Universal Fermi Gases in Mixed Dimensions

We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range $0.0351<m_{2\mathrm{D}}/m_{3\mathrm{D}}<6.35$ for the 2D-3D mixture or $0.00646<m_{1\mathrm{D}}/m_{3\mathrm{D}}<2.06$ for the 1D-3D mixture, the resulting system is stable against the Efimov effect and has universal properties. We calculate key quantities in the many-body phase diagram. Other possible scale-invariant systems with short-range few-body interactions are also elucidated.

Figure 1

(left) $a_{\mathrm{eff}}/l_{\perp }$ as a function of $l_{\perp }/a$ for $d_{\perp }=1$ (2D-3D mixture). The mass ratio is chosen to be $u=0.15$. The vertical dotted line indicates the position of the broadest resonance. (right) Lowest five values of $l_{\perp }/a$ to achieve the resonances $|a_{\mathrm{eff}}|/l_{\perp }=\infty$ as functions of $u$.

Figure 2

Same as Fig. 1 for $d_{\perp }=2$ (1D-3D mixture).

Figure 3

Phase diagram in the plane of ${\mu }_A$ and ${\mu }_B$ at zero temperature.

Figure 4

${\mu }_A^{\mathrm{cri}}/{\mu }_B$ and ${\mu }_B^{\mathrm{cri}}/{\mu }_A$ as functions of $u$ for the 2D-3D mixture (left) and 1D-3D mixture (right).