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Firenze, May 21 st 2012: New quantum states of matter in and out of equilibrium. 1700 m. Atoms with tunable interactions in optical lattice confinement. Hanns-Christoph Nägerl Institut für Experimentalphysik , Universität Innsbruck. CsIII -Project Team Members & Collaborators….

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slide1

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

1700 m

Atoms with tunable interactions in optical lattice confinement

Hanns-Christoph Nägerl

InstitutfürExperimentalphysik, Universität Innsbruck

slide2

CsIII-Project Team Members & Collaborators…

new phd and master students:

B. Rutschmann

Florian

Meinert

Philipp

Meinmann

Nobie

Redmon

Michael Gröbner

Elmar

Haller

(nowto

Glasgow)

Johann Danzl

(nowto

Göttingen)

theory support (Strasbourg/Innsbruck/Pittsburgh):

Guido Pupillo / Marcello Dalmonte / Andrew Daley

Manfred

Mark

collaborators:

P. Schmelcher (Hamburg)

V. Melezhik (Dubna)

H. Ritsch (Innsbruck)

N. Bouloufa (Orsay)

O. Dulieu (Orsay)

T. Bergeman (Stony Brook)

H.-P. Büchler (Stuttgart)

J. Aldegunde (Durham)

J. Hutson (Durham)

P. S. Julienne (NIST)

Katharina

Lauber

CsIII-Team

slide3

Motivation: Bosons in lattices and confined dimensions

Bose-Hubbard Physics

  • U<0 and U=U(n)

n = particlenumberatthelatticesites

slide4

E

twoatoms

molecule

B

Feshbach resonance

  • Tuning of interactions: Feshbach resonances

scatteringlengthaS= aS(B)

aS

abg

¢ = coupling

B0

B

slide5

this talk…

(let’s zoom in)

  • Tuning of interactions: Feshbach resonances

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

broad s-resonances

10

calculations by P. Julienne

et al., NIST

s

s

5

scattering length aS (1000 a0)

0

-5

-10

magnetic field B (Gauss)

slide6

g

d

g

g

d

g

d

…or here

zero

crossing

make BEC here

make mol’s here…

  • Tuning of interactions: Feshbach resonances

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

narrower d-resonances

verynarrow g-resonances

g

2

tune here

1

0

scattering length aS (1000 a0)

-1

-2

0

50

150

100

magnetic field B (Gauss)

calculations by P.Julienne et al., NIST

slide7

Tuning of interactions: three-body loss

K3 = three-bodyloss rate coefficient

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

½3 / K31/4

recombinationlength½3(1000 a0)

Efimovresonance

scatteringlengthaS(1000 a0)

K3 /a4

slide8

Bloch bands

Higher Bloch bands omitted

Tunneling

J

Interaction

U

External potential

ε

Interaction potential

Simple non-regularized pseudopotential

Tunneling matrix element

Interactions

U’

No nearest neighbor interaction

On-site interaction energy

Tunneling

J’

External energy shift

No next nearest neighbor tunneling

Basic concepts of lattice physics

Approximations

The standard Bose-Hubbard model

slide9

Phase diagram

Superfluid

J»U

µ/U

  • Delocalized particles
  • Coherent phase
  • No excitation gap

insulator n=2

superfluid

insulator n=1

J/U

Experiment

Mott insulator

J«U

External confinement

‘wedding cake structure’

  • Localized particles
  • No phase coherence
  • Excitation gap

Properties of the Bose-Hubbard (BH) model

Groundstates at T=0

Exp‘s: Bloch, Esslinger, Greiner,…

slide10

Experimental setup

Measurement method

Probe coherence by ToFmeasurements

superfluid

µ/U

insulator n=1

J/U

Lattice depth

Tunneling

J

Lattice depth

time

Interaction

U

Scattering length

External potential

ε

Dipole trap

superfluid

Mott insulator

Probing the phase transition

slide11

Observable

Results

‘Kink’ in FWHM

212 a0

320 a0

427 a0

Phase transition point

FWHM

µ/U

J/U

Probing the phase transition

aS=

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

slide12

Measurement method

Amplitude modulation

Experimental sequence

Lattice depth

time

U

2U

U

Measuring the excitation spectrum

MI excitation spectrum

Elementary MI excitations

slide13

Resonance splitting near U-peak

U

2U

320 a0

U

2U

U

427 a0

Density dependence

Measuring the excitation spectrum

Results

aS=212 a0

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

slide14

Three particles

3x two-particle interactions

Effective interactions

Two particles

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

Efimov physics

Energy

Energy

+1/a

-1/a

dimer

+a

-a

Busch et al.Found. ofPhysics 28, 549 (1998)

Schneider et al. Phys. Rev. A 80, 013404 (2009)

Büchler et al. Phys. Rev. Lett. 104, 090402 (2010)

Efimov trimer

Beyond the standard BH model

Approximations

Bloch bands

Interaction potential

Invalid for strong interactions

Kraemer et al. Nature 440, 315 (2006)

slide15

Measurement

High density

Intermediate

Low density

Density dependence

U(2)

3U(3)-2U(2)

U(2)

3xU(3)

427 a0

Three-body loss

Double occupancy

3U(3)-U(2)

3U(3)-2U(2)

U(2)

427 a0

427 a0

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

Beyond the standard BH model

Expectation

U

3xU

slide16

UBH

3U(3)-U(2)

2UBH

U(2)

3U(3)-2U(2)

Theory and Experiment

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

UBH

3U(3)-U(2)

2UBH

U(2)

3U(3)-2U(2)

(see also workby I. Bloch‘sgroup,

S. Will et al., Nature 465, 197 (2010))

slide17

J«|U|

Mott insulator

Γ3

Mott insulator

J«|U|

Superfluid

J»|U|

Metastable

Highly excited state of the system

Γ3

Attractive interactions

BH model with negative U

Three-body loss

Γ3

slide18

Lattice loading

Repulsive Mott insulator

Switch to attractive a

Wait / modulate

Γ3

Switch to repulsive a

Observe overall heating

Preparation of the attractive MI state

depth 20 ER

slide19

Stability of the attractive MI state

Varying interactions

hold time = 50 ms

blueareas: narrowFeshbachresonances

zerocrossing

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

slide20

Varying the hold time

-2000 a0

-240 a0

+220 a0

Stability of the attractive MI state

Varying interactions

hold time = 50 ms

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

slide21

U(2)

3U(3)-2U(2)

UBH

U*(2)

U(2)

3U(3)-2U(2)

U*(2)

?

De-excitation spectrum

Excitation resonances

U(2)

3U(3)-2U(2)

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

-306 a0

-306 a0

slide22

Three-body loss resonance

Fast broadening of the resonance

Three-body loss rate

Three-body loss

Γ3

Γ3

Rate of three-body loss without lattice

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

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

slide23

Suppressed three-body loss: Quantum Zeno effect

Analogy

Large three-body loss stabilizes!

:

slide24

Comparison of loss widths

Attractive interactions

Repulsive interactions

slide25

Comparison of loss widths

Attractive interactions

Repulsive interactions

slide26

Comparison of loss widths

Attractive interactions

Repulsive interactions

Γ3

slide27

Comparison of loss widths

Attractive interactions

Repulsive interactions

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

slide28

Ongoing work

Start withone-atom Mott insulator…

slide29

Ongoing work

Thenapplylatticetiltandcreate „doublons“…

see Greiner group

„quantummagnetism“

slide30

Ongoing work: Doublon creation (very preliminary)

in an arrayof 1D-tubes

so far: 75%

doubloncreation

slide31

Ongoing work

… andthenwatchdynamicsasthelatticedepthislowered…