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arXiv:1204.2155 · Physical Review A

Entanglement and particle correlations of Fermi gases in harmonic traps

Ettore Vicari

Published Jun 5, 2012• 51 citations
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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 ${S}_{\mathrm{HS}}\ensuremath{\approx}{c}_{l}{N}^{(d\ensuremath{-}1)/d}\mathrm{ln}N$ analogously to homogenous systems, with ${c}_{l}=1/6,\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{2}),\phantom{\rule{0.222222em}{0ex}}1/(6\sqrt{6})$ in one, two, and three dimensions, respectively. We show that the asymptotic large-$N$ relation ${S}_{A}\ensuremath{\approx}{\ensuremath{\pi}}^{2}{V}_{A}/3$, 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.

DOI
10.1103/physreva.85.062104

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