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Accueil > FR > Recherche > Physique des Atomes Froids > Séminaire du groupe

Benoît Vermersch (Univ. Innsbruck, Autriche)

par Jean-Claude GARREAU - publié le

Le 8 décembre 2017 - 11 h - salle 172 - bâtiment P5 bis

Measuring Entanglement directly

Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterizing quantum phases and quantum phase transitions. In this talk, I will present two approaches to measure it directly in an experiment, i.e without performing quantum state tomography.

In the first part of my talk, I will show how to measure Renyi entropies [1] in cold atoms systems. This approach consists in implementing an ensemble of random unitary evolution operators, applying them on the measured many-body state and extracting the desired functions from ensemble averaged observables [2]. I will present examples in one and two-dimensional Fermi (Bose-) Hubbard models and Spin models, show simulations of the measurement of area laws of 2d gapped quantum systems and of the entanglement growth in the many-body localized (MBL) phase, and finally discuss on-going experiments with trapped Ions.

The entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly correlated quantum matter from detection of topological order to characterization of quantum critical systems. In the second part of my talk, I will (briefly) show how to measure the entanglement spectrum of ground states of generic Hamiltonians based on the direct engineering of the entanglement Hamiltonian [3].

[1] A. Elben, B. Vermersch, M. Dalmonte, I. Cirac, P. Zoller, arxiv:1707.04455
[2] S. J. van Enk and C. W. J. Beenakker, Phys. Rev. Lett. 108, 110503 (2012).
[3] M. Dalmonte, B.Vermersch, P. Zoller, arxiv:1709.05060