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