Entanglement and particle correlations of Fermi gases in harmonic traps

Details Entanglement and particle correlations of Fermi gases in harmonic traps Entanglement and particle correlations of Fermi gases in harmonic traps

2012-04-10

arxiv.org/abs/1204.2155v1

Physics

Condensed Matter

Quantum Gases

15 pages, 22 figs

Scientific paper

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\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \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.

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