  Topologically-ordered matter is a novel quantum state of matter observed only
in a small number of physical systems, notably two-dimensional electron systems
exhibiting fractional quantum Hall effects. It was recently proposed that a
simple form of topological matter may be created in interacting systems of
rotating ultra-cold atoms. We describe ensemble measurements on small, rotating
clusters of interacting bosonic atoms, demonstrating that they can be induced
into quantum ground states closely analogous to topological states of
electronic systems. We report measurements of inter-particle correlations and
momentum distributions of Bose gases in the fractional quantum Hall limit,
making comparison to a full numerical simulation. The novel experimental
apparatus necessary to produce and measure properties of these deeply entangled
quantum states is described.
