Electrical current noise of a beamsplitter as a test of spin entanglement -: art. no. 115330

We investigate the spin entanglement in the superconductor-quantum dot system proposed by Recher, Sukhorukov, and Loss, coupling it to an electronic beamsplitter. The superconductor-quantum dot entangler and the beamsplitter are treated within a unified framework and the entanglement is detected via current correlations. The state emitted by the entangler is found to be a linear superposition of nonlocal spin singlets at different energies, a spin-entangled two-particle wave packet. Colliding the two electrons in the beamsplitter, the singlet spin state gives rise to a bunching behavior, detectable via the current correlators. The amount of bunching depends on the relative positions of the single particle levels in the quantum dots and the scattering amplitudes of the beamsplitter. It is found that the bunching-dependent part of the current correlations is of the same magnitude as the part insensitive to bunching, making an experimental detection of the entanglement feasible. The spin entanglement is insensitive to orbital dephasing but suppressed by spin dephasing. A lower bound for the concurrence, conveniently expressed in terms of the Fano factors, is derived. A detailed comparison between the current correlations of the nonlocal spin-singlet state and other states, possibly emitted by the entangler, is performed. This provides conditions for an unambiguous identification of the nonlocal singlet spin entanglement.