Advanced ERC Grant: QUAGATUA

1. AvH Senior Research Grant + Feodor Lynen Advanced ERC Grant: QUAGATUA Chist-Era DIQIP Quantum Simulators of Lattice Gauge Theories Hamburg Theory Prize

2. Barcelona – Quantum Optics Theory Ex-Hannoveraner-Icfonians: Anna Sanpera (ICREA full prof. UAB), Dagmar Bruβ (C4, Düsseldorf) L. Santos (W3, Hannover), Veronica Ahufinger (ICREA junior, UAB), J. Mompart (assoc. prof, UAB), Carla Faria (lect. UC, London) P. Öhberg (lect. Edinburgh), L. Sanchez-Palencia (CNRS, Palaiseau), Z. Idziaszek(Warsaw), U.V. Poulsen (adiunkt, Aarhus), U. Sen, Aditi Sen (De) (Allahabad) G. Tóth (Bilbao), Chiara Menotti (Trento), B. Damski (Los Alamos), P. Pedri (Paris Nord),O Gühne (Siegen), F. Cucchietti (Marenostrum), G. Szirmai, Edina Szirmai (Budapest), A. Kantian (Genève), J. Larson (Stockholm),M. Baranov (Innsbruck), C. Trefzger (Paris), M. Rodriguez (Madrid), A. Niederberger (Glasgow,Stanford), A. Eckardt (Dresden), Sibylle Braungardt (Freiburg), M. Ciappina (Auburn), J. Rodriguez-Laguna (Madrid), O. Tieleman (MKS), Ph. Hauke (Innsbruck), PhD ICFO: Ulrich Ebling Tobias Grass Alejandro Zamora Matthieu Alloing (exp) Piotr Migdał Jordi Tura Stephan Humeniuk Mussie Beian (exp) Postdocs ICFO: Alessio Celi Omjyoti Dutta Remigiusz Augusiak Pietro Massignan G. John Lapeyre Jarek Korbicz Bruno Julia-Díaz François Dubin (exp) Luca Tagliacozzo Simon Moulieras Christine Muschik Tahir Sharaan Tomasz Sowiński Caixa-Manresa-Fellows: Julia Stasińska Stagiers (en français) Michał Maik Anna Przysiężna

3. Compare Raymond Laflamme versus Barry Sanders, Ashok Ajoy, Ramesh Pai, present talk!

4. Atoms in optical lattices Lattice type – here triangular from K. Sengstock group (Hamburg) Dimension - 1D, 2D, 3D

5. Outline: Simulating Gauge Field Theories and More… MVPs: I. Spielman, T. Porto, W. Phillips, E. Cornell, J. Dalibard, F. Gerbier, I. Bloch, A. Hemmerich, K. Sengstock, M. Greiner, J. Simonet, T. Esslinger, N. Gemelke, B. Lev, R. Blatt, Ch. Roos. D. Wineland, J. Bollinger (exp.), … N. Goldman, A. Bermudez, M.A. Martin-Delgado, P. Zoller, G. Juzeliūnas, J. Ruseckas, E. Demler, M. Lukin, L. Santos, M. Fleischhauer, E. Mueller, H. Grabert, S. Das Sarma, Ch. Clark, I. Satija, D. Jaksch, L.-M. Duan, J.I. Cirac, B. Reznik, P. Öhberg, H-P. Büchler, M. Rizzi, L. Mazza, P. Nikolić, A. Trombettoni, C. Morais Smith, J. Pachos, U. Wiese, D. Bercieux, Y. Meurice, E. Solano, L. Lamata, J.J. García-Ripoll, J.-I. Latorre, O. Boada and many others… (th.)

6. Quantum simulators A ``working´´ definition of a quantum simulator could be: I. Quantum simulator is an experimental system that mimics a simple model, or a family of simple models of condensed matter, high energy physics, etc. II. The simulated models have to be of some relevance for applications and/or our understanding of challenges of condensed matter, high energy physics, or more generally quantum many body physics. III. The simulated models should be computationally very hard for classical computers (meaning= no efficient algorithm exists, or systems are too big). Exceptions from this rule are possible for quantum simulators that exhibit novel, only theoretically predicted and not yet observed phenomena (simulating ≠ simulating and observing). IV. Quantum simulator should allow for broad control of the parameters of the simulated model, and for control of preparation, manipulation and detection of states of the system. In particular, it should allow for validation! Compare Vladimir Korepin!

7. Quantum simulators • What shall we simulate? • Statics at zero temperature – ground state and its properties. • Statics (equilibrium) at non-zero temperature • Dynamics (Hamiltonian, but out of equilibrium) • Dissipative dynamics

8. Integer Quantum Hall effect • Hofstadter butterfly e n e r g y • Fractional Quantum Hall Effect Magnetic flux α Why gauge?

9. Why artificial? • We want to mimic effects of the Lorenz force !!! • Ions are heavy !!! • Atoms are neutral !!!

10. Why non-Abelian? Compare Go Yusa! • We want to mimic Quantum Spin Hall (QSH) effect (spin-orbit, Rashba, Dresselhaus couplings and more…) (from Physics Today, Xiao-Liang Qi and Shou-Cheng Zhang)

11. Why non-Abelian? • We want to mimic graphene and emergence of Dirac fermions… The Nobel Prize in Physics 2010 was awarded jointly to Andrei Geim and Konstantin Novoselov "for groundbreaking experiments regarding the two-dimensional material graphene" Compare Arindam Ghosh!

12. Why non-Abelian? • We want to mimic all possible topological insulators… Also: Alex Altland + Martin Zirnbauer, Andreas Schnyder + Shinsei Ryu + Akira Furasaki + Andreas W.W. Ludwig, Xiao-Liang Qi + Taylor L. Hughes + Shou-Cheng Zhang …

13. Outline: Simulating Gauge Field Theories and More… • Simulating relativistic quantum field theories • Trotterization, discretization, error correction and all that… • Gauge fields? • Simulating external gauge fields and Dirac points • Laser induced (Berry’s phase etc.) gauge fields • Lattice shakin’ • Simulating lattice gauge theories (dynamical gauge fields) • First attempts • Quantum link, or gauge magnets models • Toward simulation of non-Abelian LGTs

14. Simulating Relativistic Quantum Field Theories

15. Simulating Relativistic Quantum Field Theories

17. Simulating external gauge fields and Dirac points • Laser-induced gauge fields

18. Laser induced gauge fields (traps)

19. Physics (traps, bosons) Phys. Rev. A 86, 021603(R) (2012). Generalizations of Halperin state have non-Abelian anyonic excitations!!!

20. The scheme = combination of laser assisted tunneling, lattice tilting, employing of internal states D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003); K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 95, 010403 (2005). , Lattices: proposal Jaksch-Zoller (Abelian), Osteloh et al. (non-Abelian) Uy=1 Ux=exp(iαm) y = λm/2

21. Physics with artificial gauge fields (non-Abelian U(1)xSU(2), constant Wilson loop, fermions) Ux=exp(iασx) Uy=exp(imΦ + iβσy) x = λm/2 When |W| = |Tr(Product of U’s along the perimeter of a plaquette)| < 2, then the field is genuine non-Abelian!