Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.

Aug 9, 20140 citations

High Efficiency CVD Graphene-lead (Pb) Cooper Pair Splitter

Ivan Valerievich Borzenets, Yuya Shimazaki, Gareth J. F. Jones +4 more

Generation and manipulation of quantum entangled electrons is an important concept in quantum mechanics, and necessary for advances in quantum information processing; but not yet established in solid state systems. A promising device is a superconductor-two quantum dots Cooper pair splitter. Early nanowire based devices, while efficient, are limited in scalability and further electron manipulation. We demonstrate an optimized, high efficiency, CVD grown graphene-based Cooper pair splitter. Our device is designed to induce superconductivity in graphene via the proximity effect, resulting in both a large superconducting gap Δ = 0.5 meV, and coherence length ξ = 200 nm. The flat nature of the device lowers parasitic capacitance, increasing charging energy EC. Our design also eases geometric restrictions and minimizes output channel separation. As a result we measure a visibility of up to 86% and a splitting efficiency of up to 62%. This will pave the way towards near unity efficiencies, long distance splitting, and post-splitting electron manipulation.Generation and manipulation of quantum entangled electrons is an important concept in quantum mechanics, and necessary for advances in quantum information processing; but not yet established in solid state systems. A promising device is a superconductor-two quantum dots Cooper pair splitter. Early nanowire based devices, while efficient, are limited in scalability and further electron manipulation. We demonstrate an optimized, high efficiency, CVD grown graphene-based Cooper pair splitter. Our device is designed to induce superconductivity in graphene via the proximity effect, resulting in both a large superconducting gap Δ = 0.5 meV, and coherence length ξ = 200 nm. The flat nature of the device lowers parasitic capacitance, increasing charging energy EC. Our design also eases geometric restrictions and minimizes output channel separation. As a result we measure a visibility of up to 86% and a splitting efficiency of up to 62%. This will pave the way towards near unity efficiencies, long distance splitting, and post-splitting electron manipulation.

arXiv:1506.04597Scientific ReportsMar 14, 201655 citations

Spin blockade in Cooper pair splitters

Jami Rönkkö

Entanglement is a valuable resource for quantum computing and information technologies. A promising way to obtain spin-entangled electrons is the splitting of Cooper pairs residing in superconductors. This is realized by a nanodevice called Cooper pair splitter. A Cooper pair splitter is realized by tunnel-coupling a superconductor to two quantum dots, which are each further tunnelcoupled to separate terminal leads. This setup enables the extraction and splitting of Cooper pairs from the superconductor into the terminals via the quantum dots. The quantum dots are commonly fabricated from semiconducting materials like InAs and InSb, that can manifest spin-orbit interaction. This thesis studies the eﬀect of spin-orbit interaction on the spin state of the electron pair in the Cooper pair splitter. Activating the spin-orbit eﬀects in a Cooper pair splitter requires a static magnetic ﬁeld to be applied to the quantum dots. Together with the gate electrodes controlling the electrostatic energy of the quantum dots, the external magnetic ﬁeld provides a handle for addressing diﬀerent two-particle spin states. The spin-orbit interaction can be activated by various combinations of the gate voltage and Zeeman magnetic ﬁeld, that create resonances between diﬀerent states of the system. The most interesting coherent evolution, that can be invoked in this way, involves the simultaneous activation of the two spin-polarized triplet states. This gives a rise to an entangled Bell state, (|↑↑>+|↓↓>) / √2, that moreover exhibits spin blockade and thus stabilizes entanglement in the Cooper pair splitter. Secondly, the spin-orbit interaction can be used to bypass suppressed Cooper pair tunneling at a high superconductor-quantum dots detuning. Introducing a large Zeeman magnetic ﬁeld allows Cooper pairs to tunnel in to the dots given that their spin state ﬂips to the triplet |↓↓>. Although this regime lacks spin-entanglement, it is of interest for creating triplet Cooper pairs and spin-polarized superconducting currents.Entanglement is a valuable resource for quantum computing and information technologies. A promising way to obtain spin-entangled electrons is the splitting of Cooper pairs residing in superconductors. This is realized by a nanodevice called Cooper pair splitter. A Cooper pair splitter is realized by tunnel-coupling a superconductor to two quantum dots, which are each further tunnelcoupled to separate terminal leads. This setup enables the extraction and splitting of Cooper pairs from the superconductor into the terminals via the quantum dots. The quantum dots are commonly fabricated from semiconducting materials like InAs and InSb, that can manifest spin-orbit interaction. This thesis studies the eﬀect of spin-orbit interaction on the spin state of the electron pair in the Cooper pair splitter. Activating the spin-orbit eﬀects in a Cooper pair splitter requires a static magnetic ﬁeld to be applied to the quantum dots. Together with the gate electrodes controlling the electrostatic energy of the quantum dots, the external magnetic ﬁeld provides a handle for addressing diﬀerent two-particle spin states. The spin-orbit interaction can be activated by various combinations of the gate voltage and Zeeman magnetic ﬁeld, that create resonances between diﬀerent states of the system. The most interesting coherent evolution, that can be invoked in this way, involves the simultaneous activation of the two spin-polarized triplet states. This gives a rise to an entangled Bell state, (|↑↑>+|↓↓>) / √2, that moreover exhibits spin blockade and thus stabilizes entanglement in the Cooper pair splitter. Secondly, the spin-orbit interaction can be used to bypass suppressed Cooper pair tunneling at a high superconductor-quantum dots detuning. Introducing a large Zeeman magnetic ﬁeld allows Cooper pairs to tunnel in to the dots given that their spin state ﬂips to the triplet |↓↓>. Although this regime lacks spin-entanglement, it is of interest for creating triplet Cooper pairs and spin-polarized superconducting currents.

Työväentutkimus VuosikirjaJan 1, 20200 citations

Cooper-pair beam splitter as a feasible source of entangled electrons

B. Sharmila, Fabricio Macedo de Souza, H. M. Vasconcelos +1 more

We investigate the generation of an entangled electron pair emerging from a system composed of two quantum dots attached to a superconductor Cooper-pair beam splitter. We take into account three processes: crossed Andreev reflection, cotunneling, and Coulomb interaction. Together, these processes play crucial roles in the formation of entangled electronic states, with electrons being in spatially separated quantum dots. By using perturbation theory, we derive an analytical effective model that allows a simple picture of the intricate process behind the formation of the entangled state. Several entanglement quantifiers, including quantum mutual information, negativity, and concurrence, are employed to validate our findings. Finally, we define and calculate the covariance associated with the detection of two electrons, each originating from one of the quantum dots with a specific spin value. The time evolution of this observable follows the dynamics of all entanglement quantifiers, thus suggesting that it can be a useful tool for mapping the creation of entangled electrons in future applications within quantum information protocols.We investigate the generation of an entangled electron pair emerging from a system composed of two quantum dots attached to a superconductor Cooper-pair beam splitter. We take into account three processes: crossed Andreev reflection, cotunneling, and Coulomb interaction. Together, these processes play crucial roles in the formation of entangled electronic states, with electrons being in spatially separated quantum dots. By using perturbation theory, we derive an analytical effective model that allows a simple picture of the intricate process behind the formation of the entangled state. Several entanglement quantifiers, including quantum mutual information, negativity, and concurrence, are employed to validate our findings. Finally, we define and calculate the covariance associated with the detection of two electrons, each originating from one of the quantum dots with a specific spin value. The time evolution of this observable follows the dynamics of all entanglement quantifiers, thus suggesting that it can be a useful tool for mapping the creation of entangled electrons in future applications within quantum information protocols.

arXiv:2401.16408Physical Review AJun 28, 20241 citation

Cooper pair splitting efficiency in the hybrid three-terminal quantum dot

Grzegorz Michałek, T. Domański, Karol Izydor Wysokiński

Nanodevices consisting of a quantum dot tunnel coupled to one superconducting and two normal electrodes may serve as a source of entangled electrons. As a result of crossed Andreev reflection the Cooper pair of s-wave character may be split into two electrons and each of them goes into a distinct normal electrode, preserving entanglement. Efficiency of the process depends on the specific system and is tunable by electric means. Our calculations show that in the studied device this efficiency may attain values as large as $80 \%$ .Nanodevices consisting of a quantum dot tunnel coupled to one superconducting and two normal electrodes may serve as a source of entangled electrons. As a result of crossed Andreev reflection the Cooper pair of s-wave character may be split into two electrons and each of them goes into a distinct normal electrode, preserving entanglement. Efficiency of the process depends on the specific system and is tunable by electric means. Our calculations show that in the studied device this efficiency may attain values as large as $80 \%$.

arXiv:1608.00023Jul 29, 20160 citations

Cooper Pair Splitting Efficiency in the Hybrid Three-Terminal Quantum Dot

Grzegorz Michałek, T. Domański, Karol Izydor Wysokiński

Nanodevices consisting of a quantum dot tunnel coupled to one superconducting and two normal electrodes may serve as a source of entangled electrons. As a result of crossed Andreev reflection the Cooper pair of s-wave character may be split into two electrons and each of them goes into a distinct normal electrode, preserving entanglement. Efficiency of the process depends on the specific system and is tunable by electric means. Our calculations show that in the studied device this efficiency may attain values as large as 80 % .Nanodevices consisting of a quantum dot tunnel coupled to one superconducting and two normal electrodes may serve as a source of entangled electrons. As a result of crossed Andreev reflection the Cooper pair of s-wave character may be split into two electrons and each of them goes into a distinct normal electrode, preserving entanglement. Efficiency of the process depends on the specific system and is tunable by electric means. Our calculations show that in the studied device this efficiency may attain values as large as 80 % .

Journal of Superconductivity and Novel MagnetismSep 3, 20167 citations

80 \%