LENS European Laboratory for Nonlinear Spectroscopy, Dipartimento di FisicaUniversità di Firenze

INFM-CNR

Speckles and bichromatic optical lattices

Massimo Inguscio

Anderson localization of ultra-cold atoms

Speckles and bichromatic optical latticesBloch oscillations and control of interactionsInterplay disorder-interactionsGlassy phasesTwo-speciesMott, highly correlated phases, new diagnostics

dB dλ <<

T < TC

Bosons

tem

pera

ture

Quantum degenerate gases

dB dλ <<

ddB ≈λ

tem

pera

ture

dB dλ <<

T < TF

Fermions

tem

pera

ture

Quantum degenerate gases

dB dλ <<

ddB ≈λ

EF

tem

pera

ture

Atomic quantum mixtures

G. Modugno, G. Ferrari, G. Roati, R. Brecha,A. Simoni, and M. Inguscio, Science 294, 1320 (2001)

G. Roati , F. Riboli, G.Modugno, M. Inguscio, Phys. Rev. Lett. 89, 150403 (2002).

22

3

3( ) cos ( )

2

cV z I kz

πω

Γ=∆

Optical lattices

A periodic potential for ultracold atoms may be easily obtained from the interference of two counterpropagating off-resonant laser beams:

ω, k ω, -k

1D Optical lattice302ω ∆

analogy: electrons in a metal

The atoms interact with a “crystal” of light:

The periodic potential has no impurities

No lattice vibrations (phonons)

Full control on lattice spacing (k) and potential depth (Ι , ∆)

Energy bands

Bragg spectroscopy of a lattice gas

Bragg spectroscopy of a condensatein a 1D optical lattice

Poster (Nicole Fabbri)

Momentum transfer:

Energy transfer:

22

3

3( ) cos ( )

2

cV z I kz

πω

Γ=∆

Optical lattices

A periodic potential for ultracold atoms may be easily obtained from the interference of two counterpropagating off-resonant laser beams:

ω, k ω, -k

1D Optical lattice302ω ∆

v2L k

δω=2

230

3( ) cos ( )

2 2

cV z I kz t

π δωω

Γ= −∆

ω+δω, k+δk ω, -k

If the two laser beams producing the optical lattice have different frequencies, the resulting interference pattern provides a periodic potential moving in the laboratory frame.

lattice velocity

Band theory

Energy

Bloch velocity1st

free

1stn,qE

m

pE →=

2

2

Solid state physics

Band theory for a gas of noninteractingparticles in an infinite periodic potential

dq

dE qnn,q

,1v −= h

1

2

,2

2*,

−

=

dq

Edm qn

qn h

Effective mass

free

1st

free

1st

quasi-momentum q

The states are labelled by the band index n and the quasimomentum q

Band spectroscopy of a BEC

Center-of-mass velocity of a Bose-Einstein condensate propagating in the optical lattice

L. Fallani et al., PRL 90, 140405 (2003)

v

When impurities allow transport…

Dynamics in a 1D optical lattice

+

harmonic confinement

FERMIONS / BOSONS

Transport

Dynamics in a 1D optical lattice+ harmonic confinment

Undamped oscillationsFrequency shift (effective mass)

10 20µmx∆ = −

x∆

x positionx position

momentum space

Pos

ition

Collisionally-induced transport in periodic potentials

Fermions

0 10 20 30

Pos

ition

Time

Ott, de Mirandes, Ferlaino, Roati, Modugno, Inguscio, Phys. Rev.Lett. 92, 160601 (2004)

Fermions+bosons

Problem: constant force

External field: constant force

semiclassical equation of motion

2k periodicity in q space oscillatory motion with period

quasimomentum increases linearly with time

Bloch oscillations

Problem: constant force

External field: constant force

semiclassical equation of motion

2k periodicity in q space oscillatory motion with period

quasimomentum increases linearly with time

Bloch oscillations

Problem: constant force

External field: constant force

semiclassical equation of motion

2k periodicity in q space oscillatory motion with period

quasimomentum increases linearly with time

Bloch oscillations

Bloch oscillations (non-interacting fermions)G. Roati et al., PRL 92, 230402 (2004)

g

Bloch oscillations: full quantum approach

Solution of the time-independent Schroedinger equation for the full potential (lattice + constant force)

Set of localized Wannier-Stark states

Time-evolution of a wavepacket

Bloch oscillations as a revival in the interference of Wannier-Stark states

mg

DFCP

Features:Features:� high resolution in presence of gravity� direct measurement of forces� low sensitivity to gradients� high sensitivity (10-7g)

Bloch oscillations as a sensitive probe of forces at short range

thermal asymp. force

J. Carusotto, L. Pitaevskii, S. Stringari, G. Modugno, M. Inguscio, PRL 95, 093202 (2005).

thermal asymp. force+ point like approx.

full calculationCalculated Bloch frequency shift with respect to unperturbed value

λmg

hTB

2=

h2/λω mgB =

Semiclassical picture: Bloch oscillations

mgq −=&

q-qB +qB

ε

Landau-Zener tunnelling in a shallow lattice

)8

exp(2

2

gP

h

λε−=g

Landau-Zener tunnelling

q-qB +qB

A A AAA B B B B B

Optical Bloch oscillations

etc...

interference

interference

interference

Transmission of a fast optical pulse

Optical Bloch oscillations

<<<<<<<

L. dal Negro,…, D.S. Wiersma, Phys. Rev. Lett. 91, 263902 (2003)

0

400

0

100

binding energy (MH

z)ca

tterin

g le

ngth

(a0)

348 350 352-1

0

1

0

400

0

100

binding energy (MH

z)ca

tterin

g le

ngth

(a0) ∆a = 0.06 a0

K3 = 1.3(5)×10-29 cm6s-1

39K BEC with tunable interactions G. Roati et al., PRL 99, 010403 (2007)

340 350 360 370 380 390 400 410

-400

0

-100

0

binding energy (MH

z)

scat

terin

g le

ngth

magnetic field (G)340 350 360 370 380 390 400 410

-400

0

-100

0

binding energy (MH

z)

scat

terin

g le

ngth

magnetic field (G)

.

Interferometry: Fattori et al., PRL 100, 080405 (2008) Dipolar effects: Fattori et al., PRL 101, 190405 (2008)

222 2cos ( )

2 Ri sE kx gt m

ψ ψ ψ ∂ = − ∇ + + ∂

hh

A tunable BEC...

2t m∂

Also R.Hulet lectures

40

50

60

70

80

90

x o

r s

igm

a

100 a0

0.5 a0

Interferometry with a 39K tunable BEC

0 100 1300 1310

10

20

30

40

Time (ms)0 ms 0.4 ms 0.8 ms 1.2 ms 1.6 ms 2 ms 2.4 ms 2.8 ms 3.2 ms 3.6 ms 4 ms

Fattori et al., PRL 100, 080405 (2008)

DECOHERENCE vs SCATTERING LENGTH

Disorder is beautiful

LENS European Laboratory for Nonlinear Spectroscopy, Dipartimento di FisicaUniversità di Firenze

INFM-CNR

Anderson localization of ultra-cold atoms

Speckles and bichromatic optical latticesSpeckles and bichromatic optical latticesBloch oscillations and control of interactionsInterplay disorder-interactionsGlassy phasesTwo-speciesMott, highly correlated phases, new diagnostics

3D systems, exp. in progress 1D systems, exp. in progress

Experiments are in progress to investigate the wholephase diagram of lattice bosons in presence of disorder

Disordered interacting bosons

Roati et al, Nature 453, 895 (2008)Billy et al, Nature 453, 891 (2008)R.Hulet (Rice)

Fallani et al, Phys. Rev. Lett. 98, 130404 (2007)

J

4J

J

4J

2∆∆∆∆

J

4J

2∆∆∆∆

Realization of the Aubry-André model

The first lattice sets the tunneling energy JThe second lattice controls the site energydistribution ∆

S. Aubry and G. André, Ann. Israel Phys. Soc. 3, 133 (1980); G. Harper, Proc. Phys. Soc. A 68, 674 (1965)

2∆∆∆∆2∆∆∆∆

quasiperiodic potential:localization transition at finite ∆ = 2J

extended state localized state

Probing the momentum distribution

long free expansion: x�k

narrow peaks in p(k) broad peaks in p(k)

Momentum distribution

Momentum distribution

FOURIER TRANSFORM

Momentum distribution

experiment theoryDensity distribution after time-of-flight of the initial stationary state

G. Roati et al., Nature 453, 895 (2008)

Width of the central peak

Visibility

Momentum distribution

experiment theory

Universal behavior with ∆/J!

Density distribution after time-of-flight of the initial stationary state

G. Roati et al., Nature 453, 895 (2008)

Width of the central peak

Visibility

one localized state

two localized states

Interference of a finite number of localized states

controlled by playing with harmonic confinement and loading time

Counting localized states

three localized states

many localized states

U

Multiple localized states:no interaction: few independent localized states:ANDERSON GLASS

With interaction: localized states get more extended and lock in

Adding interactions

UU

intermediate region:multiple states almost degenerate with the true ground state � glassy phase?

MORE IS DIFFERENT?

get more extended and lock in phase

theory experiment theory experiment

Adding interactions: momentum distributions

U

∆/J = 5 ∆/J = 40interference from multiple individual states

β = 1064/866 = 1.228…

U

Increase in contrast of interference and decrease in the spread of phase � number of phases in the system decreases

Probing the relative phase

Adding interactions, localized states get more extended and lock in phase

Momentum distributions for ∆/J=15

0 0.6a0 1.2a0 3a0 4.5a0 7a0 12a0 20a0 40a0 190a0

Momentum distribution with interactions

scattering length

LENS European Laboratory for Nonlinear Spectroscopy, Dipartimento di FisicaUniversità di Firenze

INFM-CNR

Anderson localization of ultra-cold atoms

Speckles and bichromatic optical latticesSpeckles and bichromatic optical latticesBloch oscillations and control of interactionsInterplay disorder-interactionsGlassy phasesTwo-speciesMott, highly correlated phases, new diagnostics

Leonardo Fallani

Single species in a perfect lattice: delocalization

A different strategy...

Now take a perfect lattice with a LOCALIZED impurities, e.g. heavy atoms

A different strategy...

87Rb 41K/87Rb mixture

Bose-Bose mixture in an optical lattice

Shift of the “Mott-insulator” transition.

Degenerate Bose-Bose mixture in a 3D optical latticeJ. Catani, L. De Sarlo, G. Barontini, F. Minardi and M.I.PRA 77, 011603R (2008)

also Hamburg, Zurich, Mainz with Fermions

RF association of 41K/87Rb Feshbach molecules

Molecules associated by resonant modulation of the Feshbach magnetic field

G. Thalhammer et al., PRL 100, 210402 (2008)C. Weber et al., PRA (R) 78, 061601 (2008)

Efimov states in a Bose-Bose mixture

In the early ’70s, V. Efimov predicted the existence of trimer states beyond therange where dimers exist (a<0).

Original field: Nuclear Physics, but first evidence in ultracoldhomonuclear atomic systems

No experimental evidence for heteronuclear systems

V. Efimov, Phys. Lett. B 33B, 563 (1970);Sov. J. Nucl. Phys. 12, 589 (1971);Yadern. Fiz. 12 (1970), 1080-1091.

Innsbruck, Florence, Rice

0.3 µK, 100 ms

Efimov resonances in a B-B mixture

57.7(5) G-246 a

0.4 µK, 500 ms

Efimov resonances in a Bose-Bose mixture

KRbRbKKRb

38.8(1) G, -22000 a0

-246 a0

G. Barontini, C. Weber, F. Rabatti, J. Catani., G. Thalhammer, M. I., and F. Minardi, PRL (in press)

Team

The coldest side of Florence

http://quantumgases.lens.unifi.it