Strongly correlated many-body systems
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Strongly correlated many-body systems Eugene Demler
Electronic materials
Quantum Optics
Ultracold atoms
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“Standard” model of electrons in solids
High density of electrons. Band theory. Description in terms of weakly interacting Landau electrons. Au, Cu, Si, GaAs, …
First semiconductor transistor
Intel 386DX microprocessor
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Strongly correlated electron systems
Low density of electrons. Interactions localize electrons. Hubbard bands. Unusual thermodynamic and transport properties. Spin and orbital ordering. Quantum magnetism.
U
EFEnergy
Phase diagram of La 1-x Ca x MnO3
Ordered state for x=0.5
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High Tc superconductors
t
U
t
The structureof La2CuO4
Microscopic description: Hubbard model
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Artificial crystals: optical lattices
Theory: Jaksch et al. PRL (1998)
Experiment: Greiner et al., Nature (2001) and many more
Motivation: quantum simulations of strongly correlated electron systems including quantum magnets andunconventional superconductors. Hofstetter et al. PRL (2002)
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Antiferromagnetic and superconducting Tc of the order of 100 K
Atoms in optical lattice
Antiferromagnetism and pairing at sub-micro Kelvin temperatures
Same microscopic model
t
U
t
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Detection of many body states ?
Quantum noise analysis
E. Altman, A. Polkovnikov, A. Imambekov, V. Gritsev, T. Kitagawa, R. Cherng, M. Lukin
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Quantum noiseClassical measurement: collapse of the wavefunction into eigenstates of x
Histogram of measurements of x
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Second order coherence: HBT experiments Classical theory Hanburry Brown and Twiss (1954)
Used to measure the angular diameter of Sirius
Quantum theory Glauber (1963)
For bosons
For fermions
HBT experiments with matter
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Superfluid to insulator transition in an optical lattice
M. Greiner et al., Nature 415 (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
Experiment: Folling et al., Nature 434:481 (2005)
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Hanburry-Brown-Twiss stellar 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
Experiment: Folling et al., Nature 434:481 (2005)
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Second order coherence in the insulating state of fermions.Hanburry-Brown-Twiss experiment
Experiment: Tom et al. Nature 444:733 (2006)
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Probing spin order in optical lattices
Correlation Function Measurements
Extra Braggpeaks appearin the secondorder correlationfunction in theAF phase
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Detection of fermion pairing
Quantum noise analysis of TOF images is more than HBT interference
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Second order interference from the BCS superfluid
)'()()',( rrrr nnn
n(r)
n(r’)
n(k)
k
0),( BCSn rr
BCS
BEC
kF
Theory: Altman et al., PRA 70:13603 (2004)
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Momentum correlations in paired fermionsExperiments: Greiner et al., PRL 94:110401 (2005)