We consider the creation of mobile and nonlocal spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal leads of finite resistivity. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two electrons from a Cooper pair into the same lead compared to the desired pair-split process where each electron enters a different lead. Conversely, this latter process is suppressed by a finite separation between the tunneling points on the SC.We consider the creation of mobile and nonlocal spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal leads of finite resistivity. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two electrons from a Cooper pair into the same lead compared to the desired pair-split process where each electron enters a different lead. Conversely, this latter process is suppressed by a finite separation between the tunneling points on the SC.

arXiv:cond-mat/0307444Physical Review LettersDec 30, 200364 citations

Quantum entanglement and pairing correlation in the reduced BCS pairing model

Guanghua Liu, Xiaoyan Deng, Rui Wen

Physica C SuperconductivityOct 15, 20112 citations

Superconductors, Quantum Dots, and Spin Entanglement

Mahn‐Soo Choi, Christoph Bruder, Daniel Loss

Lecture notes in physicsJan 1, 20011 citation

Entanglement of electron spins in superconductors

Sangchul Oh, Jaewan Kim

We investigate entanglement of two electron spins forming Cooper pairs in an $s$ -wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.We investigate entanglement of two electron spins forming Cooper pairs in an $s$-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.

arXiv:quant-ph/0406013Physical Review BApr 29, 200535 citations

Periodic source of energy-entangled electrons in helical states coupled to a BCS superconductor

Flavio Ronetti, Bruno Bertin-Johannet, Jérôme Rech +4 more

We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electron flying qubits. The proposed device relies on the standard tools of electron quantum optics and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin-polarized electron waveguides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled states devoid of spurious electron-hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electron states are generated at the output of the normal side. We introduce a quantity related to charge current cross correlations which allows one to experimentally verify the entangled nature of the emitted state.We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electron flying qubits. The proposed device relies on the standard tools of electron quantum optics and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin-polarized electron waveguides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled states devoid of spurious electron-hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electron states are generated at the output of the normal side. We introduce a quantity related to charge current cross correlations which allows one to experimentally verify the entangled nature of the emitted state.

arXiv:2409.06591Physical review. B./Physical review. BDec 11, 20241 citation

We investigate entanglement of two electron spins forming Cooper pairs in an

s

-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.