Positive noise cross-correlation in hybrid superconducting and normal-metal three-terminal devices

Abstract

Non-local entanglement is a key ingredient to quantum information processing. For photons, entanglement has been demonstrated 1 , but it is more difficult to observe for electrons. One approach is to use a superconductor, where electrons form spin-entangled Cooper pairs, which is a natural source for entangled electrons. For a three-terminal device consisting of a superconductor sandwiched between two normal metals, it has been predicted that Cooper pairs can split into spinentangled electrons flowing in the two spatially separated normal metals 2-5 , resulting in a negative non-local resistance and a positive current-current correlation 6,7 . The former prosperity has been observed 8,9 , but not the latter. Here we show that both characteristics can be observed, consistent with Cooper-pair splitting. Moreover, the splitting efficiency can be tuned by independently controlling the energy of the electrons passing the two superconductor/normal-metal interfaces, which may lead to better understanding and control of non-local entanglement.Entanglement of electrons may arise in the spatial degree of freedom (orbital entanglement) or the spin degree of freedom (spin entanglement). Recently, orbital entanglement in a fermionic Hanbury Brown and Twiss two-particle interferometer was observed using current cross-correlation measurements 10,11 , but further investigation is still required to verify the entangled states 12 . Spin-entanglement has been predicted to exist at the superconductor/normal-metal (SN) interface 2,3 and can be understood in the context of Andreev reflection 13 , in which a low-energy electron in the normal metal impinges on the SN interface and a hole is retroreflected whereas a Cooper pair is created in the superconductor.When two normal metals are coupled to a superconductor with spatial separation comparable to the superconducting coherence length (ξ S ), roughly the size of a Cooper pair, it is predicted that electrons in the two normal metals can also be coupled by means of a non-local analogue of Andreev reflection called crossed Andreev reflection 6,7 (CAR). As a Cooper pair splits into two coupled electrons with opposite spin orientation that are then injected into the two normal-metal leads, instantaneous currents of the same sign are generated across the two SN interfaces, giving rise to a negative non-local resistance as well as a positive current-current correlation between the SN junctions. Previous experimental attempts focused on non-local resistance measurements 8,9,14,15 , but the observation of CAR is complicated by another non-local process called elastic cotunnelling, in which electrons in the normal-metal leads tunnel across the superconductor with the help of Cooper pairs, resulting in a positive non-local resistance and a negative current-current

Noise Correlations in Three-Terminal Diffusive Superconductor–Normal-Metal–Superconductor Nanostructures

“…Interestingly, positive correlations observed in a purely normal 2DEG were ascribed to different scattering mechanisms within the device [9]. Recently, cross-correlations with a bias-dependent sign were reported in a three-terminal superconducting hybrid nanostructure with tunnel contacts [10].…”

Cooper Pair Splitting by Means of Graphene Quantum Dots

“…DOI A Cooper pair, splitting from a superconductor into two different normal metal terminals [1,2], is a natural source of nonlocal entangled electrons, which is an essential resource for quantum information processing [3]. During the past decade, many efforts have been made to split Cooper pairs into metal [4][5][6][7], InAs nanowire [8][9][10], and carbon nanotube [11,12]. In a normal-superconductor-normal (NSN) type of metallic structure, evidence of entangled pairs has been reported using combined conductance and noise correlation measurements in two SN junctions [7].…”

“…During the past decade, many efforts have been made to split Cooper pairs into metal [4][5][6][7], InAs nanowire [8][9][10], and carbon nanotube [11,12]. In a normal-superconductor-normal (NSN) type of metallic structure, evidence of entangled pairs has been reported using combined conductance and noise correlation measurements in two SN junctions [7]. By replacing the normal metal with QDs, the splitter concept was essentially upgraded and efficient CPS was demonstrated by manipulating the energy levels of the two QDs [8].…”

High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation

“…Splitting them adiabatically may give birth to entangled electron pairs. Indeed, it had been predicted and measured that Cooper pairs, emanating from a superconductor, can split into two normal metallic leads in the so-called cross Andreev reflection process [4][5][6][7][8][9][10][11] . Such process can be conclusively verified by observing positive coincident arrival events, namely, positive cross-correlation of current fluctuations in two separated normal metallic leads that collect the split pairs [12][13][14][15][16][17][18] .…”