Bell-inequality checks constitute a probe of entanglement -given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross-correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of entangled electrons.

We investigate the feasibility of manipulating individual spin in a superconducting junction where Bogolyubov quasiparticles can be trapped in discrete Andreev levels. We call this system Andreev Quantum Dot (AQD) to be contrasted with a common semiconductor quantum dot. We show that AQD can be brought into a spin-1/2 state. The coupling between spin and superconducting current facilitate manipulation and measurement of this state. We demonstrate that one can operate two inductively coupled AQD's as a XOR gate, this enables quantum computing applications.PACS numbers: 05.60. Gg, Manipulation and operation of individual quantum systems and arrays of such systems, so-called "quantum machines" is now in focus of both experimental and theoretical research [1,2]. The progress in quantum computing algorithms [3] has demonstrated potential applicability of quantum mechanics thus stimulating various proposals to implement arrays of operational two-state systems (qubits) in solid-state [4,5,6,7,8,9,10,11,12,13]. Many proposals concern quantum dots. The quantum dots are often referred to as artificial atoms since they confine a discrete number of particles that occupy discrete quantum states. In contrast to atoms, the properties of quantum dots can be tuned and their charge and spin degrees of freedom can be controlled. This would allow for quantum manipulation. An interesting and elaborated proposal [4,5] utilizes spin states of semiconductor quantum dots. However, the complexity of the manipulation schemes proposed and severe difficulties with the read-out of these spin states [5,14] drives one to think of alternatives.Below we present an alternative scheme for individual spin manipulation. We concentrate on sufficiently resistive superconducting constrictions where individual Bogolybov quasiparticles can be trapped in discrete Andreev bound states. We refer to such system as Andreev Quantum Dots (AQD). An AQD resembles a common quantum dot as long as discreetness of a (quaisi)particle number, spectrum and spin is concerned. Albeit in contrast to a common quantum dot the charge of the AQD is not fixed. This allows for superconducting current in the constriction and makes electron-electron interaction negligible.We propose to utilize spin states of the AQD's. We show that an AQD can be brought to the state with spin-1/2 that persist over a long time. It is important that the spin direction in this state determines the superconducting current in the constriction, thus solving the read-out problem. We demonstrate that the spin state of a single AQD can be manipulated. Further, the two dots can be inductively coupled to make a XOR quantum gate. Quantum information theory [3] proves that this enables one to build a universal quantum computer.The AQD can be formed in any constriction between two superconducting leads that have a gap in energy spectrum. If an electron with the energy below the gap tries to escape to the bulk of a superconductor, it is reflected back as a hole (Andreev reflection [15]), which also can not escap...

The critical temperature T_c of a superconductor/ferromagnet (SF) bilayer can exhibit nonmonotonic dependence on the thickness d_f of the F layer. SF systems have been studied for a long time; according to the experimental situation, the "dirty" limit is often considered which implies that the mean free path in the layers is the second smallest spatial scale after the Fermi wavelength. However, all calculations reported for the dirty limit were done with some additional assumptions, which can be violated in actual experiments. Therefore, we develop a general method (to be exact, two independent methods) for investigating T_c as a function of the bilayer's parameters in the dirty case. Comparing our theory with experiment, we obtain good agreement. In the general case, we observe three characteristic types of T_c(d_f) behavior: 1) nonmonotonic decay of T_c to a finite value exhibiting a minimum at particular d_f, 2) reentrant behavior, characterized by vanishing of T_c in a certain interval of d_f and finite values otherwise, 3) monotonic decay of T_c and vanishing at finite d_f. Qualitatively, the nonmonotonic behavior of T_c(d_f) is explained by the interference of quasiparticles in the F layer, which can be either constructive or destructive depending on the value of d_f.Comment: 13 pages (including 7 EPS figures), REVTeX 4. Version 2: minor correction