Spin-current noise and Bell inequalities in a realistic superconductor-quantum dot entangler
Olivier Sauret, Thierry Martin, Denis Feinberg
DOI 10.1103/PhysRevB.72.024544 · Physical Review B
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Abstract
Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and −1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of nonlocality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window τ. The efficiency of the test is analyzed, comparing τ to the various time scales in the entangler operation.
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