Ultracold collisions in chromium:d-wave Feshbach resonance and rf-assisted molecule association

Q. Beaufils, T. Zanon, B. Laburthe, E. Maréchal, L. Vernac and Olivier GorceixLaboratoire de Physique des LasersUniversité Paris Nord

A. Crubellier (theory)Laboratoire Aimé-CottonUniversité Paris Sud - Orsay

CLEO/Europe-EQEC ConferenceMunich – 15 June 2009

Attractive interaction

Repulsive interaction

Dipolar effects in ultra-cold gases

Modified expansion and collapse dynamics (Pfau’s group)

Dipolar bosons in optical lattices (in our group and also in Stuttgart)

Dipolar relaxation (poster yesterday)

Feshbach resonance without hyperfine structure (this talk)

Magnetic dipole-dipole interaction :

long range and anisotropic

Chromium relevant properties:

Large dipolar effects in ultra-cold gases which stem from

the ground state electronic structure [Ar] 3d5 4s1 S=3

and magnetic moment of 6 µB

but also: Several metastable states Large inelastic Collision loss rates

new strategies to reach BEC

Chromium level scheme

7 S3

7 P4

425.

55 n

m

663-

654-

633

nm

Spontaneous decay

Rep

um

pers

= 5 MHz

7 P3

5D4,3

5S2

= 32 ns

[Ar] 3d5 4s

3d5 4p

3d4 4s2

6 µ B

6 µ B

~250 s-1

sat = 8.5 mW/cm2

427.

60 n

m

3d5 4s

Optical trapping of Cr atoms

We continuously accumulate Cr* atoms

in a mixed magnetic + optical trap

35W at 1075 nm with waist 50µm

Condensation of Cr is not possible in a magnetic trap (dipolar relaxation scales as µ3)

Sequence : MOT + OT Switch-off MOT beams and fieldRepump to ground state (ss<<dd)Spin polarization in lowest-energy sub-state m=-3“All-optical” evaporative coolingHold the sample for time tRelease then capture an absorption image to get T and N

time sequence for Cr-BEC and collision studies

Not to scaleNot to scale EvaporationEvaporation100 ms100 ms 16 s16 s

MOTMOT

Horizontal trapHorizontal trap

Vertical trapVertical trap

Repump Repump Spin polarizationSpin polarization

500 mW500 mW35 W35 W

Plate rotation 6sPlate rotation 6s

!!

Ninit = 6 106 At the ramp end, in this work, we get At the ramp end, in this work, we get

T between 2µK and 15µK and N between 3 10T between 2µK and 15µK and N between 3 1044 and 10 and 1055

Ramp end for Ramp end for collision studiescollision studies

Cr sample preparation : way down to Bose-Einstein Condensation

All-optical evaporation

After « dimple » formation, the trapping beam power is lowered from 35 W to 500 mW within 10 s.The complete cycle time is below 20 s.

Evaporation ramp can be stopped at will.

Temperature can be tuned from 15 µK to below 100 nK.The peak density is on the order of 1013 cm-3 .

BEC transition at ~~110 nK

t = 10 s – pure condensate t = 10 s – pure condensate

~20 000 atoms~20 000 atoms

t= 9.8 s - T = 80nKt= 9.8 s - T = 80nK

t=9.2 s - T = 200nKt=9.2 s - T = 200nK

Q. Beaufils, et al, Phys Rev 77, 061601 R (2008)

52Cr Feshbach resonances From Werner PhD dissertationat Stuttgart Uni

This workB close to 8.2 G

Pavlovic et al. PRA 69, 030701 (2004)

Cr2 molecular potential curves

0.4

0.3

0.2

0.1

0.0

-0.1

-0.2

4321

| 6; 6; 2; 1S lS m l m

| 6; 5; 0SS m l

Feshbach resonance in d-wave collisions at low field

• Several Feshbach resonances have been observed at Stuttgart Uni in Tilman Pfau’s group

J.Werner et al. Phys. Rev. Lett. 94, 183201 (2005)

Bg B

We work close to the Feshbach resonance at 8.2 G

Entrance channel : input : pair of free colliding atoms in d-wave

Closed channel : output s-wave excited bound molecule

Resonant coupling parameter

with

2/)12(22)( l

ddboundm V

Resonance in d-wave collisionsLoss mechanism

At ultra-low temperature scattering is inhibited in l>0, because atoms need to tunnel through a centrifugal barrier to collide. In our case, ie for a « d-wave entrance channel», tunneling is resonantly increased. by the presence of a bound molecular state. A third Cr atom triggers superelastic collisions, leading to three-body losses, as the kinetic energy gain greatly exceeds the trap depth.

Cr2* excited molecules decay to more deeply bound states

while three atoms are lost

Su

pere

last

ic c

olli

sion

KTTkBm 8@1035.5)( 5

KTTkBm 8@103.7)( 5

Theory

Experiment

Q. Beaufils et al., PRA 79, 032706 (2009)

Atom losses near resonance

We have monitored losses vs the magnetic field We have monitored losses vs the magnetic field strength at various temperatures well below the strength at various temperatures well below the Wigner threshold for d-wave collisions but above Wigner threshold for d-wave collisions but above BEC transition. BEC transition.

3

4

5

6

789

104

2

3

4

5

Ato

mN

umb

er

252015105Time (s)

Typical decay curve – 3-body loss mechanism

2.5

2.0

1.5

1.0

0.5

0.0

25.525.024.524.023.523.022.5

14

Th

ree-

body

los

s pa

ram

eter

(m

s )

Magnetic field (MHz)

6-1

3-body loss parameter strongly depends on TWidth and max of resonant loss signal strongly depend on T. B is known with B about 2mG

Fit with

where 0= M g µB (B-Bres)

Unusual T dependence

Loss signal width vs B strongly depends on T

3-body loss parameter strongly depends on T

Cr2 rf-association

Bg B

Rf photon

0.4

0.3

0.2

0.1

0.0

-0.1

-0.2

4321

We set the magnetic field close to 8 G (sligthly below the Feshbach resonance) and we add an rf-field. The colliding pair of atoms emits an rf-photon while it is colliding, and is transfered into the Cr2* bound molecular state when a resonance occurs. The loss mechanism then follows the same path as before.

30x103

25

20

15

10

5

0

Ato

m n

umbe

r af

ter

8s

2625242322

Magnetic field (MHz)

rf-peak Bare Feshbach resonance

Cr2 rf-spectroscopy

The rf peak shifts with B. This allows for precise determination of the Feshbach resonance position at 8.157 Gie for molecular spectroscopy.

9000

8000

7000

6000

Ato

m N

umbe

r

5004003002001000rf frequency (kHz)

-1000

-800

-600

-400

-200

rf r

eson

ance

(kH

z)

25.0x103

24.524.023.523.022.522.0 Magnetic field (kHz)

25x103

20

15

10

5

0

Atom

Num

ber after 7s (no rf)

rf peaks for two values of B

rf at max verifies the energy conservation equation

signal without rf

Cr2 rf-association at high power

0.4

0.3

0.2

0.1

0.0

K2/

K2(

0)

543210

kHz kHz kHz kHz kHz kHz kHz

/

1050 kHz900 kHz700 kHz500 kHz400 kHz400 kHz300 kHz

Q. Beaufils et al., arXiv:0812.4355

Association rf of molecules as a Feshbach resonance between dressed states

2

122 0,

JKK

Finally, we study how the peak intensity varies vs rf-power in the strong field regimeExperimental outcomes are best described in a dressed molecule approach:

The rf assisted loss parameter only depends on the ratio of the Rabi frequency to the rf frequency .A four-body process (three atoms and a photon) is described by a simple analytical Bessel function !

Acknowledgements

Financial support:•Conseil Régional d’Ile de France (Contrat Sésame)•Ministère de l’Enseignement Supérieur et de la Recherche (CPER, FNS and ANR)•European Union (FEDER)•IFRAF•CNRS•Université Paris Nord

Publications related to this talk:Q. Beaufils et al., PRA 77, 061601® (2008)

•Q. Beaufils et al., PRA 79, 032706 (2009)

•Q. Beaufils et al., arXiv:0812.4355

Ph.D students:Ph.D students:

Quentin Beaufils

Gabriel Bismut

Benjamin Pasquiou www-lpl.univ-paris13.frPost-docs:Post-docs:

Paolo Pedri

Thomas Zanon (now at LNE-CNAM)

Permanent staff:Permanent staff:

Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac and O. G.

Former membersArnaud Pouderous (industrial property specialist, Hirsch & Partners), Radu Chicireanu (now at NIST) Jean-Claude Keller (retired)

Group members : The Cold Atom Group in Paris Nord

THANKS!

From left to right: Laurent Vernac, Etienne Maréchal, Thomas Zanon, Jean-Claude Keller, Bruno Laburthe, Quentin Beaufils, OGAND Anne Crubellier (not shown on photo)

Interpretation4/))(()(

)()(

220

2dm

dm

kk

dd n

TkBdm )( 0Thermal averaging, when

TkhQ

lTK

Bm

T

002 exp)(

)12(2)(

Feshbach coupling Superelastic rate

F. H. Mies et al., PRA, 61, 022721 (2000)P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B. 6, 2257 (1989).

Calculation with no adjustable parameter (adiabatic elimination of d) (Anne Crubellier LAC)

2/)12(22)( l

ddboundm V

)(m psd

nnn dBm 3

Losses = Rate of coupling to the molecular bound state

= Rate of association through the barrier