We propose a scheme to realize the fractional quantum Hall system with atoms confined in a two-dimensional array of coupled cavities. Our scheme is based on simple optical manipulation of atomic internal states and intercavity hopping of virtually excited photons. It is shown that, as well as the fractional quantum Hall system, any system of hard-core bosons on a lattice in the presence of an arbitrary Abelian vector potential can be simulated solely by controlling the phases of constantly applied lasers. The scheme, for the first time, exploits the core advantage of coupled cavity simulations, namely, the individual addressability of the components, and also brings the gauge potential into such simulations as well as the simple optical creation of particles.
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