1Femto group - LCAR - Toulouse Cargese 2008

Shaping in a different wayLaboratoire Collisions AgrLaboratoire Collisions Agréégats Rgats Rééactivitactivitéé

UniversityUniversity ofof ToulouseToulouse--CNRSCNRSBBééatrice atrice ChatelChatel

Sébastien Weber (ph D), Bertrand Girard (Prof)

Adrien Besse, Jonathan Bonnet, Charlotte Fabre (undergraduatestudents)

Coll with Arnaud Arbouet (CEMES)

coll with Wolfgang Schleich (Ulm university)

Coll with D. Kaplan (Fastlite)

2Femto group - LCAR - Toulouse Cargese 2008

Menu

Shaping the probe in a pump-probeexperimentFactorization of numbers using Gauss sum.Shaping UV pulses using a new AOPDF device

3Femto group - LCAR - Toulouse Cargese 2008

Probing wavepacket interferences in I2 by scanning the probe wavelength

H. Katsuki, H. Chiba, B. Girard, C. Meier and K. Ohmori, Science 311, 1589 (2006)

pump

probe

X(0g+)

B(0u+)

E(0g+)

f(0g+)

r FC

[Å]

lpr [nm]

2 nm

1 pm

The probe is so important!!

4Femto group - LCAR - Toulouse Cargese 2008

What’s happen if the probe is shaped?Some results have been obtained to emphasize the

importance of the probe’s wavelength

Shape the phase of the probe

5Femto group - LCAR - Toulouse Cargese 2008

Quantum holography : to follow the wavefunction in real time

To implement Temporal Fresnel lens

To use the coherence of theatom to reconstruct theelectric field.

Degert et al, PRL 89, 203003-2 (2002)

Monmayrant et alPRL 96, 103002 (2006)

Monmayrant et al OL 31, 410 (2006)

6Femto group - LCAR - Toulouse Cargese 2008

Experimental Set-up

( ) ( )( )O IE H Eω ω ω=

6d, 8s

5p2P1/2

τ

5s

6p

Fluorescence(420 nm)

Rb

NOPA

Ti:SaOscillator

CPA795 nm1kHz1 mJ130 fs

607 nm1kHz5 µJ20 fs

795 nm1kHz5 µJ

Delay line

RbPM

Rbτ ( )OE ω

( )IE ω

Grating’s pair to chirpthe probe.

7Femto group - LCAR - Toulouse Cargese 2008

Our high resolution pulse shaper

Phase/Amplitude controlover 640 pixels.shaping window of 35 ps.high complexity.high amplitude dynamic (30 dB).75 % power transmission.

A. Monmayrant, B. Chatel. "A new phase and amplitude High Resolution Pulse Shaper."

Rev. Sci. Inst. 75, 2668 (2004)

8Femto group - LCAR - Toulouse Cargese 2008

-2 -1 0 1 2 3 4 5

0,0

0,5

1,0

1,5

Inte

nsity

(u.a

.)

Delay(ps)Pump TF limited

Probe strongly chirped

chirp=-1.4 105 fs2

20 pscτ ≈

on resonanceΦ’’=-8 105

fs2

t1 t22 2 "φ

-2 0 2 4 6 8 10Delay (ps)6p-5

s Fl

uore

scen

ce (a

.uPump stronglychirped/probe TF limited

9Femto group - LCAR - Toulouse Cargese 2008

Short pump

Chirped probe

delay

Chirped pump

Short probe

delay

Analogy with the Fresnel diffraction : τ corresponds to theposition of the sharp edge in the gaussian beam

( ) ( ) eg

pump

i tfb E t e dt

τ ωτ−∞

∝ ∫ ( ) ( ) fe

probe

i tfb E t e dtω

ττ

+∞∝ ∫

10Femto group - LCAR - Toulouse Cargese 2008

What does it mean?

In this experimentPump’s duration :~12 psProbe’s duration :~14 ps

The rise time is less than 100 fs!!Interferences effect!Mathematically :

Does it mean that we can have access to a very short dynamiceven the pump-probe are long?

(2) (2)pump probe

φ φ= −

-2 -1 0 1 2 3 4 5

0,0

0,5

1,0

1,5

Inte

nsity

(u.a

.)

Delay(ps)

11Femto group - LCAR - Toulouse Cargese 2008

Pump-probe experiment : a particularcase of a two-photon transition

+ -2 -1 0 1 2 3 4 5

0,0

0,5

1,0

1,5

SFG-SHG

Inte

nsity

(u.a

.)

Delay(ps)

Work in progress : Long rise time(averaging on thewhole spectrum) Short rise time (by filtering the photoespectrum)Short rise time

TPAGeneration of a pspulse

(Raoult et al,OL 1998)

Behavior as a function of the pump-probe delay?

?

12Femto group - LCAR - Toulouse Cargese 2008

Menu

Shaping the probe in a pump-probeexperimentFactorization of numbers using Gauss sum.Shaping UV pulses using a new AOPDF device

13Femto group - LCAR - Toulouse Cargese 2008

non-integerNk≡

Not a factor of k N≡

What is a Gauss sum?

8 10 12 14 16 18 20

0,0

0,2

0,4

0,6

0,8

1,0

|AN

(M) (k

)|2

k

Factorisation of N=221=13*17

1(k) 2N

0

A ( ) exp 2k

mm

Nk i mk

ρ π−

=

⎡ ⎤= ⎢ ⎥⎣ ⎦∑

Phases oscillate rapidly with m

14Femto group - LCAR - Toulouse Cargese 2008

What is a Gauss sum?

1 12

0 0( ) exp 2 1

M M

N m mm m

A k i m pρ π ρ− −

= =

⎡ ⎤= = =⎣ ⎦∑ ∑

Factor of k N≡

(integer)N pk≡

8 10 12 14 16 18 20

0,0

0,2

0,4

0,6

0,8

1,0

|AN

(M) (k

)|2

k

Factorisation of N=221=13*17

1(k) 2N

0

A ( ) exp 2k

mm

Nk i mk

ρ π−

=

⎡ ⎤= ⎢ ⎥⎣ ⎦∑

15Femto group - LCAR - Toulouse Cargese 2008

In practice : truncated Gauss sum

The first few terms are enough to discriminate factors from non-factors (W.P. Schleich et al)M is the order of the truncation and could be

adjusted.

12

N0

A ( ) exp 2M

mm

Nk i mk

ρ π−

=

⎡ ⎤= ⎢ ⎥⎣ ⎦∑

16Femto group - LCAR - Toulouse Cargese 2008

Many theoretical and experimental resultsTheory :

Merkel et al, Fortschr. Phys. 54, 856 (2006)

NMR : Mehring et al, Phys. Rev. Lett. 98, 120502(2007)Mahesh et al, Phys. Rev. A 75, 062303(2007)

Cold atoms:Gilowski et al, Phys. Rev. Lett. 100 (2008)

Our results with ultrashort pulsesBigourd et al, Phys. Rev. Lett. 100, 030202 (2008)Weber et al, Eur. Phys. Lett (2008)

17Femto group - LCAR - Toulouse Cargese 2008

In all these experiments, the terms of thesum are precalculated….

Challenge : to find a physical system in which

the Gauss sum will be calculated « automatically »

for all values of

sequentially or in parallel

between 2 andk N

18Femto group - LCAR - Toulouse Cargese 2008

Our proposition using ultrashort pulses

Several candidates :Two-photon transition usingchirped pulses

Sum frequency betweena pulse train and a chirped pulse

Experimentally difficult to implement at the moment

First step :An all optical experiment

19Femto group - LCAR - Toulouse Cargese 2008

770 780 790 800 810

0,3

0,6

0,9789 nm

Nor

malised

int

ensity

W ave length (nm )

A pulse train with carefully chosen relative phases….

700 750 800 850 9000,0

0,2

0,4

0,6

0,8

1,0

Nor

malised

int

ensity

Wavelength (nm)

SpectrometerPulse shaperOscillator

1(1)

0

2 (1)

( ) exp ( )

2 with 200 fs

M

m pm

m

H i i m

Nmk

ω θ φ ω ω

θ π φ

−

=

⎡ ⎤= + −⎣ ⎦

= =

∑

10 fs800nm80MHz

First step : An all optical experiment

20Femto group - LCAR - Toulouse Cargese 2008

90 100 110 120 130 140 150 160

0,0

0,5

1,0 theory experiment

l

|AN

(M) (l)

|21 3 5 7 9 11 13 15

0,0

0,5

1,0

First results

theory experiment

l

|AN

(M) (l)

|2

N=105=3*5*7 4 pulses N=15251=101*151 9 pulses

Good agreement between experiment and theory:

Factorization of Numbers with the temporal Talbot effect: Optical implementation bya sequence of shaped ultrashort pulsesD. Bigourd, B. Chatel, W. P. Schleich, B. Girard, PRL (2008)

21Femto group - LCAR - Toulouse Cargese 2008

Experimental Results N=1’340’333’404’807=11003*11027*11047

Sequential

Random

kkFactoring numbers with interfering random waves.

S. Weber, B. Chatel and B. Girard, EPL 2008.

30 pulses

22Femto group - LCAR - Toulouse Cargese 2008

Shaping between 200nm and400nmUsing a new AOPDF device in the UV (see Kaplan’s talk). Main limitation : only 12% of the energy on the shaped pulse (50% absorption+ diffraction efficiency).

Using cross-correlation technique by difference frequencymixing

Using two-photon absorption in the diamond as a characterization tool

23Femto group - LCAR - Toulouse Cargese 2008

ConclusionShaped probe : Coll with P. Salières (Saclay) to implement an experiment with HH

Factorization :To find a system which calculatesdirectly the Gauss sum

Shaping and Characterization in the UV :To improve our device, to compare with a new deviceusing MEMS recently developped by J.P. Wolf (Geneva)

LOOKING for a phD student (FASTQUAST)