  Neutral atomic Bose condensates and degenerate Fermi gases have been used to
realize important many-body phenomena in their most simple and essential forms,
without many of the complexities usually associated with material systems.
However, the charge neutrality of these systems presents an apparent limitation
- a wide range of intriguing phenomena arise from the Lorentz force for charged
particles in a magnetic field, such as the fractional quantum Hall states in
two-dimensional electron systems. The limitation can be circumvented by
exploiting the equivalence of the Lorentz force and the Coriolis force to
create synthetic magnetic fields in rotating neutral systems. This was
demonstrated by the appearance of quantized vortices in pioneering experiments
on rotating quantum gases, a hallmark of superfluids or superconductors in a
magnetic field. However, because of technical issues limiting the maximum
rotation velocity, the metastable nature of the rotating state and the
difficulty of applying stable rotating optical lattices, rotational approaches
are not able to reach the large fields required for quantum Hall physics. Here,
we experimentally realize an optically synthesized magnetic field for ultracold
neutral atoms, made evident from the appearance of vortices in our
Bose-Einstein condensate. Our approach uses a spatially-dependent optical
coupling between internal states of the atoms, yielding a Berry's phase
sufficient to create large synthetic magnetic fields, and is not subject to the
limitations of rotating systems; with a suitable lattice configuration, it
should be possible to reach the quantum Hall regime, potentially enabling
studies of topological quantum computation.
