Bose-Fermi mixtures in random optical lattices: From Fermi glass to fermionic spin glass and quantum percolation

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Bose-Fermi mixtures in random optical
latticesFrom Fermi glass to fermionic spin
glass and quantum percolation
Anna Sanpera. University Hannover
Cozumel 2004
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Theoretical Quantum Optics
at the University of Hannover

• Cold atoms and cold gases
• Weakly interacting Bose and Fermi gases
  (solitons, vortices, phase fluctuations, atom
  optics, quantum engineering)
• Dipolar Bose and Fermi gases
• Collective cooling, CW atom laser, quantum
  master equation
• Strongly correlated systems in AMO physics

• Quantum Information
• Quantification and classification of
  entanglement
• Quantum cryptography and communications
• Implementations in quantum optics

V. Ahufinger, B. Damski, L. Sanchez-Palencia,
A. Kantian, A. Sanpera M. Lewenstein
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Atomic physics meets condensed matter physics or
Atomic physics beats condensed matter physics ????
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Outline
OUTlLINE 1 Bose-Fermi (BF)
mixtures in optical lattices 2
Disorder and frustration in BF mixtures


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Bose gas in an optical latticeIdea D. Jaksch,
C. Bruder, J.I. Cirac, C.W. Gardiner and P. Zoller
By courtesy of M. Greiner, I. Bloch, O. Mandel,
and T. Hänsch
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Before talking about disorder, let us define
order an optical lattice with atoms loaded on it.
First band
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Some facts about Fermi-Bose Mixtures
Fermi-Bose mixtures in optical lattices

• Fermions and bosons on equal footing in a
  lattice
• Atomic physics beats condensed matter
  physics!!!

• Novel quantum phases and novel kinds of pairing
  
• Fermion-boson pairing!!!

• Novel possibilites of control of the system

Some of the people working on the subject
(theory)

• A. Albus, J. Eisert (Potsdam), F. Illuminati
  (Salerno), H.P. Büchler
• (Innsbruck), G. Blatter (ETH), A.B. Kuklov,
  B.V. Svistunov
• (Amherst/Kurchatov), M.Yu. Kagan, D.V.
  Efremov,
• A.V. Klaptsov (Kapitza), M.-A. Cazalilla
  (Donostia),
• A.F. Ho (Birmingham)

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Quantum phases of the Bose-Fermi Hubbard model

• Description
• i) Bose-Fermi Hubbard model
• Phase I Mott (n) plus Fermi gas of fermions
  with NN interactions
• Phase II Interacting composite fermions
  (fermion bosonic hole)
• Phase III Interacting composite fermions
  (fermion 2 bosonic holes)

Lewenstein et al. PRL (2003), Ferhman et al.
Optics Express (2004)
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• Low tunneling Jltlt Ubb,Ubf
• Effective Fermi-Hubbard Hamiltonian

Ubf/Ubb
Composite interactions Different quantum phases
2
1
Attractive Superfluid fermionic
Domains Repulsive Fermi liquid Density
modulations
IRD
0
IRF
IIRD
IRD
IIRF
-1
IIAS
IIRF
. .
IIRD
-2
0
1
mb/Ubb
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Ubb1 JbJf0.02 ?b10-7 ?f5x10-7 Nf40 Nb60
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2. DISORDER AND FRUSTRATION IN ULTRACOLD
ATOMICGASES
B. Damski, et al. Phys. Rev. Lett. 91, 080403
(2003) A. Sanpera, et al.. cond-mat/0402375,
Phys. Rev. Lett. 93, 040401 (2004) V. Ahufinger
et al. (a review of AMO disordered systems
work in progress)
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What are spin glasses? Spin glasses are
disordered systems with competing ferromagnetic (
)and antiferromagnetic ( ) interactions,
which generates FRUSTRATION.
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Frustration if we only have 2 possible spin
orientations and the interactions are random, no
spin configuration can simultaneously satisfy all
couplings.
Ferromagentic (J1)
Antiferromagnetic (J-1)
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Spin Glasses
70s Edwards Anderson Essential physics of
spin glasses lay not in the details of their
microscopic interaction but rather in the
competetion between quenched ferromagentic and
antiferromagentic interactions. It is enough to
study
i- site of a d-dimensional lattice
Ising classical spins
Independent Gaussian random variables with zero
mean and variance 1.
External magnetic Field
h
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Spin glasses quenched disorder
frustration. Mean Field Theory
Sherrington-Kirkpatrick model 75
KT/J
PARAMAG.
FERROMAG
1
SPIN GLASS
J
1
0
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Mean Field (infinite range) Sherrington-Kirkpatric
k model Use replicas
.
n-replicas
Solution Parisi 80s Breaking the replica
symmetry. The spin glass phase is characterized
by an infinite number of pure states organized in
an ultrametric structure, and a phase transition
occurring in a magnetic field. Order parameter
overlap between replicas
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REAL SYSTEMS (short range interactions)

• How many pure states are in a spin glass at low
  temperature?
• Which is the nature and complexity of the glassy
  phase?
• Does exist a transition in a non zero magnetic
  external field?

Despite 30 years of effort on the subject No
consensus has been reached for real systems !
Alternative Droplet model phase glass consist
in two pure states related by global inversion of
the spins and no phase transition occurring in a
magnetic field.
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From Bose-Fermi mixtures in optical lattices
to spin glasses
From disordered Bose-Fermi Hubbard Hamiltonian
to spin glass Hamiltonian
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• Low tunneling
• Low Temperature
• DISORDER (chemical potential varies site to
  site)
• Effective Fermi-Hubbard Hamiltonian (second
  order perturbation theory)

INTERACTIONS between COMPOSITES
HOPPING of COMPOSITES
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J0, no tunneling of fermions or bosons Depending
on the disorder 2 types of lattice sites
A-sites
n1,m1
B-sites
n0,m1
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Disorder
Speckle radiation or supperlattices or
Damski et al. PRL 2003
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How to make a quantum SG with atomic lattice gas?
1. Use spinless fermions or bosons with strong
repulsive interactions

• There can be Ni 1 or 0 atoms at a site!!
• We can define Ising spins si 2 Mi 1.
• What we need are
• RANDOM NEXT NEIGHBOUR INTERACTIONS,
• HQSG 1/4? Kij sisj
  quantum tunneling terms ...

Composites
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Effective n.n. coulings in FB mixture in a random
optical lattice
Here ?ij ?i - ?j
SPIN GLASS !
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Physics of Fermi-Bose mixtures in random optical
lattices
Regime of small disorder (weak randomness of
on-site potential)

• With weak repulsive interactions we deal
  essentially with a
• Fermi glass (i.e. an analog of Fermi liquid,
  but with Anderson
• localized quasi-particle states)
• With attractive interactions we deal with the
  interplay of
• superfluidity and disorder
• Both situations might occur simultaneously
  with
• quantum site percolation (some sites might
  be blocked)

Regime of strong disorder

• Using the superlattices method we may make local
  potential to
• fluctuate on n.n. sites strongly, being
  zero on the mean.
• This leads to quantum fermionic spin glass
• There is a possibility of novel metallic
  phases at the interplay
• between disorder, hopping and n.n.
  interactions

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SUMMARY OF Bose-Fermi Mixtures
Fermionic spin glasses in optical lattices

• Spin glasses (SG) are spin systems with random
  (disoredered) interactions equally probable to
  be ferro- or antiferromagnetic. The spin
  behaviour is dominated by frustration!!! The
  nature of ordering in SG poses one the most
  outstanding open questions of classical (sic!)
  and quantum statistical mechanics.

• COLD ATOMIC BOSE-FERMI (BOSE-BOSE) MIXTURES
• in optical lattices with disorder can be used to
  study in
• vivo the nature of short range spin glasses.
  (real replicas)
• - Many novel phases related to composite
  fermions in disorder lattices are
  expected! NEW RICH PHYSICS

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Transition from Fermi liquid to Fermi glass in
vivo
Here composite fermions a fermion a
bosonic hole
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Question Can AMO physics help?
YES!

1. Can cold atoms or ions be used to model complex
   systems?

• Bose gas in a disordered optical lattice From
  Anderson to Bose glass
• Fermi-Bose mixtures in random lattices From
  Fermi glass to
• fermionic spin glass and quantum percolation
• Trapped ions with engineered interactions Spin
  chains with
• long range interactions and neural networks
• Atomic lattice gases in non-abelian gauge
  fields From Hofstadter
• butterfly to Osterloh cheese

2. Can cold atoms and ions be used as quantum
simulators of complex systems?
YES!
3. Can cold atoms and ions be used for quantum
information processing in complex systems?
YES?