Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler

Abstract

We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport is dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at the same energy [P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001)]. We seek to revisit the transport of those nonlocal Cooper pairs as well as the efficiency of such an Andreev entangler when including the quantum noise (decoherence).PACS numbers: 73.23. Hk, 73.40.Gk, 73.50.Td The concept of nonlocal pairwise-entangled quantum states 1 , namely the Einstein-Podolsky-Rosen (EPR) pairs 2 is extremely fundamental for testing the violation of Bell inequality 3 and at the same time is also crucial for efficient quantum communication 4 and quantum teleportation 5 for example. Tests on the entanglement of massless particles like the photons already exist 6 but not yet for massive particles such as the electrons. A concrete challenge is to realize an entangler of electrons, i.e., a device that generates spin singlets that are made out of two electrons. Recently, an interesting setup involving an s-wave superconductor weakly-coupled to two quantum dots, which themselves are coupled to normal leads has been envisioned in Ref. 7. The spin correlations of an s-wave superconductor induce a spin-singlet state between two electrons, each of which can now reside on a separate quantum dot; this results in the formation of a nonlocal Cooper pair described by the quantum statewhere d † lσ produces an electron with spin σ on the dot l and |i = |0 S |0 D |µ l (|0 S is the quasiparticle vacuum for the superconductor, |0 D means that both dot levels ǫ l are unoccupied, and |µ l defines the occupation of the leads which are filled with electrons up to the electrochemical potential µ l ) is the initial state. A prerequisite to perform such a nonlocal spin-entangled electron state is the Coulomb blockade phenomenon which typically forbids double occupancy on each quantum dot: the spin singlet coming from the Cooper pair remains preserved in this process even though the two involved partners are well separated physically because they reside on different quantum dots. More precisely, such an Andreev entangler 8 of EPR pairs has been predicted to be well efficient when 7 E/γ ≫ (k F δr) where E −1 = 1/(π∆) + 1/U , U being twice the charging energy of a given dot, ∆ the superconducting gap, δr = |δr| which might be of the order of the distance between dots denotes the distance between the poin...

Spin-entangled electrons in solid-state systems

“…The presence of voltage noise on the two quantum dots can lead to a reduction of the ratio Eq. (34), as analyzed in (Dupont and Hur, 2006).…”

Carbon Nanotubes as Cooper-Pair Beam Splitters

“…Conventional Andreev Reflections (AR) are local and cannot readily be used to create bipartite states [5,6]. It has been suggested to make use of electron-electron interactions [6,7,8,9,10,11,12,13], spin filtering [14] or anomalous scattering in graphene [15] to promote Cooper pair splitting i.e. the Crossed Andreev Reflection (CAR) process.…”

Spin-orbital Kondo decoherence by environmental effects in capacitively coupled quantum dots

“…As detailed below, the analysis of the flow equations (14) for various values of β and r allows to determine the phase diagram of the system depicted in Fig. 3.…”

“…[10,11] for a review). Decoherence effects due to electromagnetic environment have been studied for series, 12 and parallel 13,14 double dot systems in the sequential regime. The interplay between the Kondo effect and the background charge fluctuations has however not yet been analyzed systematically; the issue was addressed only recently for some specific systems.…”