Superfluid Equation of State of Dilute Composite Bosons

We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density $n$ up to the Lee-Huang-Yang order, proportional to $n^{3/2}$, the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length $a_M$, the composite nature of the dimers appearing only in the next order term proportional to $n^2$.

Figure 1

(a) Structure of the lowest order normal self-energy (b) BCS-like contribution ${\delta }_1(k)$ (c) The diagram for ${\delta }_2(k)$.

Figure 2

Diagrammatic representation for Eq. (12) for $\Gamma$.

Figure 3

Collective mode contributions to the self-energies.