Supersolid phases of dipolar fermions in a two-dimensional-lattice bilayer array

Supersolid phases as a result of a coexistence of superfluid and density ordered checkerboard phases are predicted to appear in ultracold Fermi molecules confined in a bilayer array of two-dimensional square optical lattices. We demonstrate the existence of these phases within the inhomogeneous mean-field approach. In particular, we show that tuning the interlayer separation distance at a fixed value of the chemical potential produces different fractions of superfluid, density ordered, and supersolid phases.

Figure 1

Schematic representation of the dipolar Fermi gas. The molecules affected by a harmonic trap potential lie in the lattice sites in up and down layers.

Figure 2

Density order profile (top) and superfluid order parameter (bottom) as a function of the temperature. From left to right $k_{B}T/t=0.0,0.10,0.25$ and 0.45. For $\mathrm{\Lambda }=0.80$ and $\chi =0.3$

Figure 3

Density order profile (top) and superfluid order parameter (bottom) as a function of the temperature. From left to right $k_{B}T/t=0.0,0.10,0.25$, and 0.45. For $\mathrm{\Lambda }=0.85$ and $\chi =0.3$.

Figure 4

Local order parameters. We plot a cross section of the local density $\varphi (x,0)$ and the local gap $\mathrm{\Delta }(x,0)$ through the center of the trap for $k_{B}T/t=0.0,0.10$, and $0.25$. For $\mathrm{\Lambda }=0.85$ and $\chi =0.3$.

Figure 5

Density order profile (top) and superfluid order parameter (bottom) as a function of the temperature. From left to right $k_{B}T/t=0.0,0.10,0.25$, and 0.45. For $\mathrm{\Lambda }=0.90$ and $\chi =0.3$.

Figure 6

Local order parameters. We plot a cross section of the local density $\varphi (x,0)$ and the local gap $\mathrm{\Delta }(x,0)$ through the center for $k_{B}T/t=0.0,0.10$, and $0.25$. For $\mathrm{\Lambda }=0.90$ and $\chi =0.3$.

Figure 7

Density order profile (top) and superfluid order parameter (bottom) as a function of the temperature. From left to right $k_{B}T/t=0.0,0.10,0.25$, and 0.45. For $\mathrm{\Lambda }=1.0$ and $\chi =0.3$.

Figure 8

Order parameters obtained from BdG diagonalization. A second-order continuous phase transition is shown.

Figure 9

Phase diagram for lattices of size $2\times 37\times 37$, as a function of the dimensionless interlayer separation $\mathrm{\Lambda }=\lambda /a$. The interaction strength is $\chi =0.3$.