Quasi-particle entanglement: redefinition of the vacuum and reduced density matrix approach
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A scattering approach to entanglement in mesoscopic conductors with independent fermionic quasi-particles is discussed. We focus on conductors in the tunnelling limit, where a redefinition of the quasi-particle vacuum transforms the wavefunction from a many-body product state of non-interacting particles to a state describing entangled two-particle excitations out of the new vacuum (Samuelsson, Sukhorukov and Buttiker 2003 Phys. Rev. Lett. 91 157002). The approach is illustrated with two examples: (i) a normal - superconducting system, where the transformation is made between Bogoliubov - de Gennes quasi-particles and Cooper pairs, and (ii) a normal system, where the transformation is made between electron quasi-particles and electron - hole pairs. This is compared to a scheme where an effective two-particle state is derived from the manybody scattering state by a reduced density matrix approach.