Effective Spin Systems in Coupled Microcavities

We show that atoms trapped in microcavities that interact via the exchange of virtual photons can model an anisotropic Heisenberg spin-$1/2$ lattice in an external magnetic field. All parameters of the effective Hamiltonian can individually be tuned via external lasers. Since the occupations of excited atomic levels and photonic states are strongly suppressed, the effective model is robust against decoherence mechanisms, has a long lifetime, and its implementation is feasible with current experimental technology. The model provides a feasible way to create cluster states in these devices.