Probing Vacuum Entanglement |

We demonstrated that Bell's inequalities are violated for arbitrarily far-apart regions in the vacuum. We also showed that as a function of the separation length $L$ between the regions, entanglement decays at slower rate than $Exp( -L^2)$. To this end we employ an approach wherein vacuum entanglement is directly probed in a controlled manner, by letting a pair of initially non-entangled atom-like systems , locally interact with a field for a finite duration, such that the two systems remain in causally disconnected regions throughout the whole process quant-ph/0008006. quant-ph/0212044. By examining the final state of the two systems, we obtain a lower bound on the amount of vacuum entanglement and a condition for a violation of Bell's inequalities in the vacuum quant-ph/0310058..

See also my lecture on Vacuum-Entanglement delivered at the Conference in honor of Asher Peres's birthday (2004).

Many-Body, ModeWise Entanglement |

We found that bi-partite entanglement of bosonic, as well as fermionic,
multi-mode gaussian states, has a universal modewise structure that is (up to
local transformations) equivalent to products of 1*1 squeezed states for bosonic
modes, and to a products of "EPR-like" states for fermion modes
PRA,
quant-ph/0404176.
Therefore, with respect to *any* bipartite division of the modes, pure
gaussian states (as well as a class of isotropic mixed states) always display a
pairing structure. For fermions this pairing has the form of a BCS-like wave
function. This type of structure characterizes the ground states of a large
class of quadratic Hamiltonians arising from several interacting models (Hubbard
Models, spin-chains, BCS theory) in the mean-field approximation. For bosonic
modes this modewise structure characterizes the ground state of Harmonic-chain
models.

Entanglement structure of the harmonic-chain |

We studied the structure of vacuum entanglement for two complimentary
segments of a linear harmonic chain by applying the

modewise decomposition of entangled gaussian states discussed in
PRA.
We find that the resulting entangled mode shape

hierarchy shows a distinctive layered structure with well defined relations
between the depth of the modes, their characteristic wavelength, and their
entanglement contribution. We re-derive in the strong coupling (diverging
correlation length) regime, the logarithmic dependence of entanglement on the
segment size predicted by conformal field theory for the boson universality
class, and discuss its relation with the mode structure. We conjecture that the
persistence of vacuum entanglement between arbitrarily separated finite size
regions is connected with the localization of the highest frequency innermost
modes.

For the article see:

A. Botero, and B. Reznik, *Spatial Structure and Localization
of Vacuum Entanglement in the Linear Harmonic Chain, *Submitted to Phys. Rev. A. (2004).
quant-ph/0403233.