Universality and stability for a dilute Bose gas with a Feshbach resonance

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero-density fixed point. Moreover, we find that the $T=0$ thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.

Figure 1

The schematic phase diagram of a dilute FR Bose gas in $d=3$. The unstable region lies between the two dashed lines. In the shaded region, the ASF state is an unstable local minimum of the free-energy density.

Figure 2

The chemical potential $\mu$ [in units of $n^{2/3}/(2m)$] as a function of $\nu =-1/a_s$ (in units of $n^{1/3}$) for given atom density $n$.

Figure 3

The pressure $P$ [in units of $n^{5/3}/(2m)$] as a function of $\nu =-1/a_s$ (in units of $n^{1/3}$) for given atom density $n$.

Figure 4

The sound velocity $v_s$ [in units of $n^{1/3}/(2m)$] as a function of $\nu =-1/a_s$ (in units of $n^{1/3}$) for given atom density $n$.