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