Collaborations: M. Gajda (Varsovie), L. Santos (Hannover)Former members: A. Chotia, B. Pasquiou

A. de Paz (PhD), A. Sharma (post-doc), B. Laburthe-Tolra, E. Maréchal, L. Vernac,

P. Pedri, O. Gorceix

Quantum magnetism with a dipolar BEC

dipole – dipoleinteractions

AnisotropicLong Range

20

212m dd

ddVdW

m Va V

µ µεπ

= ∝h

comparison of theinteraction strength

0.16ddε =

Dipolar Quantum gases

alcaline 1<<ddε01.0<ddε for 87Rb

chromium

Bm µµ 6=dysprosium 1≈ddε

1>ddεfor the BEC can become unstable

polarmolecules

Bm µµ 10=

1>>ddε

3

220 cos31

4)(

rrV mdd

θµπ

µ −=

r

BJm gJ µµ =

van-der-WaalsInteractions

sam

g24 hπ

=

IsotropicShort range

R

θ

1mµr2mµr

rr

erbium

Tc=few 100 nK

BEC

Quantum magnetism with a dipolar BEC

different spin dynamics induced by dipole-dipole interactions

change of Zeeman states populations in a S=3 BEC

-2-1

01

23

-3

magnetization = Sm

m mPS

S∑

I- demagnetization of the BECat low B field

II- dipolar relaxation in a 3D lattice

III- spin exchange in a 3D lattice

change of the magnetization

constant magnetization

-1

-2

-3

+3

+2

+1

the Cr BEC candepolarize at low B fields

from the ground state from the highest energy Zeeman state

spin changing collisions become possible at low B field after an RF transfer to ms=+3 study of the transfer to the others mS

At low B field the Cr BEC is a S=3 spinor BEC Cr BEC in a 3D optical lattice : coupling between magnetic and band excitations

Bg Bµ

Spin changing collisions

dipole-dipole interactionsinduce a spin-orbit coupling

( ) ( ) 02121 ≠+−+=∆ issfssS mmmmm

0=∆+∆ lS mmrotation induced

dipolarrelaxation

V -VV'

-V' magnetici

cf

c EEE ∆+= SBmagnetic mgE ∆=∆ µ

S=3 spinor gas: the non interacting picture

1/ Bk Tβ =

Single component Bose thermodynamics Multi-component Bose thermodynamics

Bmg SiBJi µµµ +=

03/10 )12(1

cBc TS

T+

→→

3/10 94.0 atcB NTk ωh=

TkBg BBJ >>µ

( )[ ]( )∑ −−++=−=zyx nnn

zzyyxxctotth nnnNNN,,

11exp ωωωβh

( ) ( )[ ]( )∑ −−+++=zyx nnn

izzyyxxith nnnN,,

11exp βµωωωβµβ h

TkBg BBJ ≈µ

-2-1

01

23

-3-3-2-10

21

3average trap frequency

Tc is lowered

at low B field excited states are thermally populatedthanks to dipole-dipole interactions

apply even if S>0if no dipole-dipole interactions

Our results: magnetization versus T

B = 0.9 mG > Bc

Solid line: results of theorywithout interactions andfree magnetization

the kink in magnetizationreveals BEC

Tc1

The BEC is ferromagnetic:only atoms in mS=-3 condense

The good agreement shows thatthe system behaves as ifthere were no interactions(expected for S=1)

thermal gasBEC inm=-3

Tc1 is the critical temperaturefor condensation of the spinor gas(in the mS=-3 component)

0103/1)12(1

ccc TTTS

<<+

∞→B0→B

(i.e. in the absolute ground state of the system)

B > Bc

Pasquiou et al., PRL 2012

Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)

S=3 Spinor physics below Bc: emergence of new quantum phases

-2-1

01

23

-3

As a6 > a4 , it costs no energy at Bc to go from mS=-3 to mS=-2 : the stabilizationin interaction energy compensates for the Zeeman energy excitation

the BEC isferromagnetici.e. polarized in thelowest energy single particle state

Above Bc

046

2 )(27.0 n

maa

Bg cBJ

−=

hπµ

-2-1

01

23

-3

Below Bc

All the atoms in mS= -3interactions only in themolecular potential Stot= 6because ms tot = -6

The repulsive contactinteractions set by a6

If atoms are transferred in mS= -2then they can interact also in the molecularpotential Stot= 4 because ms tot = -4

The repulsive contact interactions are set by a6 and a4

the BEC is nonferromagnetici.e. it is a multicomponent BEC

S=3 Spinor physics below Bc: spontaneous demagnetization of the BEC

BEC in mS=-3

Rapidly lower magnetic field below Bcmeasure spin populations with Stern Gerlach experiment

1 mG

0.5 mG

0.25 mG

« 0 mG »

Experimental procedure:

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

B=Bc

Bi>>Bc

Bf < Bc

Performances: 0.1 mG stabilitywithout magnetic shield, up to 1 Hour stability

Magnetic field control dynamic lock, fluxgate sensorsreduction of 50 Hz noise fluctuationsfeedback on earth magnetic field, "elevators"

BEC inall Zeemancomponents !

Pasquiou et al., PRL 106, 255303 (2011)

+ Nthermal << Ntot

( )20 6 42

J B c

n a ag B

mπ

µ−

≈h

3D BEC 1D Quantum gas

Bc expected 0.26 mG 1.25 mG

1/e fitted 0.3 mG 1.45 mG

Bc depends on density

1.0

0.8

0.6

0.4

0.2

0.0543210

Magnetic field (mG)

BEC BEC in lattice

Fina

l m=-

3 fr

actio

n

2D Optical lattices increase the peak density by about 5

S=3 Spinor physics below Bc: local density effect

Pasquiou et al., PRL 106, 255303 (2011)

S=3 Spinor physics below Bc: thermodynamics change

B > BcB < Bc B < Bc

B >> Bc

Tc1Tc2

for Tc2 < T < Tc1 BEC only in mS = -3

for T < Tc2BEC in all mS !

for B < Bc, magnetization remains constantafter the demagnetization processindependent of T

This reveals the non-ferromagneticnature of the BEC below Bc

B=Bc(Tc2)

3

0

1

−=

cTT

TkBg BBJ >>µ

Pasquiou et al., PRL (2012)

hint for doublephase transition

-1

-2

-3

+3

+2

+1

the Cr BEC candepolarize at low B fields

from the ground state from the highest energy Zeeman state

spin changing collisions become possible at low B field after an RF transfer to ms=+3 study of the transfer to the others mS

At low B field the Cr BEC is a S=3 spinor BEC Cr BEC in a 3D optical lattice : coupling between magnetic and band excitations

Bg Bµ

Spin changing collisions

dipole-dipole interactionsinduce a spin-orbit coupling

( ) ( ) 02121 ≠+−+=∆ issfssS mmmmm

0=∆+∆ lS mmrotation induced

dipolarrelaxation

V -VV'

-V' magnetici

cf

c EEE ∆+= SBmagnetic mgE ∆=∆ µ

Dipolar Relaxation in a 3D lattice

dipolar relaxation is possible if:

( )zzyyxxi

c nnnE ωωω ++=∆ h)(

(and selection rules)

we observe that spinpopulationschange when :

latticec UE <∆

Ec is quantized

-3-2

-10

12

3

23,22,3

3,3)1( +++++

→++

2,2)2(

++→

kinetic energy gain

BgE Bc µ=∆ )1(

BgE Bc µ2)2( =∆

Dipolar relaxation in a 3D lattice - observation of resonances

width of the resonances: tunnel effect +field, lattice fluctuations

tunnel effect minimal in an excited states along Oy

study of the lowest resonance

nx , ny , nz

kHz

Bg BS µ

zyx nnn ,,0,0,03,3 ⊗→⊗++

1 mG = 2.8 kHz

(Larmor frequency)

23,22,3 +++++

2,2

kHzzyx )2(100,55,170 πωωω ===

yBS Bg ωµ h22 =

Initial Final

0,0,03,3 ⊗ 0,2,02,2 ⊗

pair orbital momentum

spin state

energy substructure relatedto onsite contact interactions

kHz

Bg BS µ

Dipolar relaxation in a 3D lattice – study of the first resonance

B (kHz)

Frac

tion

in m

=+3

our limit: lattice fluctuations

6,63;3 =good agreement between theory fortwo atoms per site and experimentboth for the shape and position of the resonance

Final spin states

Initial spin state

Dipolar relaxation in a 3D lattice – effect of onsite contact interactions

4,41154,6

1162;2 −=

6a

6a4a

B (kHz)

Frac

tion

dans

m=+

3

2

1test of the Mott distribution

atomic distribution expectedfor an adiabatic loading of the3D lattice (25 Er)

good agreement between theory fortwo atoms per site and experimentboth for the shape and position of the resonance

Dipolar relaxation in a 3D lattice – effect of onsite contact interactions

for a diabatic loading,sites with 3 atoms

(or more) are expected

"few-body" physicsproduction of intricated 3 body states

probe of the atomicdistribution in the lattice

Production of intricated states with a fast lattice loading

Theory for 3 atoms per site:4 resonances expected(4 different energies in the final state)

B (kHz)

Frac

tion

dans

m=+

3

good agreement between experimentand theory for three atoms per site

A. de Paz et al., (ArXiv december 2012)

0,0,23,2,20,0,03,3,3 ⊗→⊗ ∑spin orbit

-3-2-1

Spin exchange dynamics in a 3D lattice

vary time

B

dipolar relaxation suppressedevolution at constant magnetization

experimental sequence:

spin exchange from -2

first resonance0

10 mG

Preparation in an atomic excited state

-3 -2

-1

σ-π

-3

Ramantransition

-2 -3

laserpower

mS = -2

A σ- polarized laserClose to a J→J transition

(100 mW 427.8 nm)

creation of a quadratic light shift

-3 -2 -1 0 1 2 3

energy

quadratic effect

-3-2

-1

-1

0

1

-2-3 transfer in -2 ~ 80% transfer adiabatic

expected Mott distribution doublons removed = only singlons

Different Spin exchange dynamics in a 3D lattice

dipolar relaxation with

latticec UE >>∆

( )+−−+ +−= 212121ˆˆˆˆ

41ˆˆˆ SSSSSSH zzdd

Contact interaction (intrasite) Dipole-dipole interaction (intersite)

without spin changing term

4,41154,6

1162;2 −−−=−−

0.3

0.2

0.1

0.0

403020100

1.0

0.8

0.6

0.4

20151050

1.0

0.8

0.6

0.4

20151050Time (ms)

P/P

-3-2

Spin exchange dynamics in a 3D lattice: with only singlons

the spin populations change!

comparison with a plaquette model (Pedri, Santos)3*3 sites containing one atom – work in progressquadratic light shift and tunneling taken into accountProof of intersite dipolar coupling

time ms

relative populations

0.4

0.3

0.2

0.1

0.80.60.40.2time (ms)

popu

latio

ns mS=-3 mS=-2 mS=-1 mS=0

Spin exchange dynamics in a 3D lattice with doublons at short time scale

4,41154,6

1162;2 −−−=−−

Sgn0

SS am

g2

4 hπ=

initial spin state

onsite contact interaction:

( ) sggn

hTcontact µ280460

=−

=

spin oscillations with the expected periodstrong damping (rate > 1O J)

contact spin exchange in 3D lattice:Bloch PRL 2005, Sengstock Nature Physics 2012

0.4

0.3

0.2

0.1

0.014121086420

Time (ms)

mS=-3 mS=-2 mS=-1 mS=0

Popu

latio

ns

2 4 6 8 10 12 14

0.1

0.2

0.3

0.4

Time (ms)

Popu

latio

nsresult of ourtoy model:

Spin exchange dynamics in a 3D lattice with doublons at "long" time scale

two sites with two atoms

coordination factor (10)

our experiment allows the study of molecularCr magnets with larger magnetic moments than Cratoms, without the use of a Feshbach resonance

intersite dipolarcoupling

Spin exchange dynamics in a 3D lattice: strong reduction by a magnetic gradient

1.4

1.2

1.0

0.8

0.62015105

time (ms)

P/P

-2-3

0.6

0.4

0.2

0.05004003002001000

Magnetic gradient (Hz/266 nm)

Am

plitu

de

amplitude

if the spin dynamics results fromintersite coupling it should disappearwhen: >∆Bg BS µ dipolar coupling rate

-3-2-1

expected Mott distribution

doublons removed = only singlons

Different Spin exchange dynamics in a 3D lattice

intrasite contact intersite dipolar

intersite dipolar

( )1 2 1 2 1 214z zS S S S S S+ − − +− +

Heisenberg like hamiltonian

quantum magnetism withS=3 bosons and truedipole-dipole interactions

thank you for your attention!