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 !!