We compute the real-space profile of the superconducting order parameter in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter φ, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on φ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly larger than in a normal periodic conductor for special values of φ.
We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real-space Bogoliubov-de Gennes framework for three cases, namely, when states are (i) extended, (ii) localized, or (iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases (i) and (iii), stretched exponential in case (ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable [case (i)] or of its logarithm [cases (ii) and (iii)]. We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.
A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3. We propose to use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X−state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity f X to display quantum features, i.e., we find a threshold C X for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successfully then we find a filtrable outcome with average fidelity f X,0 that can be greater than f X .In addition, we find the threshold concurrence of the channel C X,0 in order for the average fidelity f X,0 to display quantum features and surprisingly, the threshold concurrence C X,0 can be less than C X . Even more, we find some special cases for which the threshold values become zero.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.