are the same as in Fig. 2.

Figure 4

(Color online) Spatial dependence of particle density $n_1\left(\vec{r}\right)+n_2\left(\vec{r}\right)$. The parameters are the same as in Fig. 2.

Figure 5

(Color online) (a) Total DOS $\rho \left(\omega \right)$ in the balanced gas $\left(P=0\right)$ at $T/{\epsilon }_{\text{F}}=0.074$. (b) Spin-resolved DOS ${\rho }^{\sigma }\left(\omega \right)$ in the imbalanced gas $\left(P=0.4\right)$ at $T/{\epsilon }_{\text{F}}=0.028$. Solid and dashed lines show the DOS for $\sigma =1$ and 2, respectively. Thick lines show the results of RSTA, while thin lines are obtained by the mean-field theory for the normal fluid with $\Delta \left(\vec{r}\right)=0$.