Atomes froids et matière condensée

T. Giamarchi

http://dpmc.unige.ch/gr_giamarchi/

M. A. Cazalilla (Donostia)A. F. Ho (Imperial)

A. Iucci (Geneva)C. Kollath (Geneva)

M. Koehl (Cambridge)

T. Esslinger (Zurich)

BEC in cold atomic gases

2001: Cornell, Ketterle, Wieman

1924: predicted by Bose and Einstein

Strong correlations

• Condensed matter:

Ecin = Ecoul

Strongcorrelations !

Atoms in a lattice

Tunnelling

Short range interaction

Optical lattices: control kinetic energy

Greiner et al. (2002);

Quantum simulators !

Interactions

StatisticsDimensionality

ENS, ETH, LENS, Mainz, MIT, NIST, Penn State,

Dream ??

D. Jaccard et al., J. Phys. C, 13 L89 (2001)

Deconfinement

0 5 10 15 20 25

60

80100

200

400

600 TMTTF2PF

6

Δa

T*

ICSDW

CSDWSpin-Peierls

Δc

Act

ivat

ion

ener

gy, T

* (K

)

Pressure (kbar)

P. Auban-Senzier, D. Jérome, C. Carcel and J.M. Fabre J de Physique IV, (2004)

TG Chemical Review 104 5037 (2004)

T. Stoferle et al.PRL 92 130403 (2004)

1D physics (Luttinger Liquids)

Cold atoms

1D Mott insulator

Bosons

[87Rb]

A. F. Ho, M. A. Cazalilla, TG PRL 92 130405 (2003)M. A. Cazalilla, A. F. Ho, TG, NJP 8 158 (2006)

10-6

10-5

10-4

10-3

10-2

10-1

1 1.5 2 2.5

J/μ

K

1D MI2D MI

Anisotropic 3D SF (BEC)

( γ = + ∞) ( γ = 3.5) ( γ = 2)( γ = 8)

Phase diagram

Array of atomic‘quantum dots’

transverse hopping

repulsion

T. Stoferle et al.PRL 92 130403 (2004)

Experiments

Shaking of the lattice

T. Stoferle et al. PRL 92 130403 (2004)

3D superfluid

Mott ins.

Not so simple !A. Iucci, M.A. Cazalilla, AF Ho, TG, PRA 73, 041608R (2006); C. Kollath, A. Iucci, TG, W. Hofstetter, U. Schollwock, PRL 97 050402 (2006)

Fermions

[6Li or 40K]

M.A. Cazalilla, A. F. Ho, TG, PRL 95 226402 (2005)

Fermionic tubes

• 2 different hoppings t (optical lattice)

• Local interaction U (Feshbach resonnance)

• N↑ = N↓

1D: phase diagram

Falikov-Kimballrepulsion

attraction

Spin gap: Raman transitions

So ... dream ??

or Nightmare ??

Confining potential

• No homogeneous phase !

U/J=10

H = ∫ r2 ρ(r)

Can change physics drastically

M.A. Cazalilla, A. F. Ho, TG, PRL 95 226402 (2005)

Coupled tubes with Spin gap

β α

AF Order

μ1

μ2

Triplet superconductivity (repulsive interactions)

Probes !

Atoms are neutral !

n(k) (time of flight) useless for fermions !

Need to probe correlations !

noise measurement: -> density-density correlations

time-of-flight measurement -> momentum distribution

periodic lattice modulation

Zurich

München

Mainz

proposed: Raman spectroscopy->Green‘s function, Fermi surface

Paris

microwave spin-changingtransitionsdensity spatially resolved

Mainz

molecule formationbinding energydoubly occupied sites

Zurich

Need local probes !!

The cat ☺

C. Kollath, M. Koehl, TG cond-mat/0704.1283

STM CAT

theoretical description

with W0~ W1 W2/D

Two- color Raman coupling

.).(~ 0 chIcMH jRaman +Ω +

i

ja

Density measurements

Antiferromagnetism (spin resolved STM)

Spectroscopy

Potential use !

O. Fischer et al. (2006)

tunneling modescanning mode

d-wave versus s-wave

Conclusions

Cold atoms/condensed matter: complementary

Cold atoms: quantum simulators

Tunability and local interactions

Inhomogeneous phases

Probes

The sky is the limit !!