Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize charge density and supersolid
phases in Jaynes-Cummings-Hubbard lattices in the presence of long-range interactions. The long-range interactions are realized by the consideration of Rydberg states in coupled atom-cavity systems and the introduction of additional capacitive couplings in quantum-electrodynamics circuits. We demonstrate the emergence of supersolid and checkerboard solid phases, for calculations which take into account nearest neighbour couplings, through a mean-field decoupling.
Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes wavefunctions to construct the Greens function, from which we obtain the Josephson currents in terms of
the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0-pi transitions and for the spin currents, and examine the appropriateness of the common delta-function approximation for the tunneling region.
