experiments with fermi e bose atomic gases in optical lattices giovanni modugno lens, università di...
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Experiments with Fermi e Bose Experiments with Fermi e Bose atomic gases in optical latticesatomic gases in optical lattices
Giovanni Modugno
LENS, Università di Firenze, and INFM
XXVII Convegno di Fisica Teorica, Cortona, May 2005
Outline of the talkOutline of the talk
Production and properties of atomic quantum gases; optical lattices
Experiments with Bose-Einstein condensates: superfluid transport, instabilities and localization driven by interactions
Experiments with Fermi gases: fundamental transport phenomena and applications
Future directions
MotivationsMotivations
Ultracold atomic gases in optical lattices are potentially a powerful model system to study condensed-matter problems (almost everything can be easily tuned)
Interesting applications beyond condensed matter are arising
Introduction
Roati et al. Phys.Rev. Lett. 89, 150403 (2002).
145 nK
110 nK
80 nK
40K 87Rbfermions bosons
Laser cooling in magneto-optical traps: T =10K
Evaporative/sympathetic cooling in magnetic traps: T =10nK
Typical parameters:
N = 105-107
n =1012 -1014 cm-3
l = 10-1000 m
Tmin=0.1 TF, 0.1 Tc
Production methods
Detection of momentum distributionby absorption imaging with resonantlight
Molecular interaction between neutral atoms: contact interaction
- Even waves for identical bosons, odd waves for identical fermions - All waves with l0 are thermally suppressed as E2l
l
oddl
evenl
lk
22
sin)12(8
No interactions between identical fermions below 100K De Marco and Jin, Phys. Rev. Lett. 1999
24 as
Ultracold collisions
Magnetically tunable resonances
tunable interaction in s, p, and other waves
observed or expected for all alkali species (both homo- and hetero-nuclear)
Fano-Feshbach resonances
Molecules formation at Fano-Feshbach resonances
Bose-Einstein condensation of molecules
JILA, Innsbruck, ENS, MIT, Rice University
Molecules formation and Cooper pairing in Fermi gases
F. Chevy and C. Salomon, Physics World, March 2005
Condensation of Cooper pairs
Optical dipole potential:
)(2
3)(
3
2
rIc
rU
1D optical lattice:
)/exp())/2cos(1(),( 220 wrzUrzU
z
Optical lattices
h
qm
hE BR
2
2
2
Natural energy and momentum scales:
= 1m, qB= 5 mm s-1, ER = 100 nK, U = 1-100 ER
Cubic lattices with various dimensionalities 1D, 2D, 3D, other geometries, lattices with large spacing 1-10 m, …
xx
ER
0
ER
0
2 2
qq-qB-qB +qB
+qB
Bose gases in optical lattices
Superfluidity and interactions in periodic potentials
macroscopic transport at low interaction strengths
insulating phases due to interactions
Gas di Bose in reticoli ottici: trasporto superfluidoGas di Bose in reticoli ottici: trasporto superfluido______________________________________________________________________________________________________________________________________
0 ms 20 ms 40 ms 60 ms 80 ms
BEC
Thermal cloud
Transport of a superfluid
Collective dipole oscillations
0 50 100 150 200 250 300 35036
38
40
42
44
Hor
izon
tal P
ositi
on (
pix)
Time (ms)
0 50 100 150 200 250 300 35036
38
40
42
44
Hor
izon
tal P
ositi
on (
pix)
Time (ms)
F. Cataliotti, et al. Science 293, 843 (2001).
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
1.5
2.0 s = 0 s = 1.3 s = 3.8
velo
city
(v/
v B)
quasimomentum (q/qB)
L. Fallani, et al. Phys. Rev. Lett. 93, 140406 (2004).
Band spectroscopy and dynamical instabilities
Optical lattices can be put in motion:
Spectroscopy of the lattice band dispersion with a BEC
222 2cos ( )
2 Ri sE kx gt m
What is the role of atomic interactions?
0.0 0.5 1.0 1.5
0.00
0.02
0.04
0.06
0.08
quasimomentum (q/qB)
loss
rat
e [m
s-1]
0.55qB
0.40qB
55
g row th o f e xc ita tion s (la ttice on )
2 5 10 20 30 35
150010 200 500 800 1000 1200
m s
m s
Band spectroscopy and dynamical instabilities
222 2cos ( )
2 Ri sE kx gt m
What is the role of atomic interactions?
L. Fallani, et al. Phys. Rev. Lett. 93, 140406 (2004).
SUPERFLUID PHASE
1. Long-range phase coherence2. High number fluctuations3. No gap in the excitation spectrum
MOTT INSULATOR PHASE
1. No phase coherence2. Zero number fluctuations3. Gap in the excitation spectrum4. Vanishing superfluid fraction5. Vanishing compressibility
(M. Greiner et al., Nature 415, 39 (2002))
†
,
1ˆ ˆ ˆ ˆ ˆ( 1)
2i j i i i ii j i i
H J a a n U n n Bose-Hubbard Hamiltonian
Localization in a Mott insulator
Fermi gases in optical lattices
Identical fermions: an ideal gas in a perfect periodic potential
transport properties of a perfect crystal of atoms
applications
Gas di Bose in reticoli ottici: trasporto superfluidoGas di Bose in reticoli ottici: trasporto superfluido______________________________________________________________________________________________________________________________________
Transport of a non interacting Fermi gas
Collective dipole oscillations
s=7
0 2 4 6
Po
sitio
n
Time s=0
Fermions remain trapped on the side of the harmonic potential
s=5
2
x
E
Ott, et al. Phys. Rev. Lett. 93, 120407 (2004), Rigol and Muramatsu, Phys.Rev. A 63, (2004), Hooley and Quintanilla, Phys. Rev. Lett. 93,080404, (2004).
An ideal crystalAn ideal crystalis an insulator.is an insulator.
EF
Transport of a non-interacting Fermi gas
0 100 200 300 400 500 600
100
1000
10000
BO
deca
y tim
e (m
s)
collisional rate (s-1)
Pezzè et al., Phys. Rev. Lett. 93, (2004); Ott et al., Phys. Rev. Lett. 92, 160601 (2004).
Tuning collisions in a boson-fermion mixture: crossover from an ideal ideal conductorconductor (that behaves like an insulator) to a real conductorreal conductor
Esaki-Tsu model for electrons in superlattices
Collision-induced transport
s=5
2
RFsweep
x
E
Atoms in delocalized states can be selectively removed with a RF knife
Ott, et al., Phys. Rev. Lett. 93, 120407 (2004).
Spectroscopy of localized states
Applications
quantum computing
atom interferometry for force sensing
FermiFermi: potential-induced localization
Two localized particle per lattice site Loading procedure confines defects to the outer shell Tunable interactions between two states via F-F resonances
Quantum registers: Bose vs Fermi
What is needed:
Macroscopic array of indidually addressable qubits Lowest possible number of defects Controllable, coherent interactions to perform operations
BoseBose: interaction-induced localization
One localized particle per lattice site Controllable interactions between neighbouring sites via spin-selective lattices
-2 -1 0 1 2
Momentum (qB)
2
mgE
REU 20
0
2/ mgB
q-qB +qB
Semiclassical picture: Bloch oscillationsBloch oscillations
mgq
Wannier-Stark states in a lattice tilted by gravity:
Fx /2
Their interferenceinterference oscillates:
Wannier-Stark states and Bloch oscillations
Bq
Bq
2 m s 2 .4 m s 2 .8 m s 3 .2 m s 3 .6 m s 4 m s 4 .4 m s 4 .8 m s 5 .2 m s 5 .6 m s
Time-resolved Bloch oscillations of trapped, non-interacting fermions
G. Roati, et al., Phys. Rev. Lett. 92, 230402 (2004).
Bloch oscillations
0 5 10 15 250 255-1.0
-0.5
0.0
0.5
1.0
Mo
me
ntu
m (
qB)
Time (ms)
mgh TB /2 410/ms)22(32789.2 gg TB
Fermions trapped in lattices: a force sensora force sensor with high spatial resolutionhigh spatial resolution ( presently 50m, but no fundamental limitations down to a few lattice sites)
Bloch oscillations
1
1
4 0
03
0
z
TkV B
CP
Casimir-Polder potential in proximity of a dielectric surface
I. Carusotto, L. Pitaevskii, S. Stringari, G. Modugno, M. Inguscio, cond-mat/0503141.
Features:Features: high resolution in presence of gravity direct measurement of forces low sensitivity to gradients high sensitivity (10-7g)
Applications:Applications: atom-surface interactions out of thermal equilibrium possible deviations from Newton’s gravitational law at short distances
Force sensing at the micrometer lengthscale
S. Dimopulos and A. A. Geraci, Phys. Rev. D 68, 124021 (2003)
10-10 g
10-7 g
Search for non newtonian forces
Bose and Fermi gases in 1D optical lattices
phenomenology of the band transport, transport of bosonic and fermionic superfluids
fermionic Bloch oscillator: application to high precision study of fundamental phenomena
Bose, Fermi and Fermi-Bose gases in 2D and 3D optical lattices
condensed matter physics: Mott insulators, high Tc superfluidity, …
low dimensionality systems: Luttinger liquids, BEC-BCS, …
applications to quantum computing
Optical lattice and random potentials
Anderson localization, Bose and Fermi glasses, …
BEC-BCS in presence of disorder
Future directions
Fermi surface in a 2D lattice
Estefania De Mirandes, Leonardo Fallani, Francesca Ferlaino, Vera Guarrera, Iacopo Catani, Luigi De Sarlo, Jessica Lye, Giacomo Roati, Herwig Ott
Chiara Fort, Francesco Minardi, Michele Modugno
Giovanni Modugno, Massimo Inguscio
The quantum gas team at LENS