Collaboration: L. Santos (Hannover) Former post doctorates : A. Sharma, A. Chotia Former Students: Antoine Reigue A. de Paz (PhD), B. Naylor (PhD), J

Collaboration: L. Santos (Hannover)

Former post doctorates : A. Sharma, A. Chotia

Former Students: Antoine Reigue

A. de Paz (PhD), B. Naylor (PhD), J. Huckans (visitor), O. Gorceix , E. Maréchal, L. Vernac , P. Pedri, B. Laburthe-Tolra

Spin Exchange with ultra cold chromium atomsSpin Exchange with ultra cold chromium atoms

Outline

Magnetism due to dipolar spin exchange with ultracold bosons

Production of a chromium Fermi sea

Dipolar physics with chromium atoms


dipole-dipole interactions permanent magnetic dipole moment= 6 µB

S=3

anisotrope

52Cr

long range

New Physics compared to "usual" BECs

Stuttgart group

Villetaneuse groupCr

Stuttgart group

Stanford group

DyInnsbruck group

Er

Van der Walls interactions



S=3

0.15

0.10

0.05

0.00

3000200010000

Frequency difference (Hz)

Fra

ctio

n of

exc

ited

atom

s

iBk ,//

iBk , anisotropic

excitation spectra

52Cr

1 mG

0.5 mG

0.25 mG

« 0 mG »

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

allow spin changing collisions

magnetizationbecomes free

spontaneous depolarization ofa Cr BEC at low B field

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

G. Bismut et al, Phys. Rev. Lett. 109, 155302 (2012 )



S=3 52Cr

allow spin exchange processesat a distance

-1

0

+1

Phys. Rev. Lett. 92, 140403 (2004)

spin 1spin 1/2

observed with contact (van der Walls) interactions

Dipolar Spin Exchange: a tool for Quantum Magnetism

termschangingspinSSSSSSr

H zzdd

2121213

2ˆˆˆˆ

4

1ˆˆcos1ˆ

Ising term Exchange term

DDIs provide a Heisenberg-like Hamiltonian with direct spin-spin interactions:

Spin Exchange can be obtained through Van der Walls interactions…

… for atoms closeby (contact interactions)

Specific study of dipolar Spin Exchangein separated geometries

3D lattices with one atom per site

double well trap

Quantum Magnetism with cold atoms

tunneling assisted super exchange

t t

2t

U

U

Heisenberg Hamiltonian

Magnetism ie quantum phases not set by ddi but by exchange interactions

What is (are) the (quantum) phase(s) of a given crystal at "low" T ?

anti ferromagnetic ferromagnetic

Quantum Magnetism: what is it about?

Quantum Magnetism with a dipolar species in a 3D lattice

long range = beyond the next neighbor

direct spin-spin interaction

real spin

magnetic dipole moment

S=3

quantum regime, high filling factor

Vdd = 10-20 Hz T < 1 nK

Spin dynamics in an out of equilibrium system

Vdd

to reach ground state

2121213

2

ˆˆˆˆ4

1ˆˆcos1ˆ SSSSSSr

H zzdd

similar work in Jun Ye groupbut there are many differences

Heisenberg like Hamiltonian

Cr BEC loaded in a 3D lattice:a Mott state

spin preparation in the excited Zeeman state ms=-2

-2

01

23

-3

-1

Quantum Magnetism with a chromium BEC in a 3D lattice

-2

01

23

-3

-1 constant magnetization

magnetization = Sm

m mPS

S

spin exchange?

S=3

measurement of the evolutionof the Zeeman states populations

expected Mott distribution

Different Spin exchange dynamics in a 3D lattice

Contact interaction (intrasite)

4,411

54,6

11

62;2

-2

-1

-3

expected Mott distribution doublons removed = only singlons

Different Spin exchange dynamics in a 3D lattice

dipolar relaxation with

latticec UE

2121213

2ˆˆˆˆ

4

1ˆˆcos1ˆ SSSSSSr

H zzdd

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

no spin changing term

4,411

54,6

11

62;2

-2

-1

-3

-2 -2-1

-3

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

the spin populations change!

1.0

0.8

0.6

0.4

0.2

0.0

302520151050

time (ms)

P-3/P-2

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

3*3 sites , 8 sites containing one atom + 1 holequadratic light shift and tunneling taken into account

Proof of intersite dipolar couplingMany Body system

E(ms) = q mS2

measured withinterferometry

comparison with a plaquette model (Pedri, Santos)

A. de paz et alPhys. Rev. Lett. 111, 185305 ( 2013)

Spin exchange dynamics in a 3D lattice: perspective

A giant Entanglement?3,1

2

11,3

2

12;2

How to prove it? Entanglement witness

entangled

separable

EW = condition fulfilled by all full separable satesIf EW violated, then state is entangled

example: jNJJJ zyx 222N

jJ

Vitagliano, Hyllus, Egusquiza, and Toth PRL 107, 240502 (2011)Collaboration withPerola Milman andThomas Coudreaugroup from Paris 7

separable

two atoms: yes !

NoYes

Problem: find one relevant for your system

2121ˆˆˆˆ SSSS

Dipolar Spin exchange dynamics with a new playground: a double well trap

-3 +3

NR

j3

0

4

N atoms N atoms

R

idea: direct observation of spin exchange with giant spins, "two body physics"

compensating the increase in R by the number of atoms realization: load a Cr BEC in a double well trap + selective spin flip

frequency of the exchange:precession of one spin in the B fieldcreated by N spins at R

R = 4 µm j = 3

B field created by one atom

N = 5000

102 Hz

Dipolar Spin exchange dynamics in a double well trap: realization

realizing a double well spin preparation

N atoms in -3

RF spin flip in a non homogeneous B field

non polarizing lateraldisplacement beam splitter N atoms in +3

Spin exchange dynamics in a double well trap: results

No spin exchange dynamics!Hz1024 3

0

N

R

j

-3 +3

Spin analysis by Stern Gerlach:as long as no ms=0 are detected, negative ms belong to one well, positive ms to the other

Inhibition of Spin exchange dynamics in a double well trap: interpretation

What happens for quantum magnets in presenceof an external B field when S increases?

2121213

2ˆˆˆˆ

4

1ˆˆcos1ˆ SSSSSSr

H zzdd

Ising term Exchange term

2S+1 intermediate states

1 2 3 4 5

1 0

1 0 0

1 0 0 0

1 0 4

"half period" of the exchangegrows exponentially

Ising contributiongives differentdiagonal terms

S

half period (au) fast

slow

-2 -2 -3 -1

-3 -3+3 +3

Inhibition of Spin exchange dynamics in a double well trap: interpretation

extB

Evolution of two coupled magnetic moments

dipolarext BBB 2,1if

no more exchange possible

It is as if we had two giant spins interactingTransition from quantum to classical magnetism1B

jR30

2

4

2

in presence of an external B field

A. de paz et al, arXiv:1407.8130 (2014) accepted at Phys Rev A

Dipolar Spin exchange

observed in 3D latticefrozen for double well

Production of a degenerate quantum gas of fermionic chromium

the Fermi sea family: 6Li 3He* 173Yb 161Dy87Sr 167Er 53Cr

dipolar

cooling strategies:- sympathetic cooling- cooling of a spin mixture- "dipolar" evaporative cooling

40K

non applicable for us


Loading a one beam Optical Trap with ultra cold chromium atoms

direct accumulation of atoms from the MOTin metastable states RF sweep to cancel the magnetic force of the MOT coils

for 53Cr : finding repumping lines

crossed dipole trap


Strategy to start sympathetic cooling

make a fermionic MOT, load the IR trap with 53Cr

make a bosonic MOT, load the IR trap with 52Cr

more than 105 53Cr

about 106 52Cr

inelastic interspecies collisions limits to 3.104 53Cr + 6.105 52Cr

not great, we tried anyway…

sympathetic cooling


Evaporation


Why such a good surprise?

BBBBBB NNfVn

dt

dN )(

FFBFBF NNfVn

dt

dN )(

)()()(

ln

)()()(

ln

212

1

212

1

tttNtN

tttNtN

B

B

F

F

BB

BF

evaporation one body losses


Results

Nat

In situ images

parametric excitation of the trap

trapfrequencies

Expansion analysis

1000370)6( 3/1 atatB

mF NifnKN

kT

500300 atNifnK

nKT 20220

slightly degenerated


What can we study with our gas?

Fermionic magnetism very different from bosonic magnetism !

0 1 2 3 4 5

0 .20 .40 .60 .81 .0

T=200 nK

T=50 nK

T=10 nK

Larmorfrequency(kHz)

Populationin mF=-9/2

Fermi T=0

Boltzmann

minimize Etot

-2-1

01

2

3

-3

Picture at T= 0 and no interactions

-7/2

-5/2

-3/2-1/2

1/2

3/2

-9/2

5/27/2

9/2

3/4

FF mmmFermi NE

FmLmFZ mNEF

FL EL

thank you for your attention!

dipole – dipoleinteractions

Anisotropic Long Range

20

212m dd

ddVdW

m V

a V

comparison of theinteraction strength

0.16dd

Dipolar Quantum gases

alcaline 1dd01.0dd for 87Rb

chromium

Bm 6dysprosium 1dd

1ddfor the BEC can become unstable

polarmolecules

Bm 10

1dd

3

220 cos31

4)(

rrV mdd

BJm gJ

van-der-WaalsInteractions

sam

g24

IsotropicShort range

R

1m 2m

r

erbium

Tc= few 100 nK

BEC

-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 B

Spin changing collisions

dipole-dipole interactions induce a spin-orbit coupling

02121 issfssS mmmmm

0 lS mmrotation induced

dipolarrelaxation

V -VV'

-V' magnetici

cf

c EEE SBmagnetic mgE

-1

-2

-3

from the ground state

spin changing collisions can depolarize the BEC at low B field

At low B field the Cr BEC is a S=3 spinor BEC

Bg B

Spin changing collisions

02121 issfssS mmmmmV -VV'

-V' magnetici

cf

c EEE SBmagnetic mgE

1 mG

0.5 mG

0.25 mG

« 0 mG »

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

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

046

2 )(27.0 n

m

aaBg cBJ

Dipolar relaxation in a 3D lattice - observation of resonances

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

nx , ny , nz

kHz

Bg BS

zyx nnn ,,0,0,03,3

1 mG = 2.8 kHz

(Larmor frequency)

2

3,22,3

2,2

kHzzyx )2(100,55,170

zzyyxxB nnnBg 21

-3-2-1

Spin exchange dynamics in a 3D lattice

vary timeLoad

optical

lattic

e

state preparation in -2

B

dipolar relaxation suppressedevolution at constant magnetization

experimental sequence:

spin exchange from -2

first resonanceof the 3D lattice

0

10 mG

Stern Gerlach analysis

Preparation in an atomic excited state

-3 -2

-1

-

-3

Ramantransition

-2 -3

laserpower

mS = -2

A - polarized laserClose to a JJ transition

(100 mW 427.8 nm)

creation of a quadratic light shift

-3 -2 -1 0 1 2 3

energy

quadratic effect(laser power)

-3-2

-1

-1

0

1

-2-3

transfer in -2 ~ 80% transfer adiabatic

Dipolar Relaxation in a 3D lattice

dipolar relaxation is possible if:

zzyyxxi

c nnnE )(

+ selection rules

latticec UE

Ec is quantized

-3-2

-10

12

3

2

3,22,3 3,3

)1(

2,2)2(

kinetic energy gain

BgE Bc )1(

BgE Bc 2)2(

latticec UE If the atoms in doubly occupied sites are expelled

0.4

0.3

0.2

0.1

0.80.60.40.2

time (ms)

popu

lati

ons

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

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

4,411

54,6

11

62;2

Sgn0

SS am

g2

4

initial spin state

onsite contact interaction:

sggn

hTcontact 300

460

spin oscillations with the expected periodstrong damping

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

result of atwo site model:

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

two sites with two atomsdipolar rate raised(quadratic sum of all couplings)

our experiment allows the study of molecularCr2 magnets with larger magnetic moments than Cratoms, without the use of a Feshbach resonance

intersite dipolarcoupling

not fast enough:the system is many body

-3-2-1

expected Mott distribution

doublons removed = only singlons

Different Spin exchange dynamics with a dipolar quantum gas in a 3D lattice

intrasite contact intersite dipolar

intersite dipolar

1 2 1 2 1 2

1

4z zS S S S S S

Heisenberg like hamiltonian

quantum magnetism withS=3 bosons and truedipole-dipole interactions

de Paz et al, Arxiv (2013)

Inhibition of Spin exchange dynamics in a double well trap: interpretation (1)

What happens for classical magnets?

evolution in a constant external B field

B

M

BMdt

Md

cteM z cteMBE z

evolution of two coupled magnetic moments

cteM zyx ,, cteBMBME 2112 ..

1B

jR30

2

4

BjM

2

Contact Spin exchange dynamics from a double well trap after merging

after merging

without merging

Spin exchange dynamics due to contact interactions

Fit of the data with theory gives an estimate of a0 the unknown scattering length of chromium


53Cr MOT :Trapping beams sketch

Lock of Ti:Sa 2 isdone with an ultrastable cavity

-245 -150 0

7 7S P3 4Lock

-12,5

R1 MOTMOT

53

52

F=5/2 F’=7/2

Zs53R2 MOT53

F=7/2 F’=9/2

-450 +305

F=9/2 F’=11/2

MOT53

ZSR1 ZS

52

53

Laser 1

225

Laser 2

+75

2*112,5

320

2*112

-413

F=3/2 F’=5/2

F=9/2

F=7/2

F=5/2

F=9/2

F=7/2

F=5/2

Coo

ling

bea

ms

R1

R2

376 MHz

293 MHz

209 MHz

66 MHz

53 MHz

40 MHz

F=11/2

F=3/2

53Cr MOT :laser frequencies production

So many lasers…

7S3

7P4


Spectroscopy and isotopic shifts

5D J=3 →7P° J=3 for the 52 // 5D J=3 F=9/2 →7P° J=3 F=9/2 for the 53

Shift between the 53 and the 52 line: 1244 +/-10 MHz

Deduced value for the isotopic shift: Center value = 1244 -156.7 + 8 = 1095.3 MHz

Uncertainty: +/-(10+10) MHz (our experiment) +/-8 MHz (HFS of 7P3)

isotopic shift:-mass term-orbital term

isotopicshiftsunknown


Results

Nat

In situ images

parametric excitation of the trap

trapfrequencies

Expansion analysis

220

2 2)( t

m

Tkwtw B

2

2

exp)(w

xxP

2

22 w

x

Temperature

1000370)6( 3/1 atatB

m NifnKNk

500300 atNifnK

nKT 20220

slightly degenerated

0 1 2 3 4

1

2

3

4

5


Degeneracy criteria

3/1)6( atB

m

B

FF N

kk

ET

3/1)(94.0 atB

mBEC N

kT

A quantum gas ?

2)( g

3D harmonic trap

FE

0)( 1

)(

e

dgNat

1

1)( e

FET )0(

FF ETT 25.0)5.0(

Chemical Potential

FF ETT 8.1)(

3

3

6ln)(F

BFT

TTkTT

FTT 1.0e

0 1 2 3 4

0.5

1.0

1.5

2.0

FTT 5.0

0 1 2 3 4

0 .0 5

0 .1 0

0 .1 5

0 .2 0

FTT

TkB

1

Documents

Collaboration: L. Santos (Hannover) Former post doctorates : A. Sharma, A. Chotia Former Students: Antoine Reigue A. de Paz (PhD), B. Naylor (PhD), J