Fermionic entanglement in superconducting systems

M. DI TULLIO; N. GIGENA; R. ROSSIGNOLI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2018

1050-2947

We examine distinct measures of fermionic entanglement in the exact ground state (GS) of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact GS and the set of fermionic gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single particle (sp) states $k$ of positive quasimomenta and their time reversed partners $ar{k}$. In contrast, the entanglement associated with the reduced density matrix of four sp modes $k,ar{k}$, $k´,ar{k}´$, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states $k,k´$ close to the fermi level and becoming small in the strong coupling regime. In the latter such reduced state exhibits, instead, a finite mutual information and quantum discord. And while the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.