2 new very accurate determinations of the s-wave

scattering length in metastable helium

Steven Moal, Maximilien Portier, Julien Dugué, Christian Buggle, Nassim Zahzam,Michèle Leduc, Claude Cohen-Tannoudji

séminaire Atomes-froids vendredi 28 octobre 2005

Study with 1 photon :

Frequency shifts of photoassociative spectra

Principle of experiment

continuum

R

S + S

S + P0

E

r

5 g+

0u+

v=14

Ev = 0 (,I)

Interatomic distance

En

erg

y

kBT

~19.8 eV

~ 2 h

He*

1083nm

23S1

11S0

23PJ

Principle of experiment

continuum

R

S + S + ħ

S + P0

E

r

5 g+

0u+

v=14

kBTv=0

dressed atom pictureE

continuum

Ev = 0

Ev = 14

0E=kBT

Experimental result

From comparisonwith theory

Our value :a = 7.2 ± 0.5 nm

0 1 2 3 4 5 6 7 8 9 10 11-35

-30

-25

-20

-15

-10

-5

0

v=0 v=1 v=2

Ligh

t shi

ft (M

Hz)

PA laser power (mW)

R

S + P0

E

0u+

v=1

v=0

v=2

Study with 2 photons :

Dark atom-molecule resonances

Mesure of lifetime and position of v=14

2 photon spectroscopy

R

S + S

S + P0

1

E

r

2

5 g+

0u+

v=14

v = 0

Interatomic distance

En

erg

y

From Autler-Townes to Raman effect

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

-1445 -1440 -1435 -1430100

150

200

250

300

350

400

450

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

R

1

scanned

E

2

fixed

v=14

v = 0

R

1

scanned

E

2

fixed

v=14

v = 0

86 88 90 92 94 96 98

-1442

-1440

-1438

-1436

-1434

-1432

-1430

Pe

ak

fre

qu

en

cie

s (M

Hz)

2-

1 (MHz)

R

1

E

2

v=14

v = 01

2

From Autler-Townes to dark resonance

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PADetuning (MHz)

3 mW in 2nd photon

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

1 mW in 2nd photon

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

500 µW in 2nd photon

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

300 µW in 2nd photon

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

100 µW in 2nd photon

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

100 µW in 2nd photon

From Autler-Townes to dark resonance

0.0 0.5 1.0 1.5 2.00

2

4

6

8

10

12

14

(MH

z)

Sqrt of Power (Sqrt of mW)

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Te

mp

era

ture

(µ

K)

PA Detuning (MHz)

From Autler-Townes to dark resonance

continuum

R

S + S

S + P0

1

E

r~ -90 MHz

5 g+

0u+

v=14

v=0

Interatomic distance

En

erg

y

kBT

2

From Autler-Townes to dark resonance

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

100 µW in 2nd photon

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

30 µW in 2nd photon

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

10 µW in 2nd photon

-1445 -1440 -1435 -14302

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

3 µW in 2nd photon

-1460 -1450 -1440 -1430 -14202

4

6

8

10

12

14

16

18

Tem

pera

ture

(µK

)

PA Detuning (MHz)

100 µW in 2nd photon

destructive interference between the absorption amplitude of

photon 1 on the free / bound v=0 transition

and of

photon 2 on the bound v=0 / bound v=14 transition

-1442 -1440 -1438 -1436 -1434 -1432 -14303

4

5

6

Te

mp

era

ture

(µ

K)

PA Detuning (MHz)

Dark resonance

R

1

E

2

v=14

v = 0

S–P0

S–Sfree atoms

Mesure of Ev=14

-1442 -1440 -1438 -1436 -1434 -1432 -14303

4

5

6

Tem

pera

ture

(µ

K)

PA Detuning (MHz)

0 2 4 6 8 10 12 14-91.9

-91.8

-91.7

-91.6

-91.5

-91.4

-91.3

1- 2

(MH

z)

Temperature (µK)

shift du to T : 3kBT/2

experimentally we have 15 % lessPosition of v=14

-91.35 ± 0.06 MHz

R

S + S

S + P0

1

E

rv=14

v=0

kBT

2

no need of the

energy of v=0

Scattering length

New value :a = 7.512 ± 0.005 nm

113.4 151.2 189.0 226.8 264.6-0.3

-0.2

-0.1

0.06.0 8.0 10.0 12.0 14.0

-300

-200

-100

0 E

v=14 (M

Hz)

a (nm)

Ev=

14 (

GH

z)

a (bohr)

Gadea1 Gadea2 StarckMeyer AsympClass

Other results

a (nm)20 30100 155 25

x 200

7.507 7.517

2 photons

Light shift

ENS 2001 a=16±8 nm

IOTA 2001a=20±10 nm

ENS 2002 a<16 nm

VU 2004 a=10±5 nm

IOTA 2004 10.3<a<13.8 nm

Gadéa, Dickinson and Leininger 20048.0<a<12.2 nm

Stark and Meyer 1994a=8 nm

Przybytek and Jeziorski 2005a=7.64±0.20 nm

Theoretical values

Mesure of lifetime v=14 v=14 has not a infinite life duration

the dark resonance doesn’t go to 0 at weak intensity

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

empe

ratu

re (

µK

)

PA Detuning (MHz)

5 µW in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

emp

era

ture

(µ

K)

PA Detuning (MHz)

4 µW in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

empe

ratu

re (

µK

)

PA Detuning (MHz)

3 µW in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

empe

ratu

re (

µK

)

PA Detuning (MHz)

2 µW in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

empe

ratu

re (

µK

)

PA Detuning (MHz)

1 µW in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432 -14304

5

6

7

8T

empe

ratu

re (

µK

)

PA Detuning (MHz)

0.5 µW in 2nd photon

0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

v=1

4/2

(M

Hz)

Power in 2nd photon (µW)

0.05 < v=14 /2 < 0.3 MHz

0.5 < v=14 /2 < 3 µs

Rough estimate : 4 µs

from Penning collision rate between two polarized atoms

Kinel = 3.10-14 cm3 s-1

(Fedichev and Shlyapnikov, 1996)

Conclusion

• 2 very accurate (and different) measurements of the scattering length :

with frequency shift : a = 7.2 ± 0.5 nmwith dark resonance : a = 7.512 ± 0.005 nm

• Creation of exotic molecules of 2 metastables with inhibited autoionisation with

a lifeduration of 0.5 < v=14 /2 < 3 µs

Soon• influence of density on v=14

• a better value for v=14 with the study of Raman signal : in fonction of temperature in fonction of the detuning

• position and width of v=14 in the potential S-S (M=0)

• study of the 2 photons signal during the transition thermal cloud / BEC

R

1 , -

E

2 , +

v=14

v = 0

S-P0

S-S MJ=2

S-S MJ=0v=142µB0

Other experiments

Grimm, Innsbrück, April 2005 in 87Rb BEC

PRL 95, 063202 (2005)

• lifetime on

the dark resonance is 140 ms

• 100 molecules Rb2

Other experiments

Lett, NIST, July 2005 in 23Na dark MOT

PRA 72, 041801R 2005 dip width around 5 MHz du to :

• thermal energy distribution at T=150 µK, kBT/h~3 MHz

• intensity of 2nd photon kept high

No influence of the B0

0 2 4 6 8 10 12 14 16 18

-92.0

-91.8

-91.6

-91.4

-91.2

-91.0

-90.8

1- 2

(MH

z)

B0 (MHz)

1.4 GHz

=0.5 MHz

30 000 GHz

280 THz1083 nm

Principle of experiment

Raman effect

-1460 -1458 -1456 -1454 -1452

200

300

400

500

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

Raman pic in the red of the main line.

= -10 MHz

-1470 -1468 -1466 -1464 -1462200

250

300

350

400

450

Tem

pera

ture

(pi

xels

^2)

PA Laser Detuning (MHz)

But the main line can be shifted.

= -30 MHz

= few MHz

-1430 -1428 -1426 -1424 -1422

4

6

8

10T

em

pe

ratu

re (

µK

)

Detuning (MHz)

Raman pic in the blue of the main line.

Mesure of PA rate transition ?

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

Therm = 400 ms

PA = 1 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

PA = 1 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

Therm = 200 ms

PA = 2 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

Therm = 100 ms

PA = 5 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

Therm = 50 ms

PA = 10 ms

Therm = 0 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

PA = 10 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

PA = 2 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

PA = 5 ms

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

PA = 10 ms

a clear signal in the Number of atom for Therm = 0 ms

we have information on PA rate transition

-1442 -1440 -1438 -1436 -1434 -1432 -14300

100

200

300

400

500

600

700

800

Nu

mb

er

of

ato

ms

(arb

. u

.)

PA Laser Detuning (MHz)

Therm = 400 ms

PA = 1 ms

Black resonance

-1442 -1440 -1438 -1436 -1434 -1432 -14304

6

8

10

12

14

16

18

20

22

24

Te

mp

era

ture

(µ

K)

PA Detuning (MHz)

-1442 -1440 -1438 -1436 -1434 -1432 -14300.0

0.1

0.2

0.3

0.4

0.5

0.6

OD

PA Detuning (MHz)

10 µW.cm-2 in 2nd photon

-1442 -1440 -1438 -1436 -1434 -1432

4

6

8

10

12

14

16

18

Te

mp

era

ture

(µ

K)

PA Detuning (MHz)

-1442 -1440 -1438 -1436 -1434 -14320.0

0.1

0.2

0.3

0.4

0.5

0.6

OD

PA Detuning (MHz)

1 µW.cm-2 in 2nd photon

-1438 -1437 -14360.15

0.20

0.25

0.30

OD

PA Detuning (MHz)

Ev=0

Ev=14

E

0Ev=14

MJ=2

-

MJ=0

+

Pour bientôt :séminaire du

vendredi 10/06/05

continuum

R

S + S + ħ

S + P0

E

r

5 g+

0u+

v=14

kBT v=0

E