Comparison of spectral linewidths for quantum degenerate bosons and fermions

We observe a dramatic difference in optical line shapes of a $^4\text{He}$ Bose-Einstein condensate and a $^3\text{He}$ degenerate Fermi gas by measuring the 1557-nm $2~^3S-2~^1S$ magnetic dipole transition ($8~\text{Hz}$ natural linewidth) in an optical dipole trap. The $15~\text{kHz}$ FWHM condensate line shape is only broadened by mean field interactions, whereas the degenerate Fermi gas line shape is broadened to $75~\text{kHz}$ FWHM due to the effect of Pauli exclusion on the spatial and momentum distributions. The asymmetric optical line shapes are observed in excellent agreement with line shape models for the quantum degenerate gases. For $^4$He a triplet-singlet s-wave scattering length $a=+50(10)_{\text{stat}}(43)_{\text{syst}}~a_0$ is extracted. The high spectral resolution reveals a doublet in the absorption spectrum of the BEC, and this effect is understood by the presence of a weak optical lattice in which a degeneracy of the lattice recoil and the spectroscopy photon recoil leads to Bragg-like scattering.