Phases of a bilayer Fermi gas

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer $s$-wave pairing, an intralayer $p$-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.

Figure 1

Conjectured phase diagram at zero temperature in the plane of the effective scattering length $(a_{\mathrm{eff}}{k}_{\mathrm{F}}){}^{-1}$ and the layer separation $k_{\mathrm{F}}d$. Here, $k_{\mathrm{F}}~k_{\mathrm{F}A}~k_{\mathrm{F}B}$ is assumed.

Figure 2

Effective interaction between two $A$ atoms (solid line) induced by the interaction with $B$ atoms (dotted line) in the weak coupling limit. Here, $i,j=1,2$ are layer indices.

Figure 3

Critical layer separation $k_{\mathrm{F}B}d$ dividing the interlayer $s$-wave pairing $({\mathrm{Ṽ}}_{12}^{(0)}<{\mathrm{Ṽ}}_{11}^{(1)})$ from the intralayer $p$-wave pairing $({\mathrm{Ṽ}}_{12}^{(0)}>{\mathrm{Ṽ}}_{11}^{(1)})$ as a function of $k_{\mathrm{F}A}/k_{\mathrm{F}B}$.

Figure 4

Three-body scattering of two $A$ atoms in different layers and one $B$ atom. The double line represents the $A$-$B$ scattering amplitude. ${\mathcal{T}}_{22}$ and ${\mathcal{T}}_{21}$ satisfy the same integral equations as ${\mathcal{T}}_{11}$ and ${\mathcal{T}}_{12}$.

Figure 5

Lowest binding energies of trimers for mass ratios $m_A/m_B=6.67$ (bottom), $1$ (middle), and $0.15$ (top) as a function of $d/a_{\mathrm{eff}}$. The dashed and dotted lines are atom-dimer and dimer-dimer thresholds; $E=E_2$ and $2E_2$.