Conditional spin counting statistics as a probe of Coulomb interaction and spin-resolved bunching

Full counting statistics is a powerful tool to characterize the noise and correlations in transport through mesoscopic systems. In this work, we propose the theory of conditional spin counting statistics, i.e., the statistical fluctuations of spin-up (down) current given the observation of the spin-down (up) current. In the context of transport through a single quantum dot, it is demonstrated that a strong Coulomb interaction leads to a conditional spin counting statistics that exhibits a substantial change in comparison to that without Coulomb repulsion. It thus can be served as an effective way to probe the Coulomb interactions in mesoscopic transport systems. In case of spin polarized transport, it is further shown that the conditional spin counting statistics offers a transparent tool to reveal the spin-resolved bunching behavior.