We briefly review current research on strongly interacting ultracold atomic polarized Fermi gases.In three dimensions the ground state of such systems is under strong debate.To gain some insights we investigate a system of one-dimensional strongly interacting polarized Fermi gases.In free space this is an integrable system,and therefore an exact phase diagram can be obtained.We show that an inhomogeneous superfluid state is most widespread in the phase diagram.We consider also the trapped case with an external harmonic trap,where two novel phase separation phases are found using the local density approximation.We briefly review current research on strongly interacting ultracold atomic polarized Fermi gases.In three dimensions the ground state of such systems is under strong debate.To gain some insights we investigate a system of one-dimensional strongly interacting polarized Fermi gases.In free space this is an integrable system,and therefore an exact phase diagram can be obtained.We show that an inhomogeneous superfluid state is most widespread in the phase diagram.We consider also the trapped case with an external harmonic trap,where two novel phase separation phases are found using the local density approximation.

Jan 1, 20070 citations

Entanglement and particle correlations of Fermi gases in harmonic traps

Ettore Vicari

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.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.

arXiv:1204.2155Physical Review AJun 5, 201251 citations

A strongly interacting two-dimensional Fermi gas

Selim Jochim

Bulletin of the American Physical SocietyMar 16, 20161 citation

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.