Massimo InguscioMassimo Inguscio

Dipartimento di Fisica e Astronomia &Dipartimento di Fisica e Astronomia &

LENS LENS –– Università di FirenzeUniversità di Firenze

INOINO--CNRCNR

SIF Napoli, 20 SIF Napoli, 20 settembresettembre 20122012

Fasi quantistiche della materiaFasi quantistiche della materia

vverso lo zero assolutoerso lo zero assoluto

Verso lo zero assoluto...Verso lo zero assoluto...

sun surface water boiling water freezing liquid nitrogen

quantum degenerate dilute gases

(Bose / Fermi)

cosmic background radiation superfluidity, superconductivity

laser cooling

tem

pera

ture

BOSONS FERMIONS

EF

Ultracold quantum gases

87Rb 2001 SCIENCE

41K boson

87Rb

40K fermion

2002 PRL

Raffreddamento laser

atom

photon

p mv

p k

conservation of momentum in the

collision between atoms and photons

hottest atoms removal

+

collisions between trapped atoms

cooling

Raffreddamento evaporativoRaffreddamento evaporativo Evaporative cooling

http://www.colorado.edu/physics/2000/bec/

Ettore Majorana (1906-1938?)

E. Majorana, Nuovo Cimento 9, 43 (1932)

Majorana spin-flip

Quadrupole trap

magnetic field = 0

spin flips

Majorana spin-flip

Ioffe-Pritchard trap

magnetic field > 0

no spin flips

Bose-Einstein condensation

Bose-Einstein condensation:

atom number: N ~ 105

size: L ~ 10 mm

density: n ~ 1014 cm-3

temperature: T ~ 10-100 nK

T > TC

T < TC

T ~ TC

BEC

“thermal”

100 mm

Principio di indeterminazione di Heisenberg

caduta libera di un condensato di 87Rb

Intrappolare con la luceIntrappolare con la luce

Trappole fatte di luce

The atomic induced electric

dipole then interacts with the e.m.

wave

Optical trapping

U(r) E(r)p

Far off resonance light induces

an electric dipole

p E

“red” traps

“blue” traps

optical dipole potential detuning

Optical traps

Single-beam trap

1 mm

1 mm

Crossed-beam trap

Optical trapping

P. Pedri et al., Phys. Rev. Lett. 87, 220401 (2001)

2001 Centenario del Premio Nobel

Josephson effect:

The oscillation frequency w*

depends on the effective mass m*

F. S. Cataliotti et al.,

Josephson junctions arrays with BECs

Science 293, 843 (2001)

depending on the tunnelling energy J:

Dipole oscillations and Josephson effect

**

m

mw w

2

2

2*m m

J

Disruption of superfluidityDisruption of superfluidity

Anderson

interaction

Mott Superfluid

Subtle interplay between disorder and interactions

(granular superconductors, superfluid He in porous media, high-Tc, …)

Disordered interacting bosons

Bose glass...

T. Giamarchi and H. J. Schultz,

Anderson localization and interactions in one-dimensional metals

Phys. Rev. B 37, 325 - 340 (1988)

Phase diagram of disordered interacting bosons

Disruption of superfluidityDisruption of superfluidity

wwith interactionsith interactions

Optical lattices

Ultracold atoms in optical lattices

atoms in optical lattices electrons in a solid

Electrons vs atoms

Transizione all’isolante di Mott

LENS, 2005

quantum phase transition induced by repulsive interactions

superfluid

Mott insulator

Light scattering

Scattering (light, neutrons, etc...) provides information on the structure of matter:

excitations

Bragg scattering

Bragg scattering as stimulated inelastic scattering of light

absorption

1st beam

stimulated emission

2nd beam

cold atoms

Physical Review Letters 102, 155301 (2009)

Bragg spectra across the SF-MI transition

MI region ~ U

low energy, superfluid

In the MI regime different contributions to the spectrum can be distinguished:

SF MI / SF

Physical Review Letters 102, 155301 (2009)

Bragg spectroscopy of quantum lattice gases

L. Fallani and M. Inguscio

Controlling cold-atom conductivity

Science 322 (5th December 2008)

…Can physics be simulated by a universal computer? Richard P. Feynman, Int. J. Theor. Phys 21, 467 (1982)

Richard P. Feynman realized that certain phenomena in

Quantum Field Theory are well imitated by certain

Condensed Matter systems…

He thought that there should be a certain class of quantum

mechanical systems which would simulate any other system, a

UNIVERSAL QUANTUM SIMULATOR

that could serve as a quantum laboratory where the validity

of several theoretical models may be tested.

Disruption of superfluidityDisruption of superfluidity

wwith disorderith disorder

Anderson

interaction

Mott Superfluid

Subtle interplay between disorder and interactions

(granular superconductors, superfluid He in porous media, high-Tc, …)

Disordered interacting bosons

Bose glass...

T. Giamarchi and H. J. Schultz,

Anderson localization and interactions in one-dimensional metals

Phys. Rev. B 37, 325 - 340 (1988)

Phase diagram of disordered interacting bosons

Disorder

Effects of disorder are quite difficult to treat theoretically

Perturbative methods generally fail: small changes in the disorder strength

may result in dramatic changes in the transport properties of the system

Transition from a conductor to an insulator predicted by P. W. Anderson in 1958

Disorder is intrinsically present in all real materials:

impurities

vacancies

interstitials

dislocations

...

340 350 360 370 380 390 400 410

-400

0

400

-100

0

100

bin

din

g e

nerg

y (M

Hz)

scatt

erin

g length

(a0)

magnetic field (G)

348 350 352

-1

0

1

340 350 360 370 380 390 400 410

-400

0

400

-100

0

100

bin

din

g e

nerg

y (M

Hz)

scatt

erin

g length

(a0)

magnetic field (G)

.

Da = 0.06 a0

K3 = 1.3(5)10-29 cm6s-1

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

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

Dynamics under a costant force

g

Momentum distribution of

ultracold 40K fermions in a

vertical optical lattice:

w, k

w, k

1at B

rillo

uin

zone

Costant force gravity

Bloch oscillations with period

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

Constant external force

Bloch oscillations

Accurate probe of forces

Bloch oscillations (BEC with tunable interactions) M. Fattori et al., PRL 100, 080405 (2008)

Adding interactions...

Schrödinger equation Gross-Pitaevskii equation

tunable with Feshbach!

Beginning of the story: BEC in a disordered potential (Florence, Orsay, Hannover, Rice, Illinois...)

BEC in disordered potentials Physical Review Letters 95, 070401 (2005)

bichromatic lattice speckle pattern

L.Fallani, C.Fort, M.Inguscio

Bose-Einstein condensates in disordered potentials

Advances Atomic, Molecular and Optical Physics vol 56, pp 119-160

edited by E.Arimondo, P.Berman, C.Lin (Academic Press 2008)

How to produce disorder

Anderson localization P. W. Anderson, Phys. Rev. 109, 1492 (1958)

Anderson model

quantum particles hopping in a disordered lattice

Anderson localization

one electron in a periodic lattice TRANSPORT

Anderson localization

introducing disorder in the lattice

Anderson localization

one electron in a disordered lattice LOCALIZATION

Localized states

Diffusion stops because the eigenstates are localized!

Periodic: wavefunction is delocalized on the whole system size

Disordered: eigenstates are localized in a finite region of space

exponentially decaying amplitude of wavefunction

Incommensurate bichromatic lattice

Tight-binding model with quasi-periodic on-site energies

The second lattice controls the site energies

Dan Shechtman Nobel Prize Chemistry 2011

no periodicity long-range order

Quasicrystals

The bichromatic lattice

The physics of bi-periodic systems interpolates between periodic systems and

disordered systems, as the degree of incommensurability is changed.

• Quasi-crystals

The physics of quasicrystals, ed. P. J. Steinhardt

and S. Ostlund (World Scientific, 1987)

• Fractal critical behavior

D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).

• Energy bands

M. Modugno, New J. Phys. 11, 033023 (2009).

• Localization transition in 1D

S. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 133 (1980)

M. Modugno, New J. Phys. 11, 033023 (2009).

Extended and localized states

Localization transition in 1D incommensurate bichromatic lattice

S. Aubry and G. André, Ann. Israel Phys. Soc. 3, 133 (1980)

localized states:

extended states:

Disordered people

L. Fallani

G. Modugno

C. D’Errico

C. Fort

G. Roati M. Fattori

M. Modugno

M. Zaccanti

Probing the transport properties

A noninteracting 39K BEC is initially confined in a harmonic trap and then left

free to expand in the bichromatic lattice

39K BEC

Feshbach coils

Optical waveguide Bichromatic lattice

BEC

D=0

DJ=1

DJ=7

Ballistic expansion

with reduced velocity

Absence of diffusion:

Ballistic expansion:

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

Expansion in the bichromatic lattice

D/J = 0 D/J = 1.8 D/J = 4.2 D/J = 7

0 ms

750 ms

tim

e

expansion

expansion at

reduced speed

localization

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

Expansion in the bichromatic lattice G. Roati et al., Nature 453, 895 (2008)

Size of the condensate after 750 ms expansion in the bichromatic lattice:

Observing the localized states

momentum distribution with

narrow peaks

broad momentum

distribution

FT imaging of the

atomic state via time-of-flight

Observing the localized states

experiment theory

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

AUBRY- ANDRE’

Hamiltonian

P. W. Anderson, Nobel lecture (1977)

… about the role of interactions

A second reason why I felt discouraged in the early days was that

I couldn’t fathom how to reinsert interactions, and I was afraid

they, too, would delocalize.

The realization that, of course, the Mott insulator localizes without

randomness, because of interactions, was my liberation on this:

one can see easily that Mott and Anderson effects supplement,

not destroy, each other…

The present excitement of the field for me is that a theory of

localization with interactions is beginning to appear…

It is remarkable that in almost all cases interactions play a vital

role, yet many results are not changed too seriously by them.

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

fine control on the

atom-atom interactions!

Feshbach resonance

Single localized state Anderson glass Fragmented BEC Bose-Einstein condensate

Interaction-induced delocalization

Delocalization scenario for increasing atom-atom repulsion

B. Deissler et al., Nature Physics 6, 354 (2010)

Single localized state Independent single-particle localized states

Creation of superfluid fragments Coherent macroscopic wavefunction

Diessler et al

Nature Physics 6, 354 (2010)

Momentum distributions for D/J=15

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

scattering length

Momentum distribution with interactions Nature Physics 6, 354 (2010)

Interaction-induced delocalization

Width of the central peak: Momentum distribution:

experiment theory

inte

ractio

ns

Repulsive interactions shift the

localization transition towards larger D!

Nature Physics 6, 354 (2010)

Ultracold quantum gases in Florence

FundingFunding byby ERC, EU FP7, IIT, MIUR, CNR, …ERC, EU FP7, IIT, MIUR, CNR, …

Ultracold quantum gases in Florence

Giacomo Giacomo RoatiRoati (Li)(Li)

2D Fermi 2D Fermi gasesgases

FundingFunding byby ERC, EU FP7, IIT, MIUR, CNR, …ERC, EU FP7, IIT, MIUR, CNR, …

K. Alexander Müller

Nobel Prize in Physics 1987 (with J. Georg Bednorz)

"for their important break-through in the discovery

of superconductivity in ceramic materials"

Relevant for high-Tc superconductors

Repulsive/attractive Fermi-Hubbard model

...tra 25 anni?

The coldest side of Florence

http://quantumgases.lens.unifi.it