Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov , Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu

Collaborators: Anne Crubellier (Laboratoire Aimé Cotton), J. Huckans, M. Gajda

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

P. Pedri (Theory), O. Gorceix (Group leader)

Magnetization dynamics of a dipolar BEC in a 3DMagnetization dynamics of a dipolar BEC in a 3Doptical latticeoptical lattice

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long range

Chromium (S=3): Van-der-Waals plus dipole-dipole interactions

R

20

212m dd

ddVdW

m V

a V

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

0.16dd Cr:

20

212m dd

ddVdW

m V

a V

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

Stuttgart: d-wave collapse, PRL 101, 080401 (2008)See also Er PRL, 108, 210401 (2012)See also Dy, PRL, 107, 190401 (2012) … and Dy Fermi sea PRL, 108, 215301 (2012) … and heteronuclear molecules…

Anisotropic explosion pattern reveals dipolar coupling.

Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007))

1dd BEC collapses

0.16dd Cr:

R

1dd BEC stable despite attractive part of dipole-dipole interactions

1.2

1.0

0.8

0.6

2015105

Asp

ect

rati

oVilletaneuse, PRL 105, 040404 (2010)

Stuttgart, PRL 95, 150406 (2005)

Collective excitations

Striction

Anisotropic speed of sound

0.15

0.10

0.05

0.00

3000200010000

Frequency difference (Hz)

Fra

ctio

n of

exc

ited

atom

s

Bragg spectroscopyVilletaneusearXiv: 1205.6305 (2012)

Hydrodynamic properties of a BEC with weak dipole-dipole interactions

Interesting but weak effects in a scalar Cr BEC

Saddle shape

Polarized (« scalar ») BEC Hydrodynamics

Collective excitations, sound, superfluidity

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long-ranged

R

Hydrodynamics:non-local mean-field

Magnetism:Atoms are magnets

Chromium (S=3): involve dipole-dipole interactions

Multicomponent (« spinor ») BEC Magnetism

Phases, spin textures…

Focus on : Magnetization dynamics in a 3D optical lattice :

- 3 regimes :

- B is of the order of the lattice band excitations. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.

- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.

-B is very low : spontaneous depolarization.

Observation of spin changing collisions resonances and band excitations:

- BEC atom number N=10^4 atoms. - Loaded adiabatically in a 3 D anisotropic optical lattice.

k1

k3

OX

k2

Lattice in horizontal plane

Typical frequencies:

x = 2kHz y = 2kHz

z = 2kHz

BEC In m=-3

Rf sweep

20 ms T

V0 ≈ 25 ErTime sequence :

m=+3

+B amplitude and direction is setStern Gerlach analysis

2

1

Mott distributionWith our parameters

2

3,22,3 3,3

)1(

2,2)2(

-3

-2-1

01

2

3

Two dipolar relaxation channels for two atoms in m=+3, sharing a same lattice site

Here, z is fixed by the B field orientation.

8000

6000

4000

2000

6040200

time

Ato

ms

rem

ain

ing

in m

=-

3

If B is higher than the lattice depth (25 Er), dipolar relaxation leads to losses. This case allows to measure the number of site with single occupancy.

B is higher than the trap depth

B is lower than the trap depth

Mott distribution

2

1

Simple measure of site with two atoms or more

If B is lower than the lattice depth : magnetization dynamics with no loss.

Dynamics very sensitive to the magnetic field orientation and value.

Bg BSL

Observation of resonances due to dipolar relaxation (fixed time T=12 ms)

Anisotropic lattice sites

Bg BSL

-Two particles in a harmonic anisotropic potential with frequencies x, y andz.- Consider the relative orbital motion-Initial relative orbital motion |nX=0, nY=0, nZ=0>-Coupling to final relative orbital motion of the atomic pair |nx,ny,nz>

Initial

Final0,0,03,3

0,2,02,2

For channel 2 :

B along OX

Predication of the resonances position:

22 )( izyV

2,23,3 L2

Width of the resonances enlarged by the tunneling

Lower energy resonance around 50 kHz :- Tunneling very small (100 Hz)- Focus on this lowest energy resonance.

Red curve :

Lowest energy resonance at L=Y

Typical frequencies:

x = 2kHz y = 2kHz

z = 2kHz

With (nY+nZ) even

Lower energy resonance. Probe of the atom number distribution.

Black curve : two atoms / site. Contact interaction : shift and splitting of the resonance.

Shift due to contact interactions

Molecular Basis :

1.2

1.0

0.8

0.6

0.4

0.2

0.0

4442403836

0.6

0.4

0.2

0.0

2 atoms per site 3 atoms per site

Note: Lineshape of dipolar resonances probes number of atoms per site

3 and more atoms per sites loaded in lattice for faster loading

B(kHz)

Frac

tion

in m

=+

3

1.2

1.0

0.8

0.6

0.4

0.2

0.0

4442403836

0.6

0.4

0.2

0.0

2 atoms per site 3 atoms per site

Few-body physics !The 3-atom state which is reached has entangled

spin and orbital degrees of freedom

Probe of atom squeezing in Mott state

0,0,23,3,20,0,03,3,3 spin orbit

Focus on : Magnetization dynamics in a 3D optical lattice :

- 3 regimes :

- B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.

- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.

-B is very low : spontaneous depolarization.

From now on : stay away from dipolar magnetization dynamics resonances,Spin dynamics at constant magnetization (<15mG)

New tool : Control the initial state by a tensor light-shift

A polarized laserClose to a JJ transition

(100 mW 427.8 nm)

In practice, a component couples mS statesMagnetic field (kHz)

1501209060300

-1

0

1

-2

-3

-3 -2 -1 0 1 2 3E

nerg

y

mS2

Quadratic light shift effect allows state preparation

3Sm

Adiabatic state preparation in 3D lattice

tquadratic effect

-2 -3

12, 2 3, 1 1, 3

2

2, 2

6 56, 4 4, 4

11 11

S S

tot tot

m m

S m S m

2

6 4

4cB B n a a

m

Initiate spin dynamics by removing quadratic effect

(2 atomes / site)

2

6 4

4cB B n a a

m

0.9

0.8

0.7

0.6

0.5

0.50.40.30.20.10.0

-2.0

-1.5

temps (ms)

magnétization

Fra

ctio

n da

ns m

=-2

On-site spin oscillations

-3-2-1

( 250 µs)

vary timeLoad

optical

lattic

e

quadratic effect

(due to contact oscillations)

(period 220 µs)

Up to now unknown source of damping

Time (ms)

popu

lati

ons

0.6

0.5

0.4

0.3

0.2

20151050

m=-3 m=-2

Long time-scale spin dynamics in lattice

vary timeLoad

optical

lattic

e

quadratic effect

Sign for intersite dipolar interaction ?

(two orders of magnitude slower than on-site

dynamics)

21212

1SSSS

1.4

1.2

1.0

0.8

0.6

0.4

20151050

pop(

m=

-3)/

pop(

m=

-2)

time (ms)

Coherent spin oscillations at lower lattice depth

The very long time scale excludes on-site oscillations

where spin-exchange collisions dominate

0.9

0.8

0.7

0.6

0.5

0.50.40.30.20.10.0

-2.0

-1.5

temps (ms)

magnétization

Fra

ctio

n da

ns m

=-2

2.0

1.5

1.0

0.5

0.0

Osc

illa

tion

am

plit

ude

16141210864201D lattice depth (Er)

1.5

1.0

0.5

0.0

Width

ofdiffractio

npea

k

Probing spin oscillations from superfluid to Mott

Intersite coherent spin oscillation seems to need phase coherence

between sites

Superfluid more robustProbes magnetism from superfluid to

insulator

(Probes coherence length)

(probes coherent spin oscillations)

Focus on : Magnetization dynamics in a 3D optical lattice :

- 3 regimes :

- B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions.Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution.

- B is below the first excitation band : Observation of intersite dynamics, with constant magnetization.

-B is very low : spontaneous depolarization.

-3.0

-2.5

-2.0

-1.5

15105Magnetic field (kHz)

Mag

neti

zati

on

At extremely low magnetic field (<1.5 mG):Spontaneous demagnetization of atoms in a 3D lattice

20 6 44

J B cg B

n a a

m

3D lattice

Critical field

4kHz

Threshold seen

5kHz

6, 6S m 4, 4S m

-3-2

4" "6" "

PRL 106, 255303 (2011) ( in bulk BEC)

Summary - Magnetism in lattice1.2

1.0

0.8

0.6

0.4

0.2

0.0

4442403836

0.6

0.4

0.2

0.0

2 atoms per site 3 atoms per site

Away from resonances: spin oscillationsSpin-exchange : intrasite and inter site dynamics

Not robust in Mott regime

1.4

1.2

1.0

0.8

0.6

0.4

20151050

pop(

m=

-3)/

pop(

m=

-2)

time (ms)

Resonant magnetization dynamicsFew body vs many body physics

Spontaneous depolarization at low magnetic fieldTowards low-field phase diagram

-3.0

-2.5

-2.0

-1.5

15105Magnetic field (kHz)

Mag

neti

zati

on

A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac,

P. Pedri, M. Efremov, O. Gorceix

Thanks for your attention!.

A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac,

P. Pedri, M. Efremov, O. Gorceix