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We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of Cavity Quantum Electrodynamics could be generalized to many other nanoscale circuits.
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We investigate theoretically the properties of a weak link between two superconducting leads, which has the form of a non-superconducting nanowire with a strong Rashba spin-orbit coupling caused by an electric field. In the Coulomb blockade regime of single-electron tunneling, we find that such a weak link acts as a spin splitter of the spin states of Cooper pairs tunneling through the link, to an extent that depends on the direction of the electric field. We show that the Josephson current is sensitive to interference between the resulting two transmission channels, one where the spins of both members of a Cooper pair are preserved and one where they are both flipped. As a result, the current is a periodic function of the strength of the spin-orbit interaction and of the bending angle of the nanowire (when mechanically bent); an identical effect appears due to strain-induced spin-orbit coupling. In contrast, no spin-orbit induced interference effect can influence the current through a single weak link connecting two normal metals.
We study the two-particle wave function of paired atoms in a Fermi gas with tunable interaction strengths controlled by Feshbach resonance. The Cooper pair wave function is examined for its bosonic characters, which is quantified by the correction of
Bose enhancement factor associated with the creation and annihilation composite particle operators. An example is given for a three-dimensional uniform gas. Two definitions of Cooper pair wave function are examined. One of which is chosen to reflect the off-diagonal long range order (ODLRO). Another one corresponds to a pair projection of a BCS state. On the side with negative scattering length, we found that paired atoms described by ODLRO are more bosonic than the pair projected definition. It is also found that at $(k_F a)^{-1} ge 1$, both definitions give similar results, where more than 90% of the atoms occupy the corresponding molecular condensates.
Electric weak links, the term used for those parts of an electrical circuit that provide most of the resistance against the flow of an electrical current, are important elements of many nanodevices. Quantum dots, nanowires and nano-constrictions that bridge two bulk conductors (or superconductors) are examples of such weak links. Here we consider nanostructures where the electronic spin-orbit interaction is strong in the weak link but is unimportant in the bulk conductors, and explore theoretically the role of the spin-orbit active weak link (which we call a Rashba spin splitter) as a source of new spin-based functionality in both normal and superconducting devices. Some recently predicted phenomena, including mechanically-controlled spin- and charge currents as well as the effect of spin polarization of superconducting Cooper pairs, are reviewed.
We have developed a quantitative theory of Cooper pair pumping in gated one-dimensional arrays of Josephson junctions. The pumping accuracy is limited by quantum tunneling of Cooper pairs out of the propagating potential well and by direct supercurrent flow through the array. Both corrections decrease exponentially with the number N of junctions in the array, but give a serious limitation of accuracy for any practical array. The supercurrent at resonant gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson phase difference across the array.
We propose two schemes to establish entanglement between two mesoscopic quantum systems through a third mesoscopic quantum system. The first scheme entangles two nano-mechanical oscillators in a non-Gaussian entangled state through a Cooper pair box. Entanglement detection of the nano-mechanical oscillators is equivalent to a teleportation experiment in a mesoscopic setting. The second scheme can entangle two Cooper pair box qubits through a nano-mechanical oscillator in a thermal state without using measurements in the presence of arbitrarily strong decoherence.
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