Strongly correlated many-body systems

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)