Crossed Andreev reflections in superconductor and fractional quantum Hall liquids hybrid system

The tunnel junction of an s-wave superconductor (SC) coupled to two spatially separated fractional quantum Hall (FQH) liquids with opposite spin polarizations is investigated theoretically. In the strong coupling limit, crossed Andreev reflection occurs, where a set of quasiparticles reflected as quasiholes on each FQH liquid side with Cooper pairs transmitted into the SC. The numbers of quasiparticles and quasiholes involved in the AR process satisfy a specific selection rule. In addition, such a setup can serve as an entangler, creating a spin singlet of two electrons, which are spatially separated.