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Springer eBooks

Double Quantum Dot Coupled to Two Superconductors: Transport and Spin Entanglement

Mahn‐Soo Choi, Christoph Bruder, Daniel Loss

Published Jan 1, 2001• 0 citations
Publisher
DOI
10.1007/978-1-4615-1245-5_31

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We study a double quantum dot, each dot of which is tunnel coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot that can be tuned by the superconducting phase difference. We show that the correlated spin states---singlet or triplets---on the double dot can be probed via the Josephson current in a dc-superconducting quantum interference device setup.
Abstract The control of nonlocal entanglement in solid state systems is a crucial ingredient of quantum technologies. We investigate a Cooper‐pair splitter based on a double quantum dot realized in a semiconducting nanowire. In the presence of interdot tunneling the system provides a simple mechanism to develop spatial entanglement even in absence of nonlocal coupling with the superconducting lead. We discuss the possibility to control the symmetry (singlet or triplet) of spatially separated, entangled electron pairs taking advantage of the spin‐orbit coupling of the nanowire. We also demonstrate that the spin‐orbit coupling does not impact over the entanglement purity of the nonlocal state generated in the double quantum dot system. Cooper‐pair splitter realized in a nanowire acting as double quantum dot which is coupled to one superconductor (S) and two normal leads (N). Electron singlets in the superconductor are split nonlocally into the different dots as schematically shown in the figure. The entangled electrons in the two quantum dots are then transferred by tunneling, with rate , to the normal leads.
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.