Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils (PhD),

J.C. Keller, T. Zanon, R. Barbé, A. Pouderous (PhD), R. Chicireanu (PhD)

Collaborator: Anne Crubellier (Laboratoire Aimé Cotton)

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

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

Dipolar chromium BECsDipolar chromium BECs

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long range

Chromium (S=3): 6 electrons in outer shell have their spin aligned

Van-der-Waals plus dipole-dipole interactions

R

Hydrodynamics Magnetism

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)Also coming up: heteronuclear molecules (e.g. K-Rb)

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

N = 4.106

T=120 μK

How to make a Chromium BECHow to make a Chromium BEC

425 nm

427 nm

650 nm

7S3

5S,D

7P3

7P4

An atom: 52Cr An oven

A small MOT

A dipole trap

A crossed dipole trap

All optical evaporation

A BEC

Oven at 1425 °C

A Zeeman slower

750700650600550500

600

550

500

450

(1) (2)

Z

1 – Hydrodynamic properties of a weakly dipolar BEC

- Collective excitations- Bragg spectroscopy

2 – Magnetic properties of a dipolar BEC

- Thermodynamics- Phase transition to a spinor BEC- Magnetism in a 3D lattice

Interaction-driven expansion of a BEC

A lie:

Imaging BEC after time-of-fligth is a measure of in-situ momentum distribution

Cs BEC with tunable interactions(from Innsbruck))

Self-similar, (interaction-driven) Castin-Dum expansionPhys. Rev. Lett. 77, 5315 (1996)

TF radii after expansion related to interactions

Pfau,PRL 95, 150406 (2005)

Modification of BEC expansion due to dipole-dipole interactions

TF profile

Eberlein, PRL 92, 250401 (2004)

Striction of BEC(non local effect)

3( ) ( ') ( ') 'dd ddr V r r n r d r

(similar results in our group)

Frequency of collective excitations

2

2.

dH

dt

��������������

��������������

Consider small oscillations, then

2 2 21 1 12 2 22 2 22 2 23 3 3

3

3

3

H

with

In the Thomas-Fermi regime, collective excitations frequency independent of number of atoms and

interaction strength:Pure geometrical factor

(solely depends on trapping frequencies)

(Castin-Dum)

1.2

1.0

0.8

0.6

2015105

Asp

ect

rati

oCollective excitations of a dipolar BEC

Repeat the experiment for two directions of the magnetic field

(differential measurement)

Parametric excitations

( )t ms

Phys. Rev. Lett. 105, 040404 (2010)

A small, but qualitative, difference (geometry is not all)

Due to the anisotropy of dipole-dipole interactions, the dipolar mean-field depends on the relative orientation of the

magnetic field and the axis of the trap

dd

Note : dipolar shift very sensitive to trap geometry : a consequence of the anisotropy of dipolar interactions

Bragg spectroscopy

Probe dispersion law

Quasi-particles, phonons

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

( )E k ck c is sound velocityc is also critical velocityLandau criterium for superfluidity

healing length

0( 2 )k k k cE E n g

Bogoliubov spectrum

1k

Moving lattice on BEC

Lattice beams with an angle.Momentum exchange

2 sin( / 2)Lk k

Anisotropic speed of sound

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)

Speed of sound depends on the relative angle between spins and excitation

20( 2 ( (3cos 1))k k k c d kE E n g g

224

( ) (3cos 1)3 k

dV k

k

k

B

A 20% effect, much larger than the (~2%) modification of the mean-field due to DDI

Anisotropic speed of sound

An effect of the momentum-sensitivity of DDI

(See also prediction of anisotropic superfluidity of 2D dipolar gases : Phys. Rev. Lett. 106, 065301 (2011))

c (mm/s) Theo Exp

Parallel 3.6 3.4

Perpendicular 3 2.8

Good agreement between theory and experiment;

Finite size effects at low q

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

1 – Hydrodynamic properties of a weakly dipolar BEC

- Collective excitations- Bragg spectroscopy

2 – Magnetic properties of a dipolar BEC

- Thermodynamics- Phase transition to a spinor BEC- Magnetism in a 3D lattice

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

-3-2

-1

01

2

3

-3 -2 -1 0 1 2 3

ddV

2

dd f BV g B

B=0: Rabi

In a finite magnetic field: Fermi golden rule (losses)

(x1000 compared to alkalis)

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

2

2

2

)1()(

R

llRVeff

f J Bg B

0l

2lcR

Interpartice distance

Ene

rgy

13,2 2,3

2

3,3

2( )in cR

Bmg

llR

BSC

2)1(

From the molecular physics point of view: a delocalized probe

PRA 81, 042716 (2010)

2-body physics

1/3cR n

c vdWR RB = 3 G

B = .3 mG

many-body physicsDistance r (nm)

g’ (

r)2

3

456

0.1

2

3

456

1

4 5 6 7 8 910

2 3 4 5 6 7 8 9100

S=3 Spinor physics with free magnetization

Alkalis :

- S=1 and S=2 only- Constant magnetization(exchange interactions)Linear Zeeman effect irrelevant

New features with Cr:

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

-No hyperfine structure- Free magnetization

Magnetic field matters !

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-Thermodynamics: how magnetization depends on temperature-Spontaneous depolarization of the BEC due to spin-dependent interactions

2 Magnetism in opical lattices-Depolarized ground state at low magnetic field-Spin and magnetization dynamics

S=3 Spinor physics with free magnetization

Alkalis :

- S=1 and S=2 only- Constant magnetization(exchange interactions)Linear Zeeman effect irrelevant

New features with Cr:

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

-No hyperfine structure- Free magnetization

Magnetic field matters !

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

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

onSpontaneous magnetization due to BEC

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

Cloud spontaneously polarizes !

900B G

Thermal population in

Zeeman excited states

Non-interacting multicomponent Bose thermodynamics: a BEC is ferromagnetic

Phys. Rev. Lett. 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

Phys. Rev. Lett. 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

Phys. Rev. Lett. 106, 255303 (2011)

Density dependent threshold

20 6 42

J B c

n a ag B

m

BEC Lattice

Critical field 0.26 mG 1.25 mG

1/e fitted 0.3 mG 1.45 mG

Load into deep 2D optical lattices to boost density.Field for depolarization 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

Phys. Rev. Lett. 106, 255303 (2011)

Note: Possible new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, 065012 (2011)

Dynamics analysis

Meanfield picture : Spin(or) precession

Ueda, PRL 96, 080405 (2006)

21/3 20( )4dd J BV r n S g n

Natural timescale for depolarization:

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Mag

netiz

atio

n

25020015010050

Time (ms)

Bulk BEC In 2D lattice

PRL 106, 255303 (2011)

Produce BEC m=-3

Rapidly lower magnetic field

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

1 Spinor physics of a Bose gas with free magnetization-Thermodynamics: Spontaneous magnetization of the gas due to ferromagnetic nature of BEC-Spontaneous depolarization of the BEC due to spin-dependent interactions

2 Magnetism in 3D opical lattices-Depolarized ground state at low magnetic field-Spin and magnetization dynamics

Loading an optical lattice

2D

3D

Optical lattice = periodic (sinusoidal) potential due to AC Stark Shift of a standing wave

(from I. Bloch)

(in our case (1 , 1 , 2.6)* /2 periodicity)

We load in the Mott regime U=10kHz, J=100 Hz

U

J

In practice, 2 per site in the center (Mott plateau)

-3.0

-2.5

-2.0

-1.5

15105Magnetic field (kHz)

Mag

neti

zati

onSpontaneous 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" "

Control the ground state by a light-induced effective Quadratic Zeeman effect

A polarized laserClose to a JJ transition

(100 mW 427.8 nm)

In practice, a component couples mS states

Typical groundstate at 60 kHz

Magnetic field (kHz)

1501209060300

-1

0

1

-2

-3

-3-2-10

-3 -2 -1 0 1 2 3

Ene

rgy

mS2

Note : The effective Zeeman effect is crucial for good state preparation

-1 0 1-2-3 2 3

Large spin-dependent (contact) interactions

in the BEC have a very large effect on the final

state

Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions)

tquadratic effect

-3

-2

BEC (no lattice)

3D lattice (1 atom per site)

Note: the spin state reached without a 3D lattice is completely different !

-3-2-10

-3

-2-101-3-2-1

Time (ms)

popu

lati

ons

0.6

0.5

0.4

0.3

0.2

20151050

m=-3 m=-2

Magnetization dynamics in lattice

vary timeLoad optic

al lat

tice

quadratic effect

Role of intersite dipolar relaxation ?

Magnetization dynamics resonance for two atoms per site

Magnetic field (kHz)

m=

3 fr

actio

n0.8

0.7

0.6

0.5

0.4

464442403836

-3-2

-10

12

3

Dipolar resonance when released energy matches band excitation

Towards coherent excitation of pairs into higher lattice orbitals ?

(Rabi oscillations)

Mott state locally coupled to excited band

Resonance sensitive to atom number

Measuring population in higher bands (1D)(band mapping procedure):

Population in different bandsdue to dipolar relaxation

m=3

m=2

-3-2

-10

12

3

0.12

0.10

0.08

0.06

0.04

0.02

0.00

16012080400

Magnetic field (kHz)

Frac

tion

of a

tom

s in

v=

1

1 BZ

st 2 BZ

nd2 BZ

nd

(a)x

z

y

y

PRL 106, 015301 (2011)

14x103

1210

8

64

20018016014012010080Magnetic field (kHz)

6040

Ato

m n

umbe

rStrong 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 (EdH effect)(problem of tunneling)

Conclusions (I)

1.2

1.0

0.8

0.6

2015105

Asp

ect

rati

o

0.15

0.10

0.05

0.00

3000200010000

Frequency difference (Hz)

Fra

ctio

n of

exc

ited

atom

s

Dipolar interactions modify collective excitations

Anisotropic speed of sound

Magnetization changing dipolar collisions introduce the spinor physics with free magnetization

0D

40302010

B (mG)

Magnetism in optical lattices magnetization dynamics in optical lattices can be made resonant could be made coherent ? towards Einstein-de-Haas (rotation in lattice sites)

New spinor phases at extremely low magnetic fields

-3 -2 -1 0 1 2 3

(a)

(b)

(c)

(d)

Conclusions

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

Tensor light-shift allow to reach new quantum phases

A. de Paz, A. Chotia, A. Sharma, B. Pasquiou (PhD), G. Bismut (PhD), B. Laburthe, E. Maréchal, L. Vernac,

P. Pedri, M. Efremov, O. Gorceix