advanced erc grant: quagatua

Advanced ERC Grant:QUAGATUA

  AvHSenior

ResearchGrant

+FeodorLynen

HamburgTheoryPrize

Quantum Simulators of Lattice Gauge

Theories

Chist-Era DIQIP

Barcelona – Quantum Optics Theory

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 SowińskiCaixa-Manresa-Fellows: Julia Stasińska

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),Stagiers (en français) Michał Maik Anna Przysiężna

Compare Raymond Laflamme versus Barry Sanders,

Ashok Ajoy, Ramesh Pai, present talk!

Atoms in optical lattices

Dimension - 1D, 2D, 3D

Lattice type – heretriangular from K. Sengstock group(Hamburg)

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.)

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!

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

Why gauge?Integer Quantum Hall effect

Hofstadter butterfly

energy

Magnetic flux αFractional Quantum Hall Effect

Why artificial?We want to mimic effects of the Lorenz force !!!

Ions are heavy !!!

Atoms are neutral !!!

Why non-Abelian?

(from Physics Today, Xiao-Liang Qi and Shou-Cheng Zhang)

We want to mimic Quantum Spin Hall (QSH) effect (spin-orbit, Rashba, Dresselhaus couplings and more…)

Compare Go Yusa!

Why non-Abelian?

The Nobel Prize in Physics 2010 was awarded jointly to Andrei Geim and Konstantin Novoselov "for groundbreaking experiments regarding the two-dimensional material graphene"

We want to mimic graphene and emergence of Dirac fermions…

Compare Arindam Ghosh!

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 …

Outline: Simulating Gauge Field Theories and More…Simulating relativistic quantum field theories

Trotterization, discretization, error correction and all that… Gauge fields?

Simulating lattice gauge theories (dynamical gauge fields)

First attemptsQuantum link, or gauge magnets models

Simulating external gauge fields and Dirac points Laser induced (Berry’s phase etc.) gauge fields Lattice shakin’

Toward simulation of non-Abelian LGTs

Simulating Relativistic Quantum Field Theories

Simulating Relativistic Quantum Field Theories

Laser-induced gauge fields

PROPOSALS PHYSICSJuzeliūnas et al. (2005);Spielman et al. (2009).

Non-Abelian Spin Singlet States

Jaksch-Zoller et al. (2003); Osterloh et al. (2005).

Mazza-Ricci et al. (2012)

Boada et al. (2012)

IQFE, Dirac physics, topological order;

Toolbox for TIs

Multiple Dirac cones

Extra dimensions

Simulating external gauge fields and Dirac points

Laser induced gauge fields (traps)

Physics (traps, bosons)

Phys. Rev. A 86, 021603(R) (2012).

Generalizations of Halperin state have non-Abelian anyonic excitations!!!

Lattices: proposal Jaksch-Zoller (Abelian), Osteloh et al. (non-Abelian)

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). ,

Uy=1

Ux=exp(iαm)

y = λm/2

Ux=exp(iασx)

Uy=exp(imΦ + iβσy)

x = λm/2

When |W| = |Tr(Product of U’s along theperimeter of a plaquette)| < 2, thenthe field is genuine non-Abelian!

Physics with artificial gauge fields (non-Abelian U(1)xSU(2), constant Wilson loop,

fermions)