E. Maréchal, O. Gorceix , P. Pedri, Q. Beaufils, B. Laburthe, L. Vernac,

B. Pasquiou (PhD), G. Bismut (PhD)

Excitation of a dipolar BEC and Quantum MagnetismExcitation of a dipolar BEC and Quantum Magnetism

We study the effects of Dipole-Dipole Interactions (DDIs) in a 52 Cr BEC

M. EfremovIFRAF post doc

A. de Paz1st year PhD student

Radu Chicireanuformer PhD student

J.C. KellerR. Barbéformer members

A. Crubeliercollaboration (theory)

6 electrons in the outer shells

Specificities of chromium

S=3 in the ground state

permanent magnetic moment 6 µBparamagnetic gas with ratherstrong dipole-dipole interactions(DDIs)

DDIs change the physics of a polarized BEC(all atoms in the same Zeeman substate)

DDIs allow the cold gas magnetization to change

High temperature oven (T=1350°C in our case)

Obtaining a chromium BEC

Preliminary works of J. Mc Clelland (NIST) - Tilman Pfau, J. Mlynek

Trapping Transition at 425 nm

High inelastic loss rates due to light assisted collisions

choice of the materials

needs to double a Ti:Sa laser

low atom number MOT

Experiment at Stuttgart (Tilman Pfau)

High dipolar relaxation rate BEC only possible in an optical trap

Accumulation in metastable states is efficient Red light repumpers required

Our way to BEC: direct loading of an optical trap in metastable states

optimization of the loading with depumping to a new metastable state + use of RF sweep

Physics of a dipolar BEC at Villetaneuse

polarized BECin the ground statemS=-3

polarized BECin the excited statemS=+3

unpolarized ultra cold gas

Study of dipolar relaxationin 3D, 2D, 1D, and 0D

Spin Flip

lowerB field

BEC excitations("quadrupole" mode)

S=3 spinor gas withfree magnetization

BEC excitations (phonons, free particle,…)

multi-component BEC

D wave Fescbach resonance

RF association of molecules

Ground State RF induced degeneracy

Braggspectroscopy

trapmodulation

I- Dipole – dipole interactions in a polarized chromium BEC

how DDIs have been evidenced in ground state BECs

why larger effects are expected with the excitations (phonons, free particles, …)

how do we observe them

II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field

study of S=3 spinor gas with free magnetization

how thermodynamics is modified when the spin degree of freedom is released

observation of a phase transition due to contact interactions:below a critical B field we observe a multi-component BEC

Summary of the talkSummary of the talk

Dipole-dipole interactions (DDIs)

Anisotropic Long Range

20

212m dd

ddVdW

m V

a V

Relative strength of dipole-dipole and Van-der-Waals interactions

0.16dd

Different interactions in a polarized Cr BEC

alkaline 1dd01.0dd for 87Rb

chromium

Bm 6dysprosium 1dd

1ddfor the BEC is unstable

polarmolecules

Bm 10

1dd

ddcext gVm

22

2

GPE :

')'()'()( 3rdrnrrVr dddd

3

220 cos31

4)(

rrV mdd

BJm gJ

R

Van-der-Waals interactions

sc am

g24

Isotropic Short Range

1m 2m

r

B

J. Stuhler, PRL 95, 150406 (2005)

Some effects of DDIs on Cr BECs

Eberlein, PRL 92, 250401 (2004)

Striction of the BEC(non local effect)

dd adds a non localanisotropic mean-field

B

Modification of theBEC expansion

0.16dd

The effects of DDIsare experimentallyevidenced bydifferential measurements,for two orthogonalorientations of the B field

DDIs

TF profile

B

1.2

1.0

0.8

0.6

2015105

Collective excitationsof a dipolar BEC

Bismut et al., PRL 105, 040404 (2010) t (ms)

Aspe

ct ra

tio

DDIs change in the few % range the ground state physics of a polarized BEC

DDIs induce changes smaller than dd !

Some effects of DDIs on Cr BECs

Trap anisotropy

Shift of the quadrupole

mode frequency (%)

Shift of the aspect ratio

(%)

)cos()(

)cos()(

)cos()(

0

0

0

tcRtR

tbRtR

taRtR

zz

yy

xx

A new and larger effect of DDIs: modification of the excitation spectrum of a Cr BEC

Experiment: probe dispersion law

c is the sound velocity

c depends on

In the BEC ground state the effects of DDIs are averaged due to their anisotropic nature

New idea: probe the effects of DDIs on other kind of excitations of the BEC

the dipolar mean field depends on trap geometry

the excitation spectrum is given by the Fourier Transform of the interactions

1cos33

)(~ 220

kmdd kV

Quasi-particles, phonons

measure the modification of c due to DDIs: 15% ?

kB all dipoles contribute

in the same way

kck

k

attractive and repulsive contributions of DDIs almost compensate

k

0.16dd

Excitation spectrum of a BEC with pure contact interactions

Rev. Mod. Phys. 77, 187 (2005)

c is the sound velocity

c is also the critical velocity

is the healing length

0( 2 )k k k cE E n g

Bogoliubov spectrum:

1k

m

kEk 2

22

/12 0 kgnE ck

Quasi-particles, phonons

1k Free particles kk E

kck

A 20% shift due to DDIs expected on the speed of sound !much larger than the (~3%) effects measured on the ground state and the "quadrupole" mode

An effect of the momentum-sensitivity of DDIs:

Excitation spectrum of a BEC in presence of DDIs

kB

1cos312 20 kddckkk gnEE

if , and if ,0k //cc 2/ k cc

0( 2 )k k k cE E n g becomes:

2.11

21///

dd

ddcc

0.16dd

k

1cos33

)(~ 220

kmdd kV

Excitation spectrum of a BEC: the local density approximation (LDA)

* the BEC is trapped, the density is not uniform

* the BEC has a non zero width momentum distribution

validity of LDA:

= the theory giving predictions that you can compare with

2222220 ///1)( TFzTFyTFx RzRyRxnrn

TFzRk /2 zuk

//with

k

LDA not valid at small k

TFzz Rk /1

two sources of broadening: the excitation spectrum of the BEC has a non zero width

and the effect of DDIs is going to be less than naively expected…

LDA = consider the gas locally uniform

Two laser beams detuned:Momentum and energy transfer

Excitation of a BEC: principle of Bragg Spectroscopy

1k

2k

21 kkk

)2/sin(2 Lkk

Lkkk 21

E

k

Bragg beams very far detunedfrom atomic resonances

For a given , tune to find a good excitation,and register the excitation spectrum

)2/sin(2 Lk

532L nm

= 100 Hz to 100 kHz

Bragg Spectroscopy: experimental realization

Two lasers "in phase" are required

We use two AOMs driven by a digital double RFsource providing two RF signals in phase

ttt )()( 21

For given (accessible) values of , we register excitation spectra

1k

2k

6° to 14°, 28°, 83°optical access we measure the excited fractionfor a given

excited and non-excited partsspatially separated by momentum transfer

Bragg Spectroscopy: experimental difficulties

* choice of t = the excitation duration (of the Bragg pulse)

* poor spatial separation of the excited fraction at low k

if t is too small, we add a Fourier broadening

if t is too large, the mechanical effect of the trap comes into play

kRk TFzz /1 to have a good spatial separation after expansion

zk

k/1k becomes hard to reach in our case

(we don't work with an elongated BEC)

nonexcited excited

excitedfraction

t << Ttrap / 4

not quite possible at low k…

t >> 1 / f

non excitedfraction

a) b)

d)c)

Bragg Spectroscopy: experimental difficulties

poor separation ofthe excited fractionat low k !

data analysiscomplicated,noisy data

no excitation = 6°

= 14° = 83°

0.15

0.10

0.05

0.00

3000200010000

Frequency difference (Hz)

Fra

ctio

n of

exc

ited

atom

s

Width of resonance curve: finite size effects (inhomogeneous broadening)The excitation spectra depends on the relative angle between spins and excitation

Bragg Spectroscopy of a dipolar BEC: experimental results

Excitation spectra at =14°

iBk ,//

iBk ,

f //f

From the different spectra,registered for a given ,we deduce the value of:

2///

//

ff

ff

= shift of the excitationspectrum due to DDIs

Bragg Spectroscopy of a dipolar BEC: experimental results

q

0.20

0.15

0.10

0.05

0.00

-0.05

43210

14

8

2

x10-3

4.2

2///

//

ff

ff

11 2 3 4

1

0

0.1

0.2

k

1.2

1.0

0.8

0.6

2015105

Asp

ect

rati

o

Villetaneuse

Collective excitations

Striction

0.16dd

Anisotropicspeed of sound

0.15

0.10

0.05

0.00

3000200010000

Frequency difference (Hz)

Fra

ctio

n of

exc

ited

atom

s

Conclusion: a 52Cr BEC is a "non-standard superfluid"

StuttgartExpansion

I- Dipole – dipole interactions in a polarized chromium BEC

how DDIs have been evidenced in ground state BECs

why larger effects are expected with the excitations

how do we observe them

II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field

Study of S=3 spinor gas with free magnetization

how thermodynamics is modified when the spin degree of freedom is released

observation of a quantum phase transition due to contact interactions: below a critical B field we observe a multi-component BEC

Summary of the talkSummary of the talk

DDIs can change the magnetization of the atomic sample

iyxr /

Elastic collision

Spin exchange

Inelastic collisions

Dipole-dipole interaction potential with spin operators:

Induces several types of collision:-101

222

111

212121

2

24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

-1

-2

-3

Cr+3

+2

+1Cr BEC in -3

magnetizationbecomes free

0 totSm

iSSfSStotS mmmmm 2121

2,1 totSm

change in magnetization:

Optical trap

DDIs can change the magnetization of the atomic sample

iyxr /

0 lStot mm

Inelastic collisions

Dipole-dipole interaction potential with spin operators:

Induces several types of collision:

222

111

212121

2

24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

-1

-2

-3

Cr+3

+2

+1Cr BEC in -3

magnetizationbecomes free

2,1 Stotm

rotation induced

=> Einstein-de-Haas effect

S=3 Spinor physics with free magnetization

- Up to now, spinor physics with S=1 and S=2 only

- Up to now, all spinor physics at constant magnetization exchange interactions (VdW), no DDIs

- The ground state for a given magnetization was investigated-> Linear Zeeman effect irrelevant

-101

New features with Cr

- First S=3 spinor (7 Zeeman states, four scattering lengths, a6 , a4 , a2 , a0)

- Dipole-dipole interactions free total magnetization

- We can investigate the true ground state of the system (need very small magnetic fields)

-10

1

-2-3

2

3

Ultra cold gas of spin 3 52Cr atoms at "ultra" low magnetic fields

ZeemanddVdWext VVVm2

2

The spin degree of freedom is unfrozen when:

7 components spinor

TkBg BBJ

Optical trap, (almost) sametrapping potential for the 7Zeeman states

3B mG at 400 nK

allows the magnetizationto change

Two different B regims for the ground state are predicted:when B > Bc , the Zeeman interactions dominate: one component (ferromagnetic) BECwhen B < Bc , the contact interactions dominate: multi-component (non-ferromagnetic) BEC

-1

-2

-3Bg BJ

Above Bc: is 52Cr close to a non-interacting S=3 gas with free magnetization ?

Why Bc ? What do we observe below Bc ?

S=3 spinor gas: the non interacting picture (I)

1/ Bk T

Single component Bose thermodynamics Multi-component Bose thermodynamics

Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)

Bmg SiBJi 03/10 )12(

1c

Bc T

ST

3/10 94.0 atcB NTk

TkBg BBJ

zyx nnn

zzyyxxctotth nnnNNN,,

11exp

zyx nnn

izzyyxxith nnnN,,

11exp

TkBg BBJ

-2

-1

01

2

3

-3-3-2-1 0

2 1

3

Similar to:M. Fattori et al., Nature Phys. 2, 765 (2006)at large B fields and in the thermal regime

average trap frequency

Tc is lowered

Magnetization

B phaseBEC in mS=-3

A phase(normal)

C phaseBEC in each component

0cT

T

0 -1 -2 -3

0.2

0.4

0.6

0.8

1.0

For Na:a double phasetransition expected

Evolution at fixedmagnetization

Evolution for a freemagnetization

Tc1(M)

Tc2(M)

3/1)12(

1

S

S=3 spinor gas: the non interacting picture (II)

For Cr:One BEC component,in mS= -3the absolute groundstate of the system

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

Our results: magnetization versus T

B = 0.9 mG > Bc

Solid line: results of theorywithout interactions and free 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(

1ccc TTT

S

B0B

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

B > Bc

Pasquiou et al., ArXiv:1110.0786 (2011)

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

measurement of Tc1(M),by varying B

0cT

T

Pasquiou et al., ArXiv:1110.0786 (2011)

Our results (II): measurements of Tc1B > Bc

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

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

histograms: spin populations

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-3.0-2.5-2.0-1.5-1.0-0.50.0

Magnetization

A

B

C

T (M)c1

T (M)c2

BEC in mS= -3

depolarized thermal gas

468

1000

2

468

-3 -2 -1 0 1 2 3

« bi-modal » spin distribution

A new thermometry

Only thermal gas depolarizes Cooling scheme if selective

losses for mS > -3e.g. field gradient

1.5

1.0

0.5

0.0

1.20.80.40.0

Time of flight Temperature ( K)

Spi

n T

empe

ratu

re (

K)

8000

6000

4000

2000

-3 -2 -1 0 1 2 3mS

popu

latio

n Boltzmanian fit

Tspin moreaccurate atlow T !

bimodal distribution

Our results (III): spin populations and thermometry B > Bc

Pasquiou et al., ArXiv:1110.0786 (2011)

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 lowest energy single particle state

Above Bc

046

2 )(27.0 n

m

aaBg cBJ

-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 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

(1,0,0,0,0,0,0)

( )a,0,0,0,0,0, ( , , )a 0,0,0,0 ,0

( , )a 0,,0,g,0,

Bc

a0 (Bohr radius)0-10 -10

Mag

netic

fiel

d

All populated0

Allpopulated

S=3 Spinor physics below Bc: new quantum phases

Santos et Pfau PRL 96, 190404 (2006)Diener et Ho PRL 96, 190405 (2006)

For an S=3 BEC, contact interactions are set by four scattering lengths, a6 , a4 , a2 , a0

Quantum phases are results of an interplay between Zeeman and contact interactions

Quantum phases are set by contact interactions and differ by total magnetization

ferromagnetici.e. polarized in lowest energy single particle state

Critical magnetic field Bc

DDIs ensure the coupling between states with different magnetization

polarphase

046

2 )(27.0 n

m

aaBg cBJ

unknown

nematicphase

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

BEC in mS=-3

Rapidly lower magnetic field below Bc

measure 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 below .5 mG (!!) 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

m

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

Fin

al m

=-3

fra

ctio

n

2D Optical lattices increase the peak density by about 5

S=3 Spinor physics below Bc: local density effect

NoteSpinor Physics in 1 D canbe qualitatively differentsee Shlyapnikov and TsvelikNew Journal of Physics 13 065012 (2011)

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

Bulk BEC

2D optical lattices

In lattices (in our experimental configuration), the volume of the cloud is multiplied by 3

Mean field due to dipole-dipole interaction is reduced

Slower dynamics, even with higher peak densities

Non local character of DDIs

S=3 Spinor physics below Bc: dynamic of the demagnetization

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

Corresponding timescale for demagnetization:

good agreement with experiment both for bulk BEC ( =3 ms)and 1 D quantum gases ( = 10 ms)

At short times, transferbetween mS = -3 and mS = -2

~ a two level system coupled by Vdd

Simple model

But dynamics still unaccounted for:

BgVBBB BJddddc /

ddVt /

Bc

S=3 Spinor physics below Bc: thermodynamics change

B > Bc

B < BcB < Bc

B >> Bc

Tc1Tc2

for Tc2 < T < Tc1

BEC only in mS = -3

for T < Tc2 BEC 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

cT

T

TkBg BBJ

Pasquiou et al., ArXiv:1110.0786 (2011)

hint for doublephase transition

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-3.0-2.5-2.0-1.5-1.0-0.50.0

Magnetization

A

B

C

T (M)c1

T (M)c2

Thermodynamics of a spinor 3 gas: outline of our results

A phase: normal (thermal)

B phase: BEC in one component

C phase: multi-component BEC

evolutionfor B > Bc

evolutionfor B < Bc

In purple: our data

measurement of Tc1(M),by varying B

0cT

T

histograms: spin populations

Pasquiou et al., ArXiv:1110.0786 (2011)

Bc

reached

Conclusion: what does free magnetization bring ?

A quench through a (zero temperaturequantum) phase transition

- We do not (cannot ?) reach the new ground state phase

- Thermal excitations probably dominate but…

- … effects of DDIs on the quantum phases have to be evaluated

The non ferromagnetic phase is setby contact interactions,

but magnetization dynamics is set by dipole-dipole interactions

first steps towards exotic spinor ground state

- Spinor thermodynamics with free magnetization of a ferromagnetic gas - Application to thermometry / cooling

Above Bc

Below Bc

Thank you for your attention

… PhD student welcome in our group…