Trapped ${}^{173}\mathrm{Yb}$ Fermi gas across an orbital Feshbach resonance

Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped ${}^{173}\mathrm{Yb}$ Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intraband Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the interband detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a spatial separation of superfluid and normal phases within the trap, and could play decisive roles in probing two-band superfluidity in these systems.

Figure 1

Radial profiles at resonance detuning. (a) The numbers of particles $n_i\left(r\right)$ [in units of $N\mathcal{V}/\left(4\pi r_F^3\right)]$, and (b) the order parameters ${\mathrm{\Delta }}_i\left(r\right)$ are shown as functions of the radial distance $r$. (c) The trap-averaged momentum distributions $n_i\left(k\right)$ are shown in units of $4\pi r_F^3/\mathcal{V}$ and as functions of the radial momentum $k$. Here, $i=\{1,2\}$ corresponds, respectively, to the lower and upper bands, where $n_1\left(r\right)>n_2\left(r\right)$ in (a), $|{\mathrm{\Delta }}_2\left(r\right)|>|{\mathrm{\Delta }}_1\left(r\right)|$ and ${\mathrm{\Delta }}_1\left(r\right)<0$ in (b), and $n_1\left(k\right)>n_2\left(k\right)$ in (c).

Figure 2

The band-population imbalance $P=(N_1-N_2)/N$ and chemical potential $\mu$ are shown as functions of (a) detuning $\delta$ at zero temperature, and (b) temperature $T$ at resonance detuning.

Figure 3

Central parameters at resonance detuning. (a) The numbers of particles $n_i(r=0)$ [in units of $N\mathcal{V}/\left(4\pi r_F^3\right)]$, (b) the order parameters ${\mathrm{\Delta }}_i(r=0)$, and (c) the trap-averaged momentum distributions $n_i(k=0)$ (in units of $4\pi r_F^3/\mathcal{V})$ are shown as functions of temperature $T$.

Figure 4

Central parameters at zero temperature. (a) The numbers of particles $n_i(r=0)$ [in units of $N\mathcal{V}/\left(4\pi r_F^3\right)]$, (b) the order parameters ${\mathrm{\Delta }}_i(r=0)$, and (c) the trap-averaged momentum distributions $n_i(k=0)$ (in units of $4\pi r_F^3/\mathcal{V})$ are shown as functions of detuning $\delta$.