Integer Quantum Hall Efect (lattices)

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Presentation transcript:

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 and Topological 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)

Proposals, looking at properties Z. Lan, A. Celi, W. Lu, P. Öhberg, and M. Lewenstein, Tunable multiple layered Dirac cones in optical lattices, Phys. Rev. Lett. 107, 253001 (2011), arXiv:1108.1326.

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 liquids Topological 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+1D ZM ~ 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) GAUGE MANGET STANDARD LGT

Simulating lattice gauge theories (dynamical gauge fields) GAUGE MANGET STANDARD LGT

Simulating lattice gauge theories (dynamical gauge fields) Charge Confinement

SINGLE SITE ADDRESSING SUFFICIENTLY COLD and FAST 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"

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

Thank You!!!!