Integer Quantum Hall Efect (lattices)

Integer Quantum Hall Efect (lattices)

Dirac physics in non-Abelian gauge fields

Why Dirac physics is generic in non-Abelian gauge fields?

In 2D square lattice SU(2) gauge fields include spin-orbit, Rashba and Dresselhaus couplings, and more…

Compare Arindam Ghosh!

Proposal Mazza-Rizzi (non-Abelian)

Ux , Uy , Uz = “anything you want”

Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices,

L. Mazza, M. Rizzi, M. Lewenstein, J.I. Cirac, Phys. Rev. A 82, 043629 (2010);An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories

andTopological Insulators, L. Mazza, A. Bermudez, N. Goldman, M. Rizzi, M.A.

Martin--Delgado, M. Lewenstein, arXiv:1105.0932, New J. Phys. 14, 015007 (2012)

A Toolbox for Topological Insulators

An Optical-Lattice-Based Quantum Simulator for Relativistic Field Theories and Topological Insulators, L. Mazza, A. Bermudez, N. Goldman, M. Rizzi, M.-A. Martin-Delgado, M. Lewenstein, pending in NJP, arXiv:1105.0932, New J. Phys. 14, 015007 (2012)

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Proposals, looking at properties

Proposals, looking at properties

Simulating external gauge fields and Dirac points

Dynamically (lattice shakin’) induced gauge fields

PROPOSALS PHYSICS

Eckert et al. (2010) (triangular lattice)

Struck et al. (2011)

Hauke et al. (2012)

Classical frustrated antiferomagnetism

Quantum frustrated antiferromagnetism, spin liquidsTopological insulators

Proposals, looking at properties

Proposals, looking at properties

Simulating lattice gauge theories (dynamical Abelian fields)

Rydberg atoms, digital open systems simulators

PROPOSALS PHYSICS

Weimer et al. (2010)

Banerjee et al. (2012)

Zohar et al. (2012)

Tagliacozzo et al. (2012)

Z2 Kogut-Susskind, U(1)

U(1) “quantum link” with matter, but 1+1DZM ~ U(1) with matter in 2+1D

U(1) “gauge magnet”

Simulating lattice gauge theories (dynamical gauge fields)

Nature Phys. 6, 382-388 (2010)

Simulating lattice gauge theories (dynamical gauge fields)

Simulating lattice gauge theories (dynamical gauge fields)

Simulating lattice gauge theories (dynamical gauge fields)

Simulating lattice gauge theories (dynamical gauge fields)

GAUGEMANGET

STANDARD LGT

Simulating lattice gauge theories (dynamical gauge fields)

GAUGEMANGETSTANDARD

LGT

Simulating lattice gauge theories (dynamical gauge fields)

Charge Confinement

Simulating lattice gauge theories (dynamical gauge fields)

SINGLE SITE ADDRESSING

SUFFICIENTLY COLD and FAST

Simulating lattice gauge theories (non-Abelian SU(2) case)

arXiv:1211.2704, see also:D. Banerjee, M. Dalmonte, M. Müller, E. Rico, P. Stebler , U.-J. Wiese and P. Zoller, arXiv:1211.2242; E. Zohar, J.I.Cirac and B. Reznik,

arXiv:1211.2241 = "arXiv:1211.2242"

Ultracold atoms in optical lattices: Simulating quantum many-body physicsM. Lewenstein, A. Sanpera, V. Ahufinger, Oxford University Press (2012)

Quantum simulators

Thank You!!!!