Laboratoire Collisions Agrégats Réactivité University of ... · Femto group - LCAR - Toulouse...
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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)