Normal mass density of a superfluid Fermi gas at unitarity

We calculate the normal mass density of a paired Fermi gas at unitarity. The dominant contribution near the superfluid transition is from fermionic quasiparticle excitations and is, thus, sensitive to the pairing gap. A comparison with the recent experiment of Sidorenkov et al. [Nature (London) 498, 78 (2013)] suggests that the superfluid gap near the transition temperature is larger than the BCS value, but the data do not permit a quantitative inference of the gap. Calculations of the quenched moment of inertia of a BCS superfluid in a harmonic trap are in reasonable agreement with the earlier experiment of Riedl et al. [New J. Phys. 13, 035003 (2011)].

Figure 1

Calculated superfluid mass density compared with the experimental measurement of Ref. [2]. The dashed curve labeled BCS uses the BCS gap structure near $T_c$, Eqs. (6) and (8), whereas the solid curve uses a gap a factor of 1.5 larger. The thin dotted curve is the BCS curve uniformly stretched in temperature to pass optimally through the data.

Figure 2

Calculated moment of inertia in units of the normal-state moment of inertia in a trap. The data along the theoretical curve have been scaled upward by a few percent from the original data for the precession parameter $\mathcal{P}$ of Ref. [3]; see text for details. The inset shows the original data.