  Among the mysteries surrounding unconventional, strongly correlated
superconductors is the possibility of spatial variations in their superfluid
density. We use atomic-resolution Josephson scanning tunneling microscopy to
reveal a strongly inhomogeneous superfluid in the iron-based superconductor
FeTe0.55Se0.45. By simultaneously measuring the topographic and electronic
properties, we find that this inhomogeneity in the superfluid density is not
caused by structural disorder or strong inter-pocket scattering, and does not
correlate with variations in Cooper pair-breaking gap. Instead, we see a clear
spatial correlation between superfluid density and quasiparticle strength,
putting the iron-based superconductors on equal footing with the cuprates and
demonstrating that locally, the quasiparticles are sharpest when the
superconductivity is strongest. When repeated at different temperatures, our
technique could further help elucidate what local and global mechanisms limit
the critical temperature in unconventional superconductors.
