Download Quantum simulators of lattice gauge theories

AvH
Senior
Research
Grant
+
Feodor
Lynen
Advanced ERC Grant:
QUAGATUA
Hamburg
Theory
Prize
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 Sowiński
Caixa-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 – here
triangular 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. GarcíaRipoll, 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
e
n
e
r
g
y
 Fractional Quantum Hall Effect
Magnetic flux α
Why artificial?
 We want to mimic effects of the Lorenz force !!!
 Ions are heavy !!!
 Atoms are neutral !!!
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)
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 twodimensional material graphene"
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 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
Simulating Relativistic Quantum Field Theories
Simulating Relativistic Quantum Field Theories
Simulating external gauge fields and Dirac points
 Laser-induced gauge fields
PROPOSALS
PHYSICS
Juzeliūnas et al.
Non-Abelian Spin
(2005);
Singlet States
Spielman et al. (2009).
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
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)
Uy=1
Ux=exp(iαm)
y = λm/2
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).
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!