Characterizing electron entanglement in multiterminal mesoscopic conductors

We show that current correlations at the exit ports of a beam splitter can be used to detect electronic entanglement for a fairly general input state. This includes the situation where electron pairs can enter the beam splitter from the same port, or be separated due to backscattering. The proposed scheme allows us to discriminate between occupation-number and degree-of-freedom entanglement.

Figure 1

Sketch of the analyzer. An external entangler prepares electron pairs in the input state of Eq. (1) and injects them into ports $1$ and $2$. The electrons are allowed to enter the analyzer from the same port (cases $\mid {\Phi }_{11}⟩$ and $\mid {\Phi }_{22}⟩$), from different ports (case $\mid {\Phi }_{12}⟩$), or in any superposition of the previous cases. Electrons propagating along lead $2$ undergo an additional (orbital or spin dependent) controllable phase shift (white circle in the figure), before impinging on a $50\%$ beam splitter (BS). Current correlations are measured at $3$ and $4$.