Download - Eugene Demler Harvard University
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Eugene Demler Harvard University
Main collaborators:
Anatoli Polkovnikov Harvard/Boston UniversityEhud Altman Harvard/WeizmannDaw-Wei Wang Harvard/Tsing-Hua UniversityVladimir Gritsev HarvardAdilet Imambekov HarvardRyan Barnett Harvard/CaltechMikhail Lukin Harvard
Simulations of strongly correlated electron systems using cold atoms
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Strongly correlated electron systems
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“Conventional” solid state materials
Bloch theorem for non-interacting electrons in a periodic potential
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B
VH
I
d
First semiconductor transistor
EF
Metals
EF
Insulators andSemiconductors
Consequences of the Bloch theorem
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“Conventional” solid state materialsElectron-phonon and electron-electron interactions are irrelevant at low temperatures
kx
ky
kF
Landau Fermi liquid theory: when frequency and temperature are smaller than EF electron systems
are equivalent to systems of non-interacting fermions
Ag Ag
Ag
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Non Fermi liquid behavior in novel quantum materials
CeCu2Si2. Steglich et al.,
Z. Phys. B 103:235 (1997)
UCu3.5Pd1.5
Andraka, Stewart, PRB 47:3208 (93)
Violation of the Wiedemann-Franz lawin high Tc superconductorsHill et al., Nature 414:711 (2001)
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Puzzles of high temperature superconductors
Maple, JMMM 177:18 (1998)Unusual “normal” state
Resistivity, opical conductivity,Lack of sharply defined quasiparticles,Nernst effect
Mechanism of Superconductivity
High transition temperature,retardation effect, isotope effect,role of elecron-electron and electron-phonon interactions
Competing orders
Role of magnetsim, stripes,possible fractionalization
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Applications of quantum materials:High Tc superconductors
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Applications of quantum materials: Ferroelectric RAM
Non-Volatile Memory
High Speed Processing
FeRAM in Smart Cards
V+ + + + + + + +
_ _ _ _ _ _ _ _
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Modeling strongly correlated systems using cold atoms
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Bose-Einstein condensation
Cornell et al., Science 269, 198 (1995)
Ultralow density condensed matter system
Interactions are weak and can be described theoretically from first principles
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New Era in Cold Atoms ResearchFocus on Systems with Strong Interactions
• Atoms in optical lattices
• Feshbach resonances
• Low dimensional systems
• Systems with long range dipolar interactions
• Rotating systems
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Feshbach resonance and fermionic condensates Greiner et al., Nature 426:537 (2003); Ketterle et al., PRL 91:250401 (2003)
Ketterle et al.,Nature 435, 1047-1051 (2005)
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One dimensional systems
Strongly interacting regime can be reached for low densities
One dimensional systems in microtraps.Thywissen et al., Eur. J. Phys. D. (99);Hansel et al., Nature (01);Folman et al., Adv. At. Mol. Opt. Phys. (02)
1D confinement in optical potentialWeiss et al., Science (05);Bloch et al., Esslinger et al.,
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Atoms in optical lattices
Theory: Jaksch et al. PRL (1998)
Experiment: Kasevich et al., Science (2001); Greiner et al., Nature (2001); Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004); and many more …
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Strongly correlated systemsAtoms in optical latticesElectrons in Solids
Simple metalsPerturbation theory in Coulomb interaction applies. Band structure methods wotk
Strongly Correlated Electron SystemsBand structure methods fail.
Novel phenomena in strongly correlated electron systems:
Quantum magnetism, phase separation, unconventional superconductivity,high temperature superconductivity, fractionalization of electrons …
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New Era in Cold Atoms ResearchFocus on Systems with Strong Interactions
Goals
• Resolve long standing questions in condensed matter physics (e.g. origin of high temperature superconductivity)
• Resolve matter of principle questions (e.g. existence of spin liquids in two and three dimensions)
• Study new phenomena in strongly correlated systems (e.g. coherent far from equilibrium dynamics)
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Outline• Introduction. Cold atoms in optical lattices. Bose Hubbard
model• Two component Bose mixtures
Quantum magnetism. Competing orders. Fractionalized phases
• Fermions in optical lattices
Pairing in systems with repulsive interactions. High Tc mechanism • Boson-Fermion mixtures
Polarons. Competing orders
• Interference experiments with fluctuating BEC
Analysis of correlations beyond mean-field
• Moving condensates in optical lattices
Non equilibrium dynamics of interacting many-body systems
Emphasis: detection and characterzation of many-body states
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Atoms in optical lattices. Bose Hubbard model
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Bose Hubbard model
tunneling of atoms between neighboring wells
repulsion of atoms sitting in the same well
U
t
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4
Bose Hubbard model. Mean-field phase diagram
1n
U
02
0
M.P.A. Fisher et al.,PRB40:546 (1989)
MottN=1
N=2
N=3
Superfluid
Superfluid phase
Mott insulator phase
Weak interactions
Strong interactions
Mott
Mott
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Set .
Bose Hubbard model
Hamiltonian eigenstates are Fock states
U
2 4
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Bose Hubbard Model. Mean-field phase diagram
Particle-hole excitation
Mott insulator phase
41n
U
2
0
MottN=1
N=2
N=3
Superfluid
Mott
Mott
Tips of the Mott lobes
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Gutzwiller variational wavefunction
Normalization
Interaction energy
Kinetic energy
z – number of nearest neighbors
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Phase diagram of the 1D Bose Hubbard model. Quantum Monte-Carlo study
Batrouni and Scaletter, PRB 46:9051 (1992)
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Optical lattice and parabolic potential
41n
U
2
0
N=1
N=2
N=3
SF
MI
MI
Jaksch et al., PRL 81:3108 (1998)
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Superfluid to Insulator transitionGreiner et al., Nature 415:39 (2002)
U
1n
t/U
SuperfluidMott insulator
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Time of flight experiments
Quantum noise interferometry of atoms in an optical lattice
Second order coherence
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Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment
Theory: Altman et al., PRA 70:13603 (2004)
Experiment: Folling et al., Nature 434:481 (2005)
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Hanburry-Brown-Twiss stellar interferometer
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Hanburry-Brown-Twiss interferometer
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Second order coherence in the insulating state of bosons
Bosons at quasimomentum expand as plane waves
with wavevectors
First order coherence:
Oscillations in density disappear after summing over
Second order coherence:
Correlation function acquires oscillations at reciprocal lattice vectors
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Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment
Theory: Altman et al., PRA 70:13603 (2004)
Experiment: Folling et al., Nature 434:481 (2005)
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Effect of parabolic potential on the second order coherence
Experiment: Spielman, Porto, et al.,Theory: Scarola, Das Sarma, Demler, cond-mat/0602319
Width of the correlation peak changes across the transition, reflecting the evolution of Mott domains
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Width of the noise peaks
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0 200 400 600 800 1000 1200
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Interference of an array of independent condensates
Hadzibabic et al., PRL 93:180403 (2004)
Smooth structure is a result of finite experimental resolution (filtering)
0 200 400 600 800 1000 1200-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
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Extended Hubbard Model
- on site repulsion - nearest neighbor repulsion
Checkerboard phase:
Crystal phase of bosons. Breaks translational symmetry
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Extended Hubbard model. Mean field phase diagram
van Otterlo et al., PRB 52:16176 (1995)
Hard core bosons.
Supersolid – superfluid phase with broken translational symmetry
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Extended Hubbard model. Quantum Monte Carlo study
Sengupta et al., PRL 94:207202 (2005)Hebert et al., PRB 65:14513 (2002)
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Dipolar bosons in optical lattices
Goral et al., PRL88:170406 (2002)
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How to detect a checkerboard phase
Correlation Function Measurements
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Magnetism in condensed matter systems
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Ferromagnetism
Magnetic memory in hard drives.Storage density of hundreds of billions bits per square inch.
Magnetic needle in a compass
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Stoner model of ferromagnetism
Spontaneous spin polarizationdecreases interaction energybut increases kinetic energy ofelectrons
Mean-field criterion I N(0) = 1
I – interaction strengthN(0) – density of states at the Fermi level
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Antiferromagnetism
High temperature superconductivity in cuprates is always foundnear an antiferromagnetic insulating state
Maple, JMMM 177:18 (1998)
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( + )
Antiferromagnetism
Antiferromagnetic Heisenberg model
( - )S =
( + )t =
AF =
AF = S t
Antiferromagnetic state breaks spin symmetry. It does not have a well defined spin
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Spin liquid states
Alternative to classical antiferromagnetic state: spin liquid states
Properties of spin liquid states:
• fractionalized excitations• topological order• gauge theory description
Systems with geometric frustration
?
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Spin liquid behavior in systems with geometric frustration
Kagome lattice
SrCr9-xGa3+xO19
Ramirez et al. PRL (90)Broholm et al. PRL (90)Uemura et al. PRL (94)
ZnCr2O4
A2Ti2O7
Ramirez et al. PRL (02)
Pyrochlore lattice
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Engineering magnetic systems using cold atoms in an optical lattice
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Spin interactions using controlled collisions
Experiment: Mandel et al., Nature 425:937(2003)
Theory: Jaksch et al., PRL 82:1975 (1999)
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Effective spin interaction from the orbital motion.Cold atoms in Kagome lattices
Santos et al., PRL 93:30601 (2004)
Damski et al., PRL 95:60403 (2005)
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t
t
Two component Bose mixture in optical latticeExample: . Mandel et al., Nature 425:937 (2003)
Two component Bose Hubbard model
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Quantum magnetism of bosons in optical lattices
Duan et al., PRL (2003)
• Ferromagnetic• Antiferromagnetic
Kuklov and Svistunov, PRL (2003)
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Exchange Interactions in Solids
antibonding
bonding
Kinetic energy dominates: antiferromagnetic state
Coulomb energy dominates: ferromagnetic state
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Two component Bose mixture in optical lattice.Mean field theory + Quantum fluctuations
2 nd order line
Hysteresis
1st order
Altman et al., NJP 5:113 (2003)
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Coherent spin dynamics in optical lattices
Widera et al., cond-mat/0505492
atoms in the F=2 state
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How to observe antiferromagnetic order of cold atoms in an optical lattice?
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Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment
Theory: Altman et al., PRA 70:13603 (2004) See also Bach, Rzazewski, PRL 92:200401 (2004)
Experiment: Folling et al., Nature 434:481 (2005)
See also Hadzibabic et al., PRL 93:180403 (2004)
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Probing spin order of bosons
Correlation Function Measurements
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Engineering exotic phases
• Optical lattice in 2 or 3 dimensions: polarizations & frequenciesof standing waves can be different for different directions
ZZ
YY
• Example: exactly solvable modelKitaev (2002), honeycomb lattice with
H Jx
i, jx
ix j
x Jy
i, jy
iy j
y Jz
i, jz
iz j
z
• Can be created with 3 sets of standing wave light beams !• Non-trivial topological order, “spin liquid” + non-abelian anyons …those has not been seen in controlled experiments
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Fermionic atoms in optical lattices
Pairing in systems with repulsive interactions. Unconventional pairing. High Tc mechanism
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Fermionic atoms in a three dimensional optical lattice
Kohl et al., PRL 94:80403 (2005)
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Fermions with attractive interaction
U
tt
Hofstetter et al., PRL 89:220407 (2002)
Highest transition temperature for
Compare to the exponential suppresion of Tc w/o a lattice
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Reaching BCS superfluidity in a lattice
6Li
40K
Li in CO2 lattice
K in NdYAG lattice
Turning on the lattice reduces the effective atomic temperature
Superfluidity can be achived even with a modest scattering length
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Fermions with repulsive interactions
t
U
tPossible d-wave pairing of fermions
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Picture courtesy of UBC Superconductivity group
High temperature superconductors
Superconducting Tc 93 K
Hubbard model – minimal model for cuprate superconductors
P.W. Anderson, cond-mat/0201429
After many years of work we still do not understand the fermionic Hubbard model
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Positive U Hubbard model
Possible phase diagram. Scalapino, Phys. Rep. 250:329 (1995)
Antiferromagnetic insulator
D-wave superconductor
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Second order correlations in the BCS superfluid
)'()()',( rrrr nnn
n(r)
n(r’)
n(k)
k
0),( BCSn rr
BCS
BEC
kF
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Momentum correlations in paired fermionsGreiner et al., PRL 94:110401 (2005)
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Fermion pairing in an optical lattice
Second Order InterferenceIn the TOF images
Normal State
Superfluid State
measures the Cooper pair wavefunction
One can identify unconventional pairing
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Boson Fermion mixtures
Fermions interacting with phonons.Polarons. Competing orders
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Boson Fermion mixtures
BEC
Experiments: ENS, Florence, JILA, MIT, Rice, …
Bosons provide cooling for fermionsand mediate interactions. They createnon-local attraction between fermions
Charge Density Wave Phase
Periodic arrangement of atoms
Non-local Fermion Pairing
P-wave, D-wave, …
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Boson Fermion mixtures
“Phonons” :Bogoliubov (phase) mode
Effective fermion-”phonon” interaction
Fermion-”phonon” vertex Similar to electron-phonon systems
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Boson Fermion mixtures in 1d optical latticesCazalila et al., PRL (2003); Mathey et al., PRL (2004)
Spinless fermions Spin ½ fermions
Note: Luttinger parameters can be determined using correlation functionmeasurements in the time of flight experiments. Altman et al. (2005)
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BF mixtures in 2d optical lattices
40K -- 87Rb 40K -- 23Na
=1060 nm(a) =1060nm
(b) =765.5nm
Wang, Lukin, Demler, PRA (1972)
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Systems of cold atoms with strong interactions and correlations
Goals
Resolve long standing questions in condensed matter physics (e.g. origin of high temperature superconductivity)
Resolve matter of principle questions (e.g. existence of spin liquids in two and three dimensions)
Study new phenomena in strongly correlated systems• Interference experiments with fluctuating BEC Analysis of high order correlation functions in low dimensional systems• Moving condensates in optical lattices Non equilibrium dynamics of interacting many-body systems
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Analysis of high order correlation functions in low dimensional systems
Interference experiments with fluctuating BEC
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Interference of two independent condensates
Andrews et al., Science 275:637 (1997)
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Interference of two independent condensates
1
2
r
r+d
d
r’
Clouds 1 and 2 do not have a well defined phase difference.However each individual measurement shows an interference pattern
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Amplitude of interference fringes, , contains information about phase fluctuations within individual condensates
y
x
Interference of one dimensional condensates
x1
d Experiments: Schmiedmayer et al., Nature Physics (2005)
x2
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Interference amplitude and correlations
For identical condensates
Instantaneous correlation function
L
Polkovnikov, Altman, Demler, PNAS (2006)
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For impenetrable bosons and
Interference between Luttinger liquidsLuttinger liquid at T=0
K – Luttinger parameter
Luttinger liquid at finite temperature
For non-interacting bosons and
Analysis of can be used for thermometry
L
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Luttinger parameter K may beextracted from the angular dependence of
Rotated probe beam experiment
For large imaging angle, ,
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Interference between two-dimensional BECs at finite temperature.Kosteritz-Thouless transition
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Interference of two dimensional condensates
Ly
Lx
Lx
Experiments: Stock, Hadzibabic, Dalibard, et al., cond-mat/0506559
Probe beam parallel to the plane of the condensates
Gati, Oberthaler, et al., cond-mat/0601392
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Interference of two dimensional condensates.Quasi long range order and the KT transition
Ly
Lx
Below KT transitionAbove KT transition
Theory: Polkovnikov, Altman, Demler, PNAS (2006)
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x
z
Time of
flight
low temperature higher temperature
Typical interference patterns
Experiments with 2D Bose gasHaddzibabic et al., Nature (2006)
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integration
over x axis
Dx
z
z
integration
over x axisz
x
integration distance Dx
(pixels)
Contrast afterintegration
0.4
0.2
00 10 20 30
middle Tlow T
high T
integration
over x axis z
Experiments with 2D Bose gasHadzibabic et al., Nature (2006)
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fit by:
integration distance Dx
Inte
grat
ed c
ontr
ast 0.4
0.2
00 10 20 30
low Tmiddle T
high T
if g1(r) decays exponentially with :
if g1(r) decays algebraically or exponentially with a large :
Exponent
central contrast
0.5
0 0.1 0.2 0.3
0.4
0.3high T low T
2
21
2 1~),0(
1~
x
D
x Ddxxg
DC
x
“Sudden” jump!?
Experiments with 2D Bose gasHadzibabic et al., Nature (2006)
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Exponent
central contrast
0.5
0 0.1 0.2 0.3
0.4
0.3 high T low T
He experiments:universal jump in
the superfluid density
T (K)1.0 1.1 1.2
1.0
0
c.f. Bishop and Reppy
Experiments with 2D Bose gasHadzibabic et al., Nature (2006)
Ultracold atoms experiments:jump in the correlation function.
KT theory predicts =1/4 just below the transition
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Experiments with 2D Bose gas. Proliferation of thermal vortices Haddzibabic et al., Nature (2006)
Fraction of images showing at least one dislocation
Exponent
0.5
0 0.1 0.2 0.3
0.4
0.3
central contrast
The onset of proliferation coincides with shifting to 0.5!
0
10%
20%
30%
central contrast
0 0.1 0.2 0.3 0.4
high T low T
Z. Hadzibabic et al., Nature (2006)
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Interference between two interacting one dimensional Bose liquids
Full distribution function of the interference amplitude
Gritsev, Altman, Demler, Polkovnikov, cond-mat/0602475
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Higher moments of interference amplitude
L Higher moments
Changing to periodic boundary conditions (long condensates)
Explicit expressions for are available but cumbersome Fendley, Lesage, Saleur, J. Stat. Phys. 79:799 (1995)
is a quantum operator. The measured value of will fluctuate from shot to shot.Can we predict the distribution function of ?
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Impurity in a Luttinger liquid
Expansion of the partition function in powers of g
Partition function of the impurity contains correlation functions taken at the same point and at different times. Momentsof interference experiments come from correlations functionstaken at the same time but in different points. Euclidean invarianceensures that the two are the same
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Relation between quantum impurity problemand interference of fluctuating condensates
Distribution function of fringe amplitudes
Distribution function can be reconstructed fromusing completeness relations for the Bessel functions
Normalized amplitude of interference fringes
Relation to the impurity partition function
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is related to the single particle Schroedinger equation Dorey, Tateo, J.Phys. A. Math. Gen. 32:L419 (1999) Bazhanov, Lukyanov, Zamolodchikov, J. Stat. Phys. 102:567 (2001)
Spectral determinant
Bethe ansatz solution for a quantum impurity can be obtained from the Bethe ansatz followingZamolodchikov, Phys. Lett. B 253:391 (91); Fendley, et al., J. Stat. Phys. 79:799 (95)Making analytic continuation is possible but cumbersome
Interference amplitude and spectral determinant
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0 1 2 3 4
P
roba
bilit
y P
(x)
x
K=1 K=1.5 K=3 K=5
Evolution of the distribution function
Narrow distributionfor .Approaches Gumbledistribution. Width
Wide Poissoniandistribution for
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When K>1, is related to Q operators of CFT with c<0. This includes 2D quantum gravity, non-intersecting loop model on 2D lattice, growth of randomfractal stochastic interface, high energy limit of multicolor QCD, …
Yang-Lee singularity
2D quantum gravity,non-intersecting loops on 2D lattice
correspond to vacuum eigenvalues of Q operators of CFT Bazhanov, Lukyanov, Zamolodchikov, Comm. Math. Phys.1996, 1997, 1999
From interference amplitudes to conformal field theories
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Moving condensates in optical lattices Non equilibrium coherent dynamics
of interacting many-body systems
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Atoms in optical lattices. Bose Hubbard model
Theory: Jaksch et al. PRL 81:3108(1998)
Experiment: Kasevich et al., Science (2001) Greiner et al., Nature (2001) Cataliotti et al., Science (2001) Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004), …
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Equilibrium superfluid to insulator transition
1n
t/U
SuperfluidMott insulator
Theory: Fisher et al. PRB (89), Jaksch et al. PRL (98)Experiment: Greiner et al. Nature (01)
U
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Moving condensate in an optical lattice. Dynamical instability
v
Theory: Niu et al. PRA (01), Smerzi et al. PRL (02)Experiment: Fallani et al. PRL (04)
Related experiments byEiermann et al, PRL (03)
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This discussion: This discussion: How to connectHow to connect the the dynamical instabilitydynamical instability (irreversible, classical) (irreversible, classical)to the to the superfluid to Mott transitionsuperfluid to Mott transition (equilibrium, quantum) (equilibrium, quantum)
U/t
p
SF MI
???Possible experimental
sequence:
Unstable
???
p
U/J
Stable
SF MI
This discussion
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Superconductor to Insulator transition in thin films
Marcovic et al., PRL 81:5217 (1998)
Bi films
Superconducting filmsof different thickness
d
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Linear stability analysis: States with p> are unstable
Classical limit of the Hubbard model. Discreet Gross-Pitaevskii equation
Current carrying states
r
Dynamical instability
Amplification ofdensity fluctuations
unstableunstable
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GP regime . Maximum of the current for .
When we include quantum fluctuations, the amplitude of the order parameter is suppressed
Dynamical instability for integer filling
decreases with increasing phase gradient
Order parameter for a current carrying state
Current
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SF MI
p
U/J
Dynamical instability for integer filling
0.0 0.1 0.2 0.3 0.4 0.5
p*
I(p)
s(p)
sin(p)
Condensate momentum p/
Dynamical instability occurs for
Vicinity of the SF-I quantum phase transition. Classical description applies for
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Dynamical instability. Gutzwiller approximation
0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0
d=3
d=2
d=1
unstable
stable
U/Uc
p/
Wavefunction
Time evolution
Phase diagram. Integer filling
We look for stability against small fluctuations
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The first instability develops near the edges, where N=1
0 100 200 300 400 500
-0.2
-0.1
0.0
0.1
0.2
0.00 0.17 0.34 0.52 0.69 0.86
Cen
ter
of M
ass
Mom
entu
m
Time
N=1.5 N=3
U=0.01 tJ=1/4
Gutzwiller ansatz simulations (2D)
Optical lattice and parabolic trap. Gutzwiller approximation
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Beyond semiclassical equations. Current decay by tunneling
pha
se
jpha
se
jpha
se
j
Current carrying states are metastable. They can decay by thermal or quantum tunneling
Thermal activation Quantum tunneling
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S – classical action corresponding to the motion in an inverted potential.
Decay of current by quantum tunnelingp
hase
j
Escape from metastable state by quantum tunneling.
WKB approximation
pha
se
j
Quantumphase slip
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Decay rate from a metastable state. Example
0
22 3
0
1 ( ) 0
2 c
dxS d x bx p p
m d
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For d>1 we have to include transverse directions. Need to excite many chains to create a phase slip
The transverse size of the phase slip diverges near a phase slip. We can use continuum approximation to treat transverse directions
|| cos ,J J p
J J
Longitudinal stiffness is much smaller than the transverse.
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SF MI
p
U/J
Weakly interacting systems. Gross-Pitaevskii regime.Decay of current by quantum tunneling
Quantum phase slips are strongly suppressed in the GP regime
Fallani et al., PRL (04)
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This state becomes unstable at corresponding to the
maximum of the current:
13cp
2 2 21 .I p p p
Close to a SF-Mott transition we can use an effective relativistivc GL theory (Altman, Auerbach, 2004)
Strongly interacting regime. Vicinity of the SF-Mott transition
SF MI
p
U/J
Metastable current carrying state:2 21 ip xp e
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Strong broadening of the phase transition in d=1 and d=2
is discontinuous at the transition. Phase slips are not important.Sharp phase transition
- correlation length
SF MI
p
U/J
Strongly interacting regime. Vicinity of the SF-Mott transitionDecay of current by quantum tunneling
Action of a quantum phase slip in d=1,2,3
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Decay of current by quantum tunneling
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0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0
d=3
d=2
d=1
unstable
stable
U/Uc
p/
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Decay of current by thermal activationp
hase
j
Escape from metastable state by thermal activation
pha
se
j
Thermalphase slip
E
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Thermally activated current decay. Weakly interacting regime
E
Activation energy in d=1,2,3
Thermal fluctuations lead to rapid decay of currents
Crossover from thermal to quantum tunneling
Thermalphase slip
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Phys. Rev. Lett. (2004)
Decay of current by thermal fluctuations
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Conclusions
We understand well: electron systems in semiconductors and simple metals.Interaction energy is smaller than the kinetic energy. Perturbation theory works
We do not understand: strongly correlated electron systems in novel materials.Interaction energy is comparable or larger than the kinetic energy.Many surprising new phenomena occur, including high temperaturesuperconductivity, magnetism, fractionalization of excitations
Our big goal is to develop a general framework for understanding stronglycorrelated systems. This will be important far beyond AMO and condensed matter
Ultracold atoms have energy scales of 10-6K, compared to 104 K forelectron systems. However, by engineering and studying strongly interactingsystems of cold atoms we should get insights into the mysterious propertiesof novel quantum materials
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