Strongly correlated many-body systems

1
Strongly correlated many-body systems
Eugene Demler
Electronic materials
Ultracold atoms
Quantum Optics
2
Standard model of electrons in solids
High density of electrons. Band theory.
Description in terms of weakly interacting
Landau electrons. Au, Cu, Si, GaAs,
Intel 386DX microprocessor
3
Strongly correlated electron systems
Low density of electrons. Interactions localize
electrons. Hubbard bands. Unusual
thermodynamic and

transport properties.
Spin and orbital ordering.
Quantum
magnetism.
Phase diagram of La 1-x Ca x MnO3
Ordered state for x0.5
4
High Tc superconductors
Microscopic description Hubbard model
5
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 and unconventional superconductors.
Hofstetter et al. PRL (2002)
6
Atoms in optical lattice
Antiferromagnetism and pairing at sub-micro
Kelvin temperatures
Same microscopic model
7
Detection of many body states ?
Quantum noise analysis
E. Altman, A. Polkovnikov, A. Imambekov, V.
Gritsev, T. Kitagawa, R. Cherng, M. Lukin
8
Quantum noise
Classical measurement collapse of
the wavefunction into eigenstates of x
Histogram of measurements of x
9
Second order coherence HBT experiments
Classical theory Hanburry Brown and Twiss
(1954)
Quantum theory Glauber (1963)
For bosons
For fermions
Used to measure the angular diameter of Sirius
HBT experiments with matter
10
Superfluid to insulator transition in an optical
lattice
M. Greiner et al., Nature 415 (2002)
11
Time of flight experiments
Quantum noise interferometry of atoms in an
optical lattice
Second order coherence
12
Second order coherence in the insulating state of
bosons.Hanburry-Brown-Twiss experiment
Experiment Folling et al., Nature 434481 (2005)
13
Hanburry-Brown-Twiss stellar interferometer
14
Second order coherence in the insulating state of
bosons
First order coherence
Oscillations in density disappear after summing
over
Second order coherence
Correlation function acquires oscillations at
reciprocal lattice vectors
15
Second order coherence in the insulating state of
bosons.Hanburry-Brown-Twiss experiment
Experiment Folling et al., Nature 434481 (2005)
16
Second order coherence in the insulating state of
fermions.Hanburry-Brown-Twiss experiment
Experiment Tom et al. Nature 444733 (2006)
17
Probing spin order in optical lattices
Correlation Function Measurements
Extra Bragg peaks appear in the second order
correlation function in the AF phase
18
Detection of fermion pairing
Quantum noise analysis of TOF images is more
than HBT interference
19
Second order interference from the BCS superfluid
Theory Altman et al., PRA 7013603 (2004)
n(k)
k
BCS
BEC
20
Momentum correlations in paired fermions
Experiments Greiner et al., PRL 94110401 (2005)