We consider two dielectric membranes suspended inside a Fabry-Perot-cavity, which are cooled to a steady state via a drive by suitable classical lasers. We show that the vibrations of the membranes can be entangled in this steady state. They thus for
m two mechanical, macroscopic degrees of freedom that share steady state entanglement.
We consider a boundary between a Mott insulator and a superfluid region of a Bose-Hubbard model at unit filling. Initially both regions are decoupled and cooled to their respective ground states. We show that, after switching on a small tunneling rat
e between both regions, all particles of the Mott region migrate to the superfluid area. This migration takes place whenever the difference between the chemical potentials of both regions is less than the maximal energy of any eigenmode of the superfluid. We verify our results numerically with DMRG simulations and explain them analytically with a master equation approximation, finding good agreement between both approaches. Finally we carry out a feasibility study for the observation of the effect in coupled arrays of micro-cavities and optical lattices.
We show that polaritons in an array of interacting micro-cavities with strong atom-photon coupling can form a two-component Bose-Hubbard model. Both polariton species are thereby protected against spontaneous emission as their atomic part is stored i
n two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers. We also describe a method to measure the number statistics in one cavity for each polariton species independently.
We show that atoms trapped in micro-cavities that interact via exchange of virtual photons can model an anisotropic Heisenberg spin-1/2 chain in an external magnetic field. All parameters of the effective Hamiltonian can individually be tuned via ext
ernal lasers. Since the occupation 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.
