BCS-BEC Crossover in a Two-Dimensional Fermi Gas

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at $T=0$ using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan’s contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.

Figure 1

Equation of state in the BCS-BEC crossover. Squares refer to the BCS and circles to the JS wave function. The solid (red) line is a fit to the data, the dotted (green) line is half of the molecular binding energy and the dashed (blue) line is the prediction of MF theory. The horizontal dotted (black) line denotes the energy per particle $E_{\mathrm{FG}}$ of the noninteracting gas. Inset: 2D scattering length $a_{2\mathrm{D}}$ as a function of the depth $V_0$ for a SW potential of radius $R$. The BCS and BEC regimes correspond, respectively, to $k_F{a}_{2\mathrm{D}}\gg 1$ and $k_F{a}_{2\mathrm{D}}\ll 1$.

Figure 2

Equation of state in the BCS-BEC crossover with ${\epsilon }_b/2$ subtracted from $E/N$. Symbols are as in Fig. 1. The solid (red) line is a fit to the data, the other dotted lines show the equation of state (3) of composite bosons and the perturbation expansion holding in the BCS regime (see text). The dashed (blue) line is the result of MF theory. Inset: short-range behavior of $g_{\uparrow \downarrow }$ for $\eta =2.15$.

Figure 3

Excitation gap in the BCS-BEC crossover. The solid (red) line is the result of MF theory. Inset: excitation gap with $|{\epsilon }_b|/2$ subtracted from ${\Delta }_{\mathrm{gap}}$. The dashed (blue) line is a fit using the energy functional of a Fermi-Bose mixture.

Figure 4

Contact parameter in the BCS-BEC crossover. The solid line corresponds to the calculation from the derivative of the equation of state reported in Fig. 1. Inset: Contact parameter with the two-body contribution $C_0$ subtracted.