Entanglement and particle correlations of Fermi gases in harmonic traps

2012/04/10 by Ettore Vicari · 1 citation
Physics and Astronomy · #cond-mat.quant-gas #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreva.85.062104

published as Phys Rev A 85, 062104 (2012) · 15 pages, 22 figs

arxiv created 2012/04/10 · arxiv updated 2013/05/29

Abstract

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6√(2)), 1/(6√(6)) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A≈ π² V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.

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