Charge transfer statistics and entanglement in normal-quantum dot-superconductor hybrid structures

Abstract

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to multiple metallic electrodes in the normal state and a superconductor for arbitrary transmission. We present an analytical solution of the problem taking into account the full energy dependence of the transmission coefficient. We identify two transport processes as sources of entanglement between the current carriers by observing positive cross current correlations. Furthermore, we consider ferromagnetic electrodes and show how they can be used as detectors in experiments violating the Bell-Clauser-Horne-Shimony-Holt inequality.PACS numbers: 73.21. La, Correlations represent one of the main ingredients of quantum mechanics. They may persist even if the particles are causally disconnected which allows for experimental Bell inequality tests, quantum cryptography and quantum teleportation 1 . In quantum optics using e. g. parametric downconversion 2 many interesting experiments investigating the fundamentals of quantum mechanics became possible 3 . Solid state entanglers have only recently been shown to work experimentally using a superconducting finger coupled to normal leads directly 4-6 or via two quantum dots 7,8 . They rely on the non-local or crossed Andreev reflection (CAR) in multi-terminal structures with a superconducting lead where an incident electron from one of the electrodes is reflected by the superconductor into another electrode. This process produces entanglement between the current carriers in the two leads since the correlations of the spin singlet (Cooper pair) are transferred to the spatially separated electrons. The nature of CAR has been investigated further using ferromagnetic contacts 9,10 . Recently, the nonlocal conductance in superconductor hybrid structures has been extensively studied theoretically using different approaches 11-18 . On the one hand the conductance properties of interacting quantum dots with a superconducting lead have been discussed 7,19-21 . On the other hand the full counting statistics (FCS) of multi-terminal systems with a chaotic cavity and a superconducting connector were investigated 22-26 . Among other things the cross-correlation noise has been found to be an efficient tool for discrimination of the current caused by CAR from other current contributions [27][28][29][30][31][32][33][34][35] .Even in its basic realization the noninteracting quantum dot usually shows a highly nonlinear transmission leading to nonlinear current-voltage relations. Combined with a superconducting electrode, the single-particle density of states of which is itself highly nonlinear due to the finite gap, the resulting structure is expected to possess transport properties with a nontrivial voltage dependence. Thus far these aspects have not been fully taken into account. In this paper we would like to close this gap by considering a quantum dot modelled by a noninteracting resonant level. This setup enables one to access the full energy dependence of transmission characteristics generated by the supe...

Interplay between direct and crossed Andreev reflections in hybrid nanostructures

“…In this case the collective many body state 60 is responsible for the effect. Similar behavior related to the increase of the effective transmittance has been previously observed in studies of different tunnel structures [71][72][73] in high transparency limit.…”

Current Noise and Higher Order Fluctuations in Semiconducting Bilayer Systems

“…This is very different from the setup in which a superconductor is contacted to two normal drains, in which one observes a positive cross correlation of the two currents in the normal leads via crossed Andreev reflection. 33,44,45 This discrepancy is due to the fact that we observe the correlation of electrons and holes and not correlations of electron pairs as in the case of superconductors. In this case the positive cross-correlation mediated by crossed Andreev reflection turns into an anti-correlation.…”

“…[30][31][32][33][34] Here the task is to work out the spin-dependent case, to take care of the presence of electrons instead of holes in the lower layer and to address the case of a bilayer contacted from two sides. However, the ∆(x)-coupling in Eq.…”

Superconductor Hybrids-Electronic Paths to Quantum Computing

“…In case of a voltage close to the superconductor gap being applied across the two normal conductors the dominant charge transfer process becomes an Andreev reflection with one normal conductor and as consecutive Andreev reflection to the second normal conductor via the superconductor. This is the process of Andreev reflection enhanced transmission [25].…”

“…The above model involving a superconducting and a normal conducting lead can be solved exactly [25] [26] [27] [28] and lead to the same transport phenomena as described in Figure 1. In this case, however the transport is related both to the energy-dependence of the density of states of the superconductor as the density of state of the quantum dot which is an electronic level peaked around the bare energy.…”