Creation of nonlocal spin-entangled electrons via Andreev tunneling, Coulomb blockade, and resonant transport

We discuss several scenarios for the creation of nonlocal spin-entangled electrons which provide a source of electronic Einstein-Podolsky-Rosen (EPR) pairs. Such EPR pairs can be used to test nonlocality of electrons in solid state systems, and they form the basic resources for quantum information processing. The central idea is to exploit the spin correlations naturally present in superconductors in form of Cooper pairs possessing spin-singlet wavefunctions. We show that nonlocal spin-entanglement in form of an effective Heisenberg spin interaction is induced between electron spins residing on two quantum dots with no direct coupling between them, but each of them being tunnel-coupled to the same superconductor. We then discuss a nonequilibrium setup with an applied bias where mobile and nonlocal. spin-entanglement can be created by coherent injection of two electrons, in a pair (Andreev) tunneling process, into two spatially separated quantum dots and subsequently into two Fermi liquid leads. The current for injecting two spin-entangled electrons into different leads shows a resonance and allows the injection of electrons at the same orbital energy, which is a crucial requirement for the detection of spin-entanglement via the current noise. On the other hand, tunneling via the same dot into the same lead is suppressed by the Coulomb blockade effect of the quantum dots. We discuss Aharonov-Bohm oscillations in the current and show that they contain h/e and h/2e periods, which provides an experimental means to test the nonlocality of the entangled pair. Finally, we discuss a structure consisting of a superconductor weakly coupled to two separate one-dimensional leads with Luttinger liquid properties. We show that strong correlations again suppress the coherent subsequent tunneling of two electrons into the same lead, thus generating again nonlocal spin-entangled electrons in the Luttinger liquid leads.