BCS-BEC crossover with a finite-range interaction

We study the crossover from BEC to BCS pairing for dilute systems but with a realistic finite-range interaction. We exhibit the changes in the excitation spectrum that provide a clean qualitative distinction between the two limits. We also study how the dilute system converges to the results from a zero-range pseudopotential derived by Leggett.

Figure 1

(Color online) Scattering length $a_0$ and effective range of the interaction $r_0$ as a function of the potential depth $V_0∕E_0$, where the energy scale $E_0={\hslash }^2∕\left(m{⟨r⟩}^2\right)$.

Figure 2

(Color online) Momentum distributions ${\rho }_k$ (top) and the quasiparticle excitation spectra $E_k∕{\epsilon }_F$ (bottom) as a function of $k\equiv \mid \mathbf{k}\mid$, at fixed density $\left(k_F\right)$ and various potential scattering lengths $a_0$, where ${\epsilon }_F$ is the Fermi energy and $k_F⟨r⟩\approx 0.37$.

Figure 3

(Color online) Density of states $N_k$ (as a function of momentum), at fixed $k_F$ and various potential scattering lengths $a_0$, where $k_F⟨r⟩\approx 0.37$.

Figure 4

(Color online) Density of states $N_E$ (as a function of energy), at fixed $k_F$, where $k_F⟨r⟩\approx 0.37$, and various potential scattering lengths $a_0$.

Figure 5

(Color online) Density of states $N_k$ (as a function of momentum), at fixed potential scattering length $(a_0∕⟨r⟩=2.4)$, and various values of $k_F$.

Figure 6

(Color online) Momentum distribution of the condensate wave function, at fixed density $\left(k_F\right)$ and various potential scattering lengths $a_0$, where $k_F⟨r⟩\approx 0.37$.

Figure 7

(Color online) Profiles of the chemical potential $\mu ∕{\epsilon }_F$ as a function of $\eta ={\left(a_0{k}_F\right)}^{-1}$. The points mark the BEC-BCS crossover.

Figure 8

(Color online) Comparison with Leggett’s “universal” curve: We keep $k_F$ constant, and vary the scattering length $a_0$.

Figure 9

(Color online) Comparison with Leggett’s “universal” curve: The scattering length $a_0$ is held constant, the density $\left(k_F\right)$ is varied.