séminaire interne du groupe Atomes Froids

Vendredi 08 octobre 2004

Steven MOAL, Maximilien PORTIER, Jaewan KIM

Michèle LEDUC, Claude COHEN-TANNOUDJI

Determination of the s-wave scattering

length in metastable helium :

experimental results withsingle photon photoassociation

1st STEP :

TWO PHOTONS EXPERIMENT

PRINCIPLE OF EXPERIMENT

continuum

R

S + S

S + P0

1

E

r

2

5 g+

0u+

v=14

v = 0

interatomic distance

energ

y

kBT

FRUSTRATED PA vs. RAMAN TRANSITION

1

fixed

2

scanned

5g+ (v=14)

S + S

0u+ (v =

0)

Tem

pera

ture

(a.u

.)

-20 -10 0 10 20

Detuning with respect v=14 (MHz)

Tem

pera

ture

(a.u

.)

-20 -10 0 10 20

Detuning with respect v=14 (MHz)

5 g+

(v=14)

S + S

0u+ (v =

0)

1

scanned

2

fixed

-15 -10 -5 0 5 10 15

0

110-13

210-13

310-13

410-13

-20 -10 0 10 200

110-13

210-13

310-13

410-13

• a large range scan to exploreOrsay value : 11 4 nm range of –15 MHz <

< -110 MHz

• transition probabilities (FC factors) are not known precisely : too many differents combinations of relative power. • large line width of the PA laser (3 MHz) :

SOME DIFFICULTIES

-20 -10 0 10 20

510-14

110-13

1.5 10-13

210-13

2.5 10-13

310-13

3.5 10-13

-15 -10 -5 0 5 10 150

210-14

410-14

610-14

810-14

Tem

pera

ture

(a.u

.)Tem

pera

ture

(a.u

.)

Detuning with respect v=14 (MHz) Detuning with respect v=14 (MHz)

larg

e w

idth

Tem

pera

ture

(a.u

.)Tem

pera

ture

(a.u

.)

2nd STEP :

ONE PHOTON EXPERIMENT

1- MEASURE OF LOSS SIGNAL

MESURE OF LOSS SIGNAL (1)

-675 -670 -665 -660 -6550

50

100

150

200

250

300

350N

umbe

r of

Ato

ms

(a.u

.)

PA Laser Detuning (MHz)

0 50 100 150 200 250 300 350 400 450 50010-7

10-6

1x10-5

1x10-4

10-3

10-2

10-1

100 v=4

v=3v=2v=1

v=0

rela

tives

inte

nsi

ties

of

mole

cula

r lin

es

scattering length a (a0)

the loss of atoms depend of the Franck Condon factor

one idea :we can measure the relative intensities of molecular lines

• the loss measurement is too noisy for a very precise value of « a »• FC calculation is not enough precise in our case

measurement

of the scattering length « a »

BUT :

MESURE OF LOSS SIGNAL (2)

• it’s NOT very precise

• a very fast non-linear effect (some 60 ISAT)

• not good agreement with this reference

John L. Bohn and P. S. Julienne, Phys. Rev. A 60, 414 (1999)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.450.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8line v=0

Are

a L

ose

Intensity of PA pulse (mW)

0.00 0.05 0.10 0.15 0.20 0.250.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 line v=1

Are

a L

ose

Intensity of PA pulse (mW)

ONE PHOTON EXPERIMENT

2- MEASURE OF OSCILLATION OF THE CLOUD

THE CLOUD MOVES !

when we put one photon at resonance with different Thermalization time :

0 10 20 30 40 5075

76

77

78

93.594.094.595.095.5

Offset 76.99 ±0.03Amplit 1.62 ±0.04Freq 90.03 ±0.26phase -0.94 ±0.14

X0

& Y

0 (

pix

els

)

Thermalisation time (ms)

… with the frequency of the trapthe cloud moves…

-20 0 20 40 60 80 100 120 140 160-0.1

0.0

0.1

0.2

0.3

0.4

0.5

X

pixel

Therm

= 19.5 ms

Therm = 14.4 ms

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.0

0.5

1.0

1.5

2.0

2.5

3.0 line v = 0

y = a * x + bR^2 = 0.967 a 0.57 ±0.02b 0 ±0

Am

plit

ud

e (

pix

el)

PA Pulse Intensity (mW)

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.5

1.0

1.5

2.0

2.5line v = 1

y = a * x + bR^2 = 0.886 a 2.02 ±0.11b 0 ±0

Am

plit

ud

e (

pix

el)

PA Pulse Intensity (mW)

it’s linear !

slope ratio :

BUT : • the trap is harmonic.• for high intensities, the line is not at resonance because of a shift with laser intensity.

FCFC 0.3 3.54

0.572.02

0v slope1v slope

0v

1v

?

THE CLOUD MOVES ! (2)

ONE PHOTON EXPERIMENT

3- MEASURE OF THE SHIFTWITH LASER INTENSITY

DISCOVER OF A SHIFT WITH LASER INTENSITY

when we explore high power of PA beam :

-675 -670 -665 -660 -655150

200

250

300

350

400

450

Te

mp

era

ture

(p

ixe

ls^2

)

PA Laser Detuning (MHz)

line v=1 with 0.5 mW

position = -667.7 MHz

-690 -685 -680 -675 -670

200

400

600

800

1000

1200

Te

mp

era

ture

(p

ixe

ls^2

)

PA Laser Detuning (MHz)

line v=1 with 4 mW

position = -685.0 MHz

• shift of 17.3 MHz !• deformation of the line at high intensities

continuum

INTERPRETATION

one approach : A. Simoni, P. S. Julienne et al, Phys. Rev. A 66, 63406 (2002)

shiftdue to thecontinuum

shiftdue to a

bound state

El

0e

0g

Veg

v = 14 S - S

v = 0

Veg

DIRECTION OF THE SHIFT

• shift due to the bound state v=14

BLUE SHIFT

• shift due to the continuum

: energy of the continuum: energy of v=14

contribution :

if RED SHIFT

BLUE SHIFTRED SHIFT

EXPERIMENTAL SHIFT

0 1 2 3 4 5 6 7 8 9-1450

-1448

-1446

-1444

-1442

-1440

-1438

-1436

-1434 line v=0

y = a * x + bR^2 = 0.9975 a -1.54 ±0.03b -1435.67 ±0.16

Pos

ition

de

v=0

(MH

z)

Intensité du PA-Pulse (mW)

0.0 0.5 1.0 1.5 2.0 2.5-678

-676

-674

-672

-670

-668

-666

-664 line v=1

y = a * x + bR^2 = 0.96662 a -4.48 ±0.23b -665.48 ±0.22

Po

sitio

n de

v=

1 (M

Hz)

Intensité du PA-Pulse (mW)

we have a RED SHIFT for v=0always a RED SHIFT for v=1

BUT :

slope ratio : 0.2 2.91 1.544.48

0v slope1v slope

• some uncertainty on the laser intensity

difficulty in deducing absolute values of FC factor

CONCLUSION

for evaluation of Franck Codon factor :

• the measurement of loss signal : too much uncertainty• the measurement of oscillation : ratio of 3.54 0.3

we need to understand the phenomenon of oscillations

for precise value of the scattering length :

• the measurement of the light shift of the molecular line

BUT we need to finish the theory :

to calculate accurately the shifts

AFTER…

1- spectroscopy of D2

He*23S1

11S0

1083 nm

J=0

123PJ

2 2.29 GHz

29.6 GHz

to continue Raman 2 photons PA with a potentiel more adapted than 0u

+

2- optical Feshbach

to study Mott transition

3- BEC in linear lattice

to change the scattering length « a » with light