  Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum
emulation as they exhibit convenient state preparation and measurement, and
in-situ tuning of parameters. We show how to realise strongly correlated states
of light in Jaynes-Cummings-Hubbard arrays under the introduction of an
effective magnetic field. The effective field is realised by dynamic tuning of
the cavity resonances. We demonstrate the existence of Fractional Quantum Hall
states by com- puting topological invariants, phase transitions between
topologically distinct states, and Laughlin wavefunction overlap.
