  Extensions of Berry's phase and the quantum Hall effect have led to the
discovery of new states of matter with topological properties. Traditionally,
this has been achieved using gauge fields created by magnetic fields or spin
orbit interactions which couple only to charged particles. For neutral
ultracold atoms, synthetic magnetic fields have been created which are strong
enough to realize the Harper-Hofstadter model. Despite many proposals and major
experimental efforts, so far it has not been possible to prepare the ground
state of this system. Here we report the observation of Bose-Einstein
condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum
per lattice unit cell. The diffraction pattern of the superfluid state directly
shows the momentum distribution on the wavefuction, which is gauge-dependent.
It reveals both the reduced symmetry of the vector potential and the twofold
degeneracy of the ground state. We explore an adiabatic many-body state
preparation protocol via the Mott insulating phase and observe the superfluid
ground state in a three-dimensional lattice with strong interactions.
