1. Integer Quantum Hall Efect (lattices)

2. Integer Quantum Hall Efect (lattices)

3. Dirac physics in non-Abelian gauge fields

4. 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!

5. 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, (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: , New J. Phys. 14, (2012)

6. 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: ,
New J. Phys. 14, (2012)

7. 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, (2011), arXiv:

8. Proposals, looking at properties

9. 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

10. Proposals, looking at properties

11. Proposals, looking at properties

12. 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”

13. Simulating lattice gauge theories (dynamical gauge fields)
Nature Phys. 6, (2010)

14. Simulating lattice gauge theories (dynamical gauge fields)

15. Simulating lattice gauge theories (dynamical gauge fields)

16. Simulating lattice gauge theories (dynamical gauge fields)

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

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

19. Simulating lattice gauge theories (dynamical gauge fields)
Charge Confinement

20. SINGLE SITE ADDRESSING SUFFICIENTLY COLD and FAST
Simulating lattice gauge theories (dynamical gauge fields)
SINGLE SITE ADDRESSING
SUFFICIENTLY COLD and FAST

21. Simulating lattice gauge theories (non-Abelian SU(2) case)
arXiv: , see also:
D. Banerjee, M. Dalmonte, M. Müller, E. Rico, P. Stebler , U.-J. Wiese and
P. Zoller, arXiv: ; E. Zohar, J.I.Cirac and B. Reznik, arXiv: = "arXiv: "

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

23. Thank You!!!!