Elastic and inelastic dipolar effects in chromium BECsElastic and inelastic dipolar effects in chromium BECs

Laboratoire de Physique des LasersUniversité Paris NordVilletaneuse - France

B. Laburthe-Tolra

Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu

Collaborator: Anne Crubellier (Laboratoire Aimé Cotton)

Invited professors: W. de Souza Melo (Brasil), D. Ciampini (Italy), T. Porto (USA)

Internships (since 2008): M. Trebitsch, M. Champion, J. P. Alvarez, M. Pigeard, E. Andrieux, M. Bussonier, F. Hartmann, R. Jeanneret, B. Bourget

G. Bismut (PhD), B. Pasquiou (PhD) B. Laburthe, E. Maréchal, L. Vernac,

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

Types of interactions in BECs

Van-der Waals, short range and isotropic. Pure s-wave collisions at low temperature.Effective potential aS (R), with aS scattering lenght,

tunable thanks to Feshbach resonances

Dipole-dipole interactions (magnetic atoms, Cr, Er, Dy, dipolar molecules, Rydberg atoms)

Quantum phase transitionsFerromagnetic / Polar/ Cyclic phases

Multicomponent BECs: More than one state, more than one scattering length. Exchange interactions decide which spin configuration reaches the lowest energy

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

Long range

Alkalis: Van-der-Waals interactions (effective potential)

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

R

« Elastic »:

Non local anisotropic mean-field

« Inelastic »:

Coupling between spin and rotation

Elastic

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)

Anisotropic explosion pattern reveals dipolar coupling.(Breakdown of self similarity)

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

1dd BEC collapses

Parabolic ansatz still good. Striction of BEC. (Eberlein, PRL 92, 250401 (2004))

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

0.16dd Cr:

R

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, 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

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Consider small oscillations, then 2 2 21 1 12 2 22 2 22 2 23 3 3

3

3

3

H

with

2Smv gn

2 21

2m R gn

SvER

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)

Interpretation

Sound velocity

TF radius

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

A consequence of anisotropy : trap geometry dependence of the frequency shift

•Related to the trap anisotropy

Shift of the quadrupole

mode frequency

(%)

Shift of the aspect ratio

(%)

Eberlein, PRL 92, 250401 (2004)

Good agreement with Thomas-Fermi predictions

Sign of dipolar mean-field depends on trap geometry(oblate / elongated)

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

Non local anisotropic meanfield

-Static and dynamic properties of BECs

Small effects in Cr… Need Feshbach resonances or larger dipoles.

With… ? Cr ? Er ? Dy ? Dipolar molecules ?

Then…, Tc, solitons, vortices, Mott physics, new phases (checkboard), 1D or 2D physics, breakdown of integrability in 1D…

Interest for quantum computation ?

Inelastic

Spin degree of freedom coupled to orbital degree of freedom

- Spinor physics and magnetization dynamics

Dipole-dipole interactions

22 203

11 3cos ( )

4dd J BV S gR

Anisotropic

R

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

Introduction to dipolar relaxation

-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)

Energy scales

Trap depth : 1 MHz

30 mGBand excitation in lattice : 100 kHz

300 mG

Chemical potential : 4 kHz 1 mG

Vortex : 100 Hz .01 mG

Molecular binding enery : 10 MHz Magnetic field = 3 G

0.0001

0.001

0.01

0.1

1

10

100

1000

Mag

netic

fie

ld (

G)

(T. Pfau’s Feshbach resonance – pure dipolar fluid)

Suppression of dipolar relaxation due to inter-atomic repulsion

Spin relaxation and band excitation in optical lattices

Magnetization dynamics of spinor condensates

A journey in dipolar physics through 7 decades of magnetic field intensities

4 Gauss

…spin-flipped atoms gain so much energy they leave the trap

11S BE m g B MHz

-3-2

-10

12

3

Dipolar relaxation in a Cr BEC

Produce BEC m=-3 detect BEC m=-3

Rf sweep 1

Rf sweep 2

BEC m=+3, vary time

Inel

asti

c lo

ss p

aram

eter

10 c

m s

-13

3-1

M ag n e tic fie ld (G )

1

2

3

4

567

1 0

2

3

4

567

1 0 0

0 .0 12 4 6 8

0 .12 4 6 8

12 4 6 8

1 0

See also Shlyapnikov PRL 73, 3247 (1994)Never observed up to now

Born approxim

ation Pfau

, Appl. P

hys. B, 7

7, 765 (2

003)

PRA 81, 042716 (2010)

2

dd fV

f J Bg B

Fermi golden rule

0l

2l

In

Out

Interpretation

Sc aR Zero coupling

Determination of scattering lengths S=6 and S=4

2

2

2

)1()(

R

llRVeff

f J Bg B

cR

Interpartice distance

Ene

rgy

13,2 2,3

2

3,3

2( )in cR

Rc = Condon radius

New estimates of Cr scattering lengths Collaboration Anne Crubellier

PRA 81, 042716 (2010)

Feshbach resonance in d-wave PRA 79, 032706 (2009)

a6 = 103 ± 4 a0.

a6 = 102.5 ± 0.4 a0

A probe of correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model

Dipolar relaxation: a localized phenomenonIn

tera

tom

ic p

oten

tial

s

Interparticle distance

Bmg

llR

BSC

2)1(

Distance 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

2

2 ( ) 1 /g r a r

L. H. Y. Phys. Rev. 106, 1135 (1957)

VdWr R

40 mGauss

…spin-flipped atoms go from one band to another

2

3

1

• Lattices provide very tightly confined geometries

Dipolar relaxation in optical lattices

Energy to nucleate a « mini-vortex » in a lattice site

LvE 2

LBBg (~120 kHz)

A gain of two orders of magnitude on the magnetic field requirements to observe rotation due to spin-flip (Einstein-de Haas effect) !

Optical lattices: periodic potential made by AC-stark

shift of a standing wave

2 BgmE BS 3,22,32

13,3

m=3

m=2

Reduction of dipolar relaxation in optical lattices

Load the BEC in a 1D or 2D Lattice

Produce BEC m=-3 detect m=-3

Rf sweep 1

Rf sweep 2

BEC m=+3, vary time

Load optic

al lat

tice

One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

2

dd fV

0.01

0.1

1

10

7 8 90.01

2 3 4 5 6 7 8 90.1

Magnetic field (G)

Rat

e pa

ram

eter

(10

m

s )

-19

3-1

2D2D

3 D3 D

1 D1 D

PRA 81, 042716 (2010)

Phys. Rev. Lett. 106, 015301 (2011)

1 BZ

st 2 BZ

nd2 BZ

nd

(a)

(b)

x

z

y

z

y

What we measure in 1D (band mapping procedure):

Non equilibrium velocity ditribution

along tubesIntegrability

Population in different bandsdue to dipolar relaxation

m=3

m=2

-3-2

-10

12

3

Heating due to collisional de-excitation from excited band

What we measure in 1D:

(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices

B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)

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

3

2

1

1401006020

Magnetic field (kHz)Te

mpe

ratu

re (

K)

(a) (b)

m=3

m=2

Theoretical model:

Fermi-Golden rule, taking into account:

-The width of the excited band (tunneling)-All excited states along the tubes

Calculated : 2. 10-19 m3 s-1

Measured : 5. 10-20 m3 s-1

Qualitatively ok. Correlations (and more) ignored

z

(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices:

a consequence of angular momentum conservation

0 lS mm

1Sm

2

2( 2)B L

L

g B E E lma

Above threshold :

should produce vortices in each lattice site (EdH effect)(problem of tunneling)

Towards coherent excitation of pairs into higher lattice orbitals ?

Below threshold:

a (spin-excited) metastable 1D quantum gas ;

Interest for spinor physics, spin excitations in 1D…

L

a

.4 mGauss

…spin-flipped atoms loses energy

-2-1

01

23

-3-3-2-1 0

2 1

3

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

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, no dipole-dipole interactions)

- They investigate the ground state for a given magnetization -> Linear Zeeman effect irrelavant

-101

New features with Cr

-First S=3 spinor

- Dipole-dipole interactions free total magnetization

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

-10

1

-2-3

2

3

S=3 Spinor physics with free magnetization

Santos PRL 96, 190404 (2006)Ho PRL. 96, 190405 (2006)

-2-1

01

23

-3-3-2-1 0

2 1

3

7 Zeeman states; all trappedfour scattering lengths, a6, a4, a2, a0

20 6 42

J B c

n a ag B

m

(at Bc, it costs no energy to go from m=-3 to m=-2 : difference in interaction energy compensates for the loss in Zeeman energy)

Phases set by contact interactions (a6, a4, a2, a0) – differ by total magnetization

Mag

neti

c fi

eld

a0/a6

ferromagnetici.e. polarized in lowest energy single particle state

At VERY low magnetic fields, spontaneous depolarization of 3D and 1D quantum gases

Produce BEC m=-3

vary time

Rapidly lower magnetic field

Stern Gerlach experiments

Magnetic field control below .5 mG (dynamic lock)

(.1mG stability) (no magnetic shield…)

Time (ms)

Popu

lati

on

m S

Mean-field effect

20 6 42

J B c

n a ag B

m

BEC Lattice

Critical field 0.26 mG 1.25 mG

1/e fitted 0.4 mG 1.45 mG

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

1.0

0.8

0.6

0.4

0.2

0.0

2 3 4 5 6 7 8 9100

2 3 4 5

Dynamics analysis

Time (ms)

Rem

aini

ng a

tom

s in

m=

-3

Meanfield picture : Spin(or) precession (Majorana flips)When mean field beats magnetic field

Ueda, PRL 96, 080405 (2006)Kudo Phys. Rev. A 82, 053614 (2010)

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

Natural timescale for depolarization: (a few ms)

Magnetic field due to dipoles

-2-1

01

23

-3

A quench through a zero temperature (quantum) phase transition

2 1

3

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

« quantum magnetism »

- Operate near B=0. Investigate absolute many-body ground-state- We do not (cannot ?) reach those new ground state phases !!- Thermal excitations probably dominate

-3-2-1 0

2 1

3

Thermal effect: (Partial) Loss of BEC when demagnetizationSpin degree of freedom is released ; lower Tc

Time (ms)

Popu

lati

on

mS

As gas depolarises, temperature is constant, but condensate fraction goes down !

0.8

0.6

0.4

0.2

0.0

300250200150100500

Time (ms)

Con

dens

ate

frac

tion

Thermal effect: (Partial) Loss of BEC when demagnetizationSpin degree of freedom is released ; lower Tc

PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000)

1/3

1

(2 1)c cT TS

lower Tc: a signature of decoherence

Dipolar interaction open the way to spinor thermodynamics with free magnetization

1.0

0.8

0.6

0.4

0.2

0.0

0.50.40.30.20.1

Temperature

Con

d ens

ate

frac

tion

B=0

B=20 mG

Conclusion

Collective excitations – effect of non-local mean-field

Dipolar relaxation in BEC – new measurement of Cr scattering lengthscorrelations

Dipolar relaxation in reduced dimensions - towards Einstein-de-Haasrotation in lattice sites

Spontaneous demagnetization in a quantum gas - New phase transition– first steps towards spinor ground state

(Spinor thermodynamics with free magnetization – application to thermometry)

(d-wave Feshbach resonance) (BECs in strong rf fields)

(rf-assisted relaxation) (rf association)

(MOT of fermionic 53Cr)