Production of Nonlocal Quartets and Phase-Sensitive Entanglement in a Superconducting Beam Splitter

Abstract

Three BCS superconductors ${S}_{a}$, ${S}_{b}$, and $S$ and two short normal regions ${N}_{a}$ and ${N}_{b}$ in a three-terminal ${S}_{a}{N}_{a}S{N}_{b}{S}_{b}$ setup provide a source of nonlocal quartets spatially separated as two correlated pairs in ${S}_{a}$ and ${S}_{b}$, if the distance between the interfaces ${N}_{a}S$ and $S{N}_{b}$ is comparable to the coherence length in $S$. Low-temperature dc transport of nonlocal quartets from $S$ to ${S}_{a}$ and ${S}_{b}$ can occur in equilibrium, and also if ${S}_{a}$ and ${S}_{b}$ are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases ${\ensuremath{\phi}}_{a}$ and ${\ensuremath{\phi}}_{b}$ in ${S}_{a}$ and ${S}_{b}$. Phase-sensitive entanglement is obtained at zero temperature if ${N}_{a}$ and ${N}_{b}$ are replaced by discrete levels.