  Water freezes into ice, atomic spins spontaneously align in a magnet, liquid
helium becomes superfluid: Phase transitions are dramatic phenomena. However,
despite the drastic change in the system's behaviour, observing the transition
can sometimes be subtle. The hallmark of Bose-Einstein condensation (BEC) and
superfluidity in trapped, weakly interacting Bose gases is the sudden
appearance of a dense central core inside a thermal cloud. In strongly
interacting gases, such as the recently observed fermionic superfluids, this
clear separation between the superfluid and the normal parts of the cloud is no
longer given. Condensates of fermion pairs could be detected only using
magnetic field sweeps into the weakly interacting regime. The quantitative
description of these sweeps presents a major theoretical challenge. Here we
demonstrate that the superfluid phase transition can be directly observed by
sudden changes in the shape of the clouds, in complete analogy to the case of
weakly interacting Bose gases. By preparing unequal mixtures of the two spin
components involved in the pairing, we greatly enhance the contrast between the
superfluid core and the normal component. Furthermore, the non-interacting
wings of excess atoms serve as a direct and reliable thermometer. Even in the
normal state, strong interactions significantly deform the density profile of
the majority spin component. We show that it is these interactions which drive
the normal-to-superfluid transition at the critical population imbalance of
70(5)%.
