Hanns-Christoph Nägerl

Institut für Experimentalphysik, Universität Innsbruck

Atoms with tunable interactions in optical lattice confinement

1700 m

Firenze, May 21st 2012: New quantum states of matter in and out of equilibrium

theory support (Strasbourg/Innsbruck/Pittsburgh):

Guido Pupillo / Marcello Dalmonte / Andrew Daley

new phd and master students:

NobieRedmon

Florian Meinert

PhilippMeinmann

Michael Gröbner

P. Schmelcher (Hamburg)

V. Melezhik (Dubna)

H. Ritsch (Innsbruck)

N. Bouloufa (Orsay)

O. Dulieu (Orsay)

collaborators:T. Bergeman (Stony Brook)

H.-P. Büchler (Stuttgart)

J. Aldegunde (Durham)

J. Hutson (Durham)

P. S. Julienne (NIST)

ElmarHaller

(now to Glasgow)

Johann Danzl(now to

Göttingen)

KatharinaLauber

Manfred Mark

B. Rutschmann

CsIII-Team

CsIII-Project Team Members & Collaborators…

Bose-Hubbard Physics

U<0 and U=U(n)n = particle number at the lattice sites

Motivation: Bosons in lattices and confined dimensions

Feshbach resonance

two atoms

B

E

molecule

0

1BB

aa bgS

B

aS

abg

B0

¢ = coupling

scattering length aS = aS (B)

Tuning of interactions: Feshbach resonances

Tuning of interactions: Feshbach resonances

scattering length for 2 atoms in hyperfine states (F,mF)= (3,3)

magnetic field B (Gauss)

0

10

scatt

eri

ng length

aS (

1000

a0)

-10

5

-5 this talk…(let’s zoom in)

s s

broad s-resonances

calculations by P. Julienne et al., NIST

Tuning of interactions: Feshbach resonances

0 50

100 150

0

d

ddgg g

g

magnetic field B (Gauss)

scatt

eri

ng length

aS (

1000

a0)

1

2

-2

-1zero

crossing

…or here

make mol’s here…

make BEC here

g

tune here

narrower d-resonancesvery narrow g-resonances

scattering length for 2 atoms in hyperfine states (F,mF)= (3,3)

calculations by P.Julienne et al., NIST

Tuning of interactions: three-body loss

Kraemer et al., Nature 440, 315 (2006)

scattering length aS (1000 a0)

reco

mb

inati

on

len

gth

½3 (

1000

a0)

½3 / K31/4

K3 = three-body loss rate coefficient

K3 / a4

Efimov resonance

Basic concepts of lattice physics

The standard Bose-Hubbard model

Tunneling matrix element

On-site interaction energy

External energy shift

External potential

εTunneling

JInteraction

U

Approximations

Bloch bands

Higher Bloch bands omitted

U’

No nearest neighbor interaction

Interactions

Tunneling

No next nearest neighbor tunneling

J’

Interaction potential

Simple non-regularized pseudopotential

Properties of the Bose-Hubbard (BH) model

Groundstates at T=0

Superfluid J»U

• Delocalized particles

• Coherent phase

• No excitation gap

Phase diagram

J/U

µ/U

insulator n=2

insulator n=1

superfluid

Mott insulator J«U

• Localized particles

• No phase coherence

• Excitation gap

ExperimentExternal confinement

‘wedding cake structure’

Exp‘s: Bloch, Esslinger, Greiner,…

Probing the phase transition

Experimental setup

Tunneling

J

Interaction

U

External potential

ε

Lattice depth

Scattering length

Dipole trap

Probe coherence by ToF measurements

Measurement method

µ/U

insulator n=1

superfluid

J/U

superfluid Mott insulator

Latt

ice d

ep

thtime

Probing the phase transition

Mark et al. Phys. Rev. Lett. 107, 175301 (2011)

FWHM

Observable

‘Kink’ in FWHM

Results

212 a0

320 a0

427 a0

J/U

µ/U

Phase transition point

aS=

Measuring the excitation spectrum

MI excitation spectrum

Elementary MI excitations

U 2U U

Measurement method

Amplitude modulation

timeLatt

ice d

ep

th

Experimental sequence

Measuring the excitation spectrum

Results

U 2U

aS=212 a0

Mark et al. Phys. Rev. Lett. 107, 175301 (2011)

U 2U U

320 a0

Resonance splitting near U-peak

427 a0

Density dependence

Beyond the standard BH model

Approximations

Bloch bands

Interaction potential

Invalid for strong interactions

Three particles

3x two-particle interactions

Effective interactions

Johnson et al. New J. Phys. 11, 093022 (2009)

Efimov physics

dimer

Efimov trimer

+1/a

Energy

-1/a

Two particles

Busch et al. Found. of Physics 28, 549 (1998)Schneider et al. Phys. Rev. A 80, 013404 (2009)Büchler et al. Phys. Rev. Lett. 104, 090402 (2010)

+a

Energy

-a

Kraemer et al. Nature 440, 315 (2006)

Beyond the standard BH model

Expectation

U(2) 3U(3)-U(2)

3U(3)-2U(2)

Double occupancyThree-body loss

427 a0 427 a0

Mark et al. Phys. Rev. Lett. 107, 175301 (2011)

3xU

U

3xU(3)

U(2)Density dependence

High density

Intermediate

Low density

427 a0

Measurement

3U(3)-2U(2) U(2)

Theory and Experiment

2UBH

UBH3U(3)-U(2)

3U(3)-2U(2)

U(2)

Mark et al. Phys. Rev. Lett. 107, 175301 (2011)

2UBH

UBH3U(3)-U(2)

3U(3)-2U(2)

U(2)

(see also work by I. Bloch‘s group,S. Will et al., Nature 465, 197 (2010))

Attractive interactions

BH model with negative U

Three-body loss

Γ3

Superfluid J»|U|

Γ3

Mott insulatorJ«|U|

Γ3

Mott insulatorJ«|U|

Metastable

Highly excited state of the system

Preparation of the attractive MI state

Lattice loading

Repulsive Mott insulator

Switch to attractive a

Γ3

Wait / modulate

Switch to repulsive a

Observe overall heating

depth 20 ER

Stability of the attractive MI state

Varying interactions

Mark et al., to appear in PRL (2012)

hold time = 50 ms

blue areas: narrow Feshbach resonances

zero crossing

Stability of the attractive MI state

Varying interactions

Mark et al., to appear in PRL (2012)

hold time = 50 ms

Varying the hold time

-2000 a0

-240 a0

+220 a0

De-excitation spectrum

UBH

3U(3)-2U(2)

U(2)

U*(2)

U(2)

3U(3)-2U(2)

U*(2)Excitation resonances

U(2) 3U(3)-2U(2)

-306 a0

-306 a0

?

Mark et al., to appear in PRL (2012)

Three-body loss resonance

Fast broadening of the resonance

Rate of three-body loss without lattice

Kraemer et al., Nature 440, 315 (2006)

Three-body loss rate

Γ3 Γ3

Three-body loss

Mark et al., to appear in PRL (2012)

Suppressed three-body loss: Quantum Zeno effect

Analogy

Large three-body loss stabilizes!:

Comparison of loss widths

Attractive interactions Repulsive interactions

Comparison of loss widths

Attractive interactions Repulsive interactions

Comparison of loss widths

Attractive interactions Repulsive interactions

Γ3

Comparison of loss widths

Attractive interactions Repulsive interactions

superfluid of dimers? (Theroy: A. Daley et al., PRL 2009)

Ongoing work

Start with one-atom Mott insulator…

Ongoing work

Then apply lattice tilt and create „doublons“…

see Greiner group„quantum magnetism“

Ongoing work: Doublon creation (very preliminary)

in an array of 1D-tubes

so far: 75% doublon creation

Ongoing work

… and then watch dynamics as the lattice depth is lowered…

Thank you!