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Eugene Demler. Strongly correlated many-body systems. Electronic materials. Ultracold atoms. Quantum Optics. First semiconductor transistor. “Standard” model of electrons in solids. High density of electrons. Band theory. Description in terms of weakly interacting Landau electrons. - PowerPoint PPT Presentation
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Strongly correlated many-body systems Eugene Demler
Electronic materials
Quantum Optics
Ultracold atoms
“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
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
High Tc superconductors
t
U
t
The structureof La2CuO4
Microscopic description: Hubbard model
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)
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
Detection of many body states ?
Quantum noise analysis
E. Altman, A. Polkovnikov, A. Imambekov, V. Gritsev, T. Kitagawa, R. Cherng, M. Lukin
Quantum noiseClassical measurement: collapse of the wavefunction into eigenstates of x
Histogram of measurements of x
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
Superfluid to insulator transition in an optical lattice
M. Greiner et al., Nature 415 (2002)
U
1n
t/U
SuperfluidMott insulator
Time of flight experiments
Quantum noise interferometry of atoms in an optical lattice
Second order coherence
Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment
Experiment: Folling et al., Nature 434:481 (2005)
Hanburry-Brown-Twiss stellar interferometer
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
Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment
Experiment: Folling et al., Nature 434:481 (2005)
Second order coherence in the insulating state of fermions.Hanburry-Brown-Twiss experiment
Experiment: Tom et al. Nature 444:733 (2006)
Probing spin order in optical lattices
Correlation Function Measurements
Extra Braggpeaks appearin the secondorder correlationfunction in theAF phase
Detection of fermion pairing
Quantum noise analysis of TOF images is more than HBT interference
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)
Momentum correlations in paired fermionsExperiments: Greiner et al., PRL 94:110401 (2005)