Abstract

Quantum optics has been an important source of inspiration for many recent experiments in nanoscale electric circuits. One of the basic goals is the generation of entangled electronic states in solid state systems. Superconductors have been suggested as a natural source of spin entanglement, due to the singlet pairing state of Cooper pairs. One important building block required for the implementation of entanglement experiments using superconductors is a Cooper-pair beam splitter which should split the singlet state into two different electronic orbitals. The basic mechanism for converting Cooper pairs into quasiparticles is the Andreev reflection in which an originally quantum coherent electron pair in the singlet spin state is produced at an interface between a superconductor and a normal conductor. Conventional Andreev reflections are local and cannot readily be used to create bipartite states. Many theoretical proposals for circumventing this fact have been around for the last decade. It has been suggested to make use of electron-electron interactions, spin filtering or anomalous scattering in graphene to promote Cooper-pair splitting, i.e., the crossed Andreev reflection process. In this work, we have used Coulomb interactions as well as size quantization in order to favor the crossed Andreev reflection processes in carbon nanotubes, realizing an efficient Cooper pair splitter [1,2]. The devices studied are double quantum dots which can be viewed as artificial molecules connected to one superconducting reservoir and two normal reservoirs. Thanks to their tunability, they allow to change in situ the probability of emitting spit Cooper pairs. These findings open an avenue for more complex quantum optics like experiments with electronics sates which should allow, among other things, to test the coherence of the emitted split Cooper pairs.

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