Elastic and inelastic dipolar effects in chromium Elastic and inelastic dipolar effects in chromium Bose-Einstein condensatesBose-Einstein condensates

Laboratoire de Physique des LasersUniversité Paris NordVilletaneuse - France

Former PhD students and post-docs: T. Zanon, R. Chicireanu, A. Pouderous

Former members of the group: J. C. Keller, R. Barbé

B. PasquiouO. Gorceix

P. PedriB. Laburthe

L. Vernac

E. MaréchalG. Bismut

Q. BeaufilsA. Crubellier (LAC)

Dipole-dipole interactions

3

2220 )(cos31

4 RgSV BJdd

-Intersites effects in optical lattices Inguscio (Bloch oscillations)

-Use for quantum computingPolar molecules, de MilleBlockade and entanglement of Rydberg atoms (Browaeys)

-Checkerboard phases (Lewenstein) (Resembles ionic Wigner cristals)

Non local meanfield

Non local correlations

-Strong correlations in 1D and 2D dipolar systems (Astrakharchik)

Chromium : S=3

Long range interactions- 2-body physics (thermalization of polarized fermions)

-Static and dynamic properties of BECs Stuttgart, Villetaneuse

Inelastic dipolar effects

3

2220 )(cos31

4 RgSV BJdd

- Feshbach resonances due to dipole-dipole interactions (Stuttgart, Villetaneuse)

Anisotropic dipole-dipole interactions

Spin degree of freedom coupled to orbital degree of freedom

- Dipolar relaxation (Stuttgart, Villetaneuse)

- Spinor physics; spin dynamics (Stamper-Kurn)

How to make a Chromium BEC in 14s and one slide ?How to make a Chromium BEC in 14s and one slide ?

425 nm

427 nm

650 nm

7S3

5S,D

7P3

7P4

An atom: 52Cr

N = 4.106

T=120 μK

750700650600550500

600

550

500

450

(1) (2)

Z

An oven

A small MOT

A dipole trap

A crossed dipole trap

All optical evaporation

A BEC

(Rb=109 or 10)

(Rb=780 nm)

Oven at 1350 °C(Rb 150 °C)

A Zeeman slower

Similar results in Stuttgart

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)

Parabolic ansatz is still a good ansatz

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

Full symbols : experimentEmpty squares : numerical

30

25

20

15

TF

Ra

dii

12001000800600

Excitation frequency (Hz)

Collective excitations in dipolar BECs (parametric excitation)

1.2

1.0

0.8

0.6

1086420

« Quadrupole » (intermediate)

17

16

15

14

20151050

Excitation BEC mode "quadrupolaire" le plus basExcitation: 465Hz, 130mVpp, 20 cycles (43.01ms)IR: recompression à 220mV, lame à 28°-2°, 47,3WEvaporation jusqu'à 158mVDonnées enregistrées en n°3

RayonTFYV1 RayonTFYH1 fit_RayonTFYV1 fit_RayonTFYH1

« Quadrupole » (lower)

20

19

18

17

16

15

TF

ra

diu

s

43210Time (ms)

« Monopole »

Smaller effect (4%), but (possibly) better spectroscopic accuracy

Ongoing experiment…

When dipolar mean field beats local contact meanfield(i.e. dd>1), implosion of (spherical) condensates

Stuttgart: d-wave collapse

Pfau, PRL 101, 080401 (2008)

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

And…, Tc, solitons, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D…

(Tune contact interactions using Feshbach resonances (i.e. dd>1) Nature. 448, 672 (2007)

>

Other fascinating phenomena when dipolar mean field beats magnetic field

Ueda, PRL 96, 080405 (2006)Similar theoretical results by Santos and Pfau. Some differences and open questions

Meanfield picture : Spin(or) precession (Majorana flips)Spin degree of freedom released, with creation of orbital momentum (vortices)Analog of the Einstein –de Haas effect

Dipole inelastic interactions modify the (already rich) S=3 spinor physics, and, most noticeably, its dynamics

Santos and Pfau PRL 96, 190404 (2006)

At the heart of the Einstein-de Haas effect with Cr BECs : dipolar relaxation

What is dipolar relaxation ?

3,22,32

13,3

3

212120 ).)(.(3.

4 R

uSuSSSgV RR

BJdd

- Only two channels for dipolar relaxation in m=3:

2,23,3

Rotate the BEC ? (Einstein-de-Haas)

222

111

212121

2

.24

32

1

SrSrzS

SrSrzS

SSSSSS

z

z

zz

rotation ! iyxr

2

BgmE BS

Need of an extremely good control of B close to 0

0 lS mm

3

4

5

6

7

8

910

4

Ato

mN

umbe

r

100806040200Tim e (m s)

Dipolar relaxation in a Cr BEC

Fit of decay gives

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

Remains a BEC for ~30 ms

Born approxim

ation Pfau

, Appl. P

hys. B, 7

7, 765 (2

003)

Inte

rato

mic

pot

enti

als

Interparticle distance

Interpretation

Sc aR Zero coupling

Determination of scattering lengths S=6 and S=4

Sa

2

2

2

)1()(

R

llRVeff

0,6,6 lmSin

2,5,6 lmSout

Gap ~

BgE BJf

ddV

cR

3,22,32

13,3

New estimates of Cr scattering lengthsCollaboration Anne Crubellier (LAC, IFRAF)

(a) Dipolar relaxation

(b) Feshbach resonance

In

Out

0l

2l

2l

0l

- The 2-body loss parameter is always twice smaller in the BEC than in thermal gases- Effect of thermal (HBT-like) correlations

3.0

2.5

2.0

1.5

1.0

543210

Temperature ( K)

Los

s pa

ram

eter

(10

m s

)3

-19

-1

DR in a BEC accounted for by a purely s-wave theory. No surprise, as the pair wave-function in a BEC is purely l=0

What about DR in thermal gases ? Dipole-dipole interactions are long-range: all partial waves may contribute

The dip in DR is as strong for thermal gases and BECsPartial waves l>0 do not contribute to dipolar relaxation

7

1

2

3

4

567

10

2

3

4

567

100

Tw

o-b

od

y lo

ss p

ara

m (

10

^(-1

3)

cm^3

/s)

4 6 8

0.12 4 6 8

12 4 6 8

10Magnetic field (G)

)exp()4

exp()exp()exp(2

2

2

2

2

2

2

2

w

X

w

x

w

x

w

x BA BA xxx

2/)( BA xxX

Perspectives :- no DR in fermionic dipolar mixtures

- use DR as a non-local probe for correlations

Red : l=0Blue: l=2Green : l=4Magenta: l=6

Overlap calculationsAnne Crubellier (LAC, IFRAF)

All partial waves contribute to elastic dipolar collisions… but …For large enough magnetic fields, only s-wave contributes to dipolar relaxation(because the input and output wave functions always oscillate at very different spatial frequencies)

Ove

rlap

Magnetic field

Inte

rato

mic

pot

enti

als

Interparticle distance

Bmg

llR

BSC

2)1(

Towards Einstein-de-Haas ?

• (i) Go to very tightly confined geometries

(BEC in 2D or 3D optical lattices)

• (ii) Modify output energy

(rf fields)

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

LvE 2

LB Bg

Ideas to ease the magnetic field control requirementsCreate a gap in the system:

B now needs to be controlled around a finite non-zero value

(~300 kHz)

Below Ev no dipolar relaxation allowed. Resonant dipolar relaxation at Ev.

Bg B2

(i) Reduction of dipolar relaxation in reduced dimension (2D gaz)

Load the BEC in a 1D Lattice (retro-reflected Verdi laser)

Produce BEC m=-3detect m=-3

Rf sweep 1

Rf sweep 2

BEC m=+3, vary timeLoad

optical

lattic

e

Lose BEC(2D thermal gas)

Band mapping

Dipolar relaxation in reduced

dimension (2D)

1st BZ

Dip

olar

rel

axat

ion

rat

e p

aram

eter

(1

0

m s

))

-19

-3-1

0.140.120.100.080.060.040.02

Magnetic field (G)

8

1

2

3

4

5

678

10

2

Dipolar relaxation in 2D Dipoolar relaxation in 3D 3D Born theory

Strong reduction of dipolar relaxation when

!!! !!! but instead

Prospect : go to 2D or 3D optical lattices

LBJ Bmg

aa6 cR aL

am

(ii) Controlling the output energy in dipolar relaxation: rf-assisted dipolar relaxation

),()'( '

2

'',' rffmmNNrf

mmNN BEmmJ

Within first order Born approximation:

(Brf parallel to B)Calculation by Paolo Pedri(IFRAF post-doc, now joined our group)Coll. Anne Crubellier (LAC)

See also Verhaar, PRA 53 4343 (1996)Never observed

Inte

rato

mic

pot

enti

als

Interparticle distance

NlmSin ,0,6,6

1,2,5,6 NlmSout 2,5,6 lmSout

0,6,6 lmSin

Similar mechanism thandipolar relaxation

Gap ~

BgE BJrff

ddVJ

1

Without rf, no DR in m=-3

Dipolar relaxation between dressed states, to control:

f J B rfE mg B N

2

'N NJ m

1.0x10-18

0.8

0.6

0.4

0.2

0.0

43210

Tw

o b

ody

loss

par

amet

er (

m^3

/s)

Coupling:

Output energy

Prospect: operate at to observe resonant DRrfBJ Bg 2

Conclusion

Rapid and simplified production of (slightly dipolar) Cr BECs

(BECs in strong rf fields) Collective excitations

(rf association)

(d-wave Feshbach resonance)

dipolar relaxation

rf-assisted relaxation

dipolar relaxation in reduced dimensions

(MOT of 53Cr)

Optical lattice and low-D physics(breakdown of integrability in 1D)

DR as a probe for correlations

Einstein-de-Haas effect

Spinor diagram

Production of a (slightly) dipolar Fermi sea

Load into optical lattices – superfluidity ?

Perspectives

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

Collaboration: Anne Crubellier (Laboratoire Aimé Cotton)

B. Pas

quio

u

O. G

orce

ix

Q. B

eauf

ils

Paolo

Ped

ri

B. Lab

urth

e

L. V

erna

c

J. C

. Kel

ler

E. Mar

écha

l

G. B

ismut

Why Bessel functions ? (Floquet analysis)

Modulate the eigenenergy of an eigenstate:

mrfm tHmH

dt

di cos e.g. different Zeeman states

Pillet PRA, 36, 1132 (1987)

Phase modulation -> Bessel functions

Arimondo PRL 99 220403 (2007))Q. Beaufils et al., arXiv:0812.4355

rf association Rydberg in -waves Shaken lattice