Have left: B. Pasquiou (PhD), G. Bismut (PhD), A. Chotia, 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. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac,

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

Dipolar chromium BECs, and magnetismDipolar chromium BECs, and magnetism

(magnetic) dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long range

Chromium : an artificially large spin (S=3):

R

Bd 6

24( ) ( )SV R a R

m

6

6( )

CV R

R

Van-der-Waals (contact) interactions

Short rangeIsotropic

20

212m dd

ddVdW

m V

a V

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

Anisotropic explosion pattern reveals dipolar

coupling.

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

1dd Spherical BEC collapses

0.16dd Cr:

R

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

Small (but interesting) effects observed – at the % level :- Striction – Stuttgart, PRL 95, 150406 (2005)- Collective excitations - Villetaneuse, PRL 105, 040404 (2010) - Anisotropic speed of sound, Villetaneuse, PRL 109, 155302 (2012)

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… )

1(137~

22

ddV

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…

Interactions couple spin and orbital degrees of freedom

Key idea:

Study magnetism with large spins (S=3, S=6…)

This talk:

0 Introduction to spinor physics

1 Spinor physics of a Bose gas with free magnetization

2 (Quantum) magnetism in opical lattices

Exchange energyCoherent spin oscillation

Chapman, Sengstock…

10,0 1, 1 1,1

2

Quantum effects!KlemptStamper-Kurn

Domains, spin textures, spin waves, topological states

Stamper-Kurn, Chapman, Sengstock, Shin…

Quantum phase transitions

Stamper-Kurn, Lett,Gerbier

Introduction to spinor physics

Main ingredients for spinor physics

Spin-dependent contact interactions

Spin exchange

22 04 (a a

m

0,03

10,2

3

2

0,0

tottot

SS

mSmS

mm

Quadratic Zeeman effect

S=1,2,…

Main new features with Cr

S=3

7 Zeeman states4 scattering lengths

New structures

Purely linear Zeeman effect

Strong spin-dependent contact interactions

And

Dipole-dipole interactions

-101

Dipolar interactions introduce magnetization-changing collisions

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

R

-101

-10

1

-2-3

2

3

without ddV

with ddV

Important to control magnetic field

Rotate the BEC ? Spontaneous creation of vortices ?

Einstein-de-Haas effect

2 BgmE BS

0 lS mm

Angular momentum conservation

Dipolar relaxation, rotation, and magnetic field

-3-2

-10

12

3

3,22,32

13,3

Ueda, PRL 96, 080405 (2006)Santos PRL 96, 190404 (2006)Gajda, PRL 99, 130401 (2007)B. Sun and L. You, PRL 99, 150402 (2007)

-3

-2

-1

0

1

2

3

B=1GParticle leaves the trap

B=10 mGEnergy gain matches band

excitation in a lattice

B=.1 mGEnergy gain equals to

chemical potential in BEC

S=3 Spinor physics with free magnetization

Technical challenges :

Good control of magnetic field needed (down to 100 G) Active feedback with fluxgate sensors

Low atom number – 10 000 atoms in 7 Zeeman states

1 Spinor physics of a Bose gas with free magnetization

2 (Quantum) magnetism in opical lattices

Spin temperature equilibriates with mechanical degrees of freedom

Time of flight Temperature ( K)

Spi

n T

empe

ratu

re (

K)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

1.21.00.80.60.40.2

We measure spin-temperature by fitting the mS population(separated by Stern-Gerlach

technique)

At low magnetic field: spin thermally activated

-10

1

-2-3

2

3

B Bg B k T

-3 -2 -1 0 1 2 3

Related to Demagnetization Cooling expts, Pfau, Nature Physics 2, 765 (2006)

1.0

0.8

0.6

0.4

0.2

0.01.21.00.80.60.40.2

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

1.21.00.80.60.40.20.0

Temperature ( K)

Temperature ( K)

Mag

neti

zati

onC

onde

nsat

e fr

acti

on

Spontaneous magnetization due to BEC

BEC only in mS=-3(lowest energy state)

Cloud spontaneously polarizes !

900B G

Thermal population in

Zeeman excited states

A non-interacting BEC is ferromagneticNew magnetism, differs from solid-state

PRL 108, 045307 (2012)

T>Tc T<Tc

a bi-modal spin distribution

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

Below a critical magnetic field: the BEC ceases to be ferromagnetic !

Temperature ( K)

Mag

netiz

atio

n

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

1.20.80.40.0

1.0

0.8

0.6

0.4

0.2

0.0

0.50.40.30.20.1

Temperature ( K)C

onde

nsat

e fr

acti

on-Magnetization remains small even when the condensate fraction approaches 1!! Observation of a depolarized condensate !!

Necessarily an interaction effect

B=100 µG

B=900 µG

PRL 108, 045307 (2012)

Santos PRL 96, 190404 (2006)

-2

-1

-3-3-2-1 0

2 1

3

20 6 42

J B c

n a ag B

m

-2-1

01

23

-3

Large magnetic field : ferromagnetic Low magnetic field : polar/cyclic

Ho PRL. 96, 190405 (2006) -2

-3

4" "6" "

Cr spinor properties at low field

PRL 106, 255303 (2011)

2, 2

6 56, 4 4, 4

11 11

S S

tot tot

m m

S m S m

Good agreement between field below which we see

demagnetization and Bc

Open questions about equilibrium state

Santos and Pfau PRL 96, 190404 (2006)Diener and HoPRL. 96, 190405 (2006)

Phases set by contact interactions, magnetization dynamics set by

dipole-dipole interactions

- Operate near B=0. Investigate absolute many-body ground-state-We do not (cannot ?) reach those new ground state phases -Quench should induce vortices…-Role of thermal excitations ?

!! Depolarized BEC likely in metastable state !!

Demler et al., PRL 97, 180412 (2006)

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

Polar Cyclic

11,0,0,0,0,0,1

2 11,0,0,0,0,1,0

2

Mag

neti

c fi

eld

Magnetic phase diagram

Measure Tc(B) and M(Tc,B) for different

magnetic fields BGet Tc(M)

Quasi-Boltzmann distribution

Bi-modal spin distribution

Phase diagram adapted from J. Phys. Soc. Jpn,   69, 12, 3864 (2000) See also PRA, 59, 1528 (1999)

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

T/T

c

A

B

C

cB BcB B

0 Introduction to spinor physics

1 Spinor physics of a Bose gas with free magnetization

2 (Quantum) magnetism in opical lattices

Load optic

al lat

tice

3

212120 ).)(.(3.

4 R

uSuSSSgV RR

BJdd

Study quantum magnetism with dipolar gases ?

3

212120 ).)(.(3.

4 R

uSuSSSgV RR

BJdd

222

111

212121

2

.24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

Dipole-dipole interactions between real spins

Hubard model at half filling, Heisenberg model of magnetism (effective spin model)

Magnetization changing collisions

21 SS

1 2 1 2 1 2

1

2z zS S S S S S

Magnetization dynamics resonance for a Mott state with two atoms per site (~15 mG)

Magnetic field (kHz)

m=

3 fr

actio

n

0.8

0.7

0.6

0.5

0.4

464442403836

-3-2

-10

12

3

Dipolar resonance when released energy matches band excitation

Mott state locally coupled to excited band

Produce BEC m=-3detect m=-3

Rf sweep 1

Rf sweep 2

m=+3, wait time

Load optic

al lat

tice

14x103

1210

8

64

20018016014012010080Magnetic field (kHz)

6040

Ato

m n

umbe

rDirect manifestation of anisotropic interactions :

Strong anisotropy of dipolar resonances

Anisotropic lattice sites

22

5

3 ( )

2r

x iyV Sd

r

See also PRL 106, 015301 (2011)

At resonance

May produce vortices in each lattice site (Einstein-de-Haas

effect)(problem of tunneling)

1 2 1 2 1 2

1

2z zS S S S S S

1 2 1 2 1 2

1

4z zS S S S S S Magnetization

changing collisionsCan be suppressed in

optical lattices

21 SS

Differs from Heisenberg magnetism:

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

Related research with polar molecules:

1 2 1 2 1 2

1

2z zS S S S S S

A. Micheli et al., Nature Phys. 2, 341 (2006).A.V. Gorshkov et al., PRL, 107, 115301 (2011), See also D. Peter et al., PRL. 109, 025303 (2012)

Other differences from Heisenberg magnetism:

-Bosons…

-Not a spin ½ system: S=3

-Anisotropy

--1/r3 dependence

-Does not rely on Mott physics

- Can have more than one atom per site

Effective St

3 3 6,4,2,0...tS S S

=

6

4

6

4

46 ddV

2212121 31)(

4

1. zSSSSSS zz

Control the initial state by a tensor light-shift

A polarized laserClose to a JJ transition

(100 mW 427.8 nm)-1

0

1

-2

-3

-3 -2 -1 0 1 2 3

mS2

Quadratic effect allows state preparation

Adiabatic state preparation in 3D lattice

tquadratic effect

-2 -3

Initiate spin dynamics by removing quadratic effect

(2 atomes / site)

vary time

Load optic

al lat

tice

quadratic effect

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

Short times : fast oscillations due to spin-dependent contact interactions

-3-2-1

( 250 µs)

(period 220 µs)Up to now unknown source of damping

(sudden melting of Mott insulator ?)

2, 2

6 56, 4 4, 4

11 11

S S

tot tot

m m

S m S m

PRELIMINARY

Long time-scale spin dynamics in lattice : intersite dipolar exchange

Sign for intersite dipolar interaction

(two orders of magnitude slower than on-site

dynamics)

21212

1SSSSMagnetization is constant

0.4

0.3

0.2

0.1

0.0

Pop

ula

tion

s

14121086420

Time (ms)

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

PRELIMINARY

Oscillations arise from interactions between doubled-occupied sites

1.4

1.2

1.0

0.8

0.6

0.4

302520151050

Both doublons and singlons Only singlons Only singlons, shifted

Time (ms)

(m=

-3)/

(m=

-2)

Effect of doublons ?

Very slow spin dynamics for one particle per site:Intersite dipole-dipole coupling

PRELIMINARY

Our current understanding:

Spin oscillations due to inter-site dipolar exchange between doublons

1 2 1 2 1 2

1

4z zS S S S S S

(Very) long time-scale dynamics due to inter-site dipolar exchange between singlons

Exact diagonalization 2 pairs, 2 sitesFaster coupling because larger effecive spin

Timescale = 4 ms

1/e timescale = 25 ms

0.5

0.4

0.3

0.2

0.1

0.0

Fra

ctio

n

86420

Time (ms)

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

Theoretical estimate : 2 atoms, 2 sites : exchange timescale = 50 ms

Bulk Magnetism: spinor physics with free magnetization

New spinor phases at extremely low magnetic fields

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

Conclusions1.4

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

T/T

c

A

B

C

Lattice Magnetism:

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

0.4

0.3

0.2

0.1

0.0

Pop

ula

tion

s

14121086420

Time (ms)

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

Magnetization dynamics is resonant Intersite dipolar spin-exchange

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

P. Pedri, M. Efremov, O. Gorceix

Aurélie De Paz Amodsen

Chotia

Arijit Sharma