BCS-BEC crossover in bilayers of cold fermionic polar molecules

We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS-theory approach that is most reliable at weak coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecule in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low-density limit and a paired superfluid (BCS) state in the high-density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly coupled dimer picture yield similar predictions for the parameters of the crossover regime. The Berezinskii-Kosterlitz-Thouless transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.

Figure 1

Schematic of a few particles in a bilayer with (a) inter- ($V_1$) and intralayer ($V_0$) interactions in the BCS limit and (b) the effective interaction ($V_{\mathrm{eff}}$) between the dimers in the BEC limit (see text). (c) Quantum phase diagram for a bilayer with fermionic polar molecules in the interaction-density plane. Interactions are characterized by $U=m{D}^2/{\hslash }^{2}d$ and by $k_{F}d$, where $m$, $D$, $d$, and $k_F$ are respectively the molecular mass, dipole moment, interlayer distance, and Fermi momentum. The crossover I region includes the effect of intralayer interactions, while the crossover II region does not. In the upper right-hand corner we speculate that the system could potentially display a roton instability as discussed in the text.

Figure 2

(a) Normalized gap ${\Delta }_k/{\Delta }_0$ as a function of $k/k_F$ at $k_{F}d=0.4$ and $U=1$ (solid) and $U=5$ (dashed). (b) Temperature dependence of ${\Delta }_0\left(T\right)/E_F$ as a function of $T/T_F$ for $k_{F}d=0.4$ ($E_F=0.16E_0$). (c) BCS critical temperature as a function of $k_{F}d$ at $U=2$ in units of $E_0={\hslash }^2/2m{d}^2$. (d) Ratio of the roton wavelength ${\lambda }_r$ at the instability to the dimer size $l_B$ as a function of $k_{F}d$.

Figure 3

Transition temperature ($T_{\text{BKT}}$, solid black line) as a function of interaction strength for $k_{F}d=0.4$. BCS result ($T_c$, dashed blue line) is shown for comparison. The dashed vertical line marks the position of ${\mu }_{\text{BCS}}=0$ [see Fig. 1c].