Spin correlation and entanglement detection in Cooper pair splitters by current measurements using magnetic detectors

Abstract

We analyze a model of double quantum dot Cooper pair splitter coupled to two ferromagnetic detectors, and demonstrate the possibility of determination of spin correlation by current measurements. We use perturbation theory taking account of the exchange interaction with the detectors, which leads to complex spin dynamics in the dots. This affects the measured spin and restricts the use of ferromagnetic detectors to the nonlinear current-voltage characteristic regime at current plateau, where the relevant spin projection is conserved, in contrast to the linear current-voltage characteristic regime, in which the spin information is distorted. Moreover, we show that for separable states the spin correlation can only be determined in a limited parameter regime, much more restricted than in the case of entangled states. We propose an entanglement test based on the Bell inequality.