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LASER SPECTROSCOPY AND QUANTUM CHAOS : AN EXAMPLE THROUGH THE FOURIER
TRANSFORM OF A STIMULATED EMISSION PUMPING SPECTRA OF C2H2 AT VERY HIGH
VIBRATIONAL ENERGY
J. P. Pique, Y. Chen, R. Field, J. Kinsey
To cite this version:
J. P. Pique, Y. Chen, R. Field, J. Kinsey. LASER SPECTROSCOPY AND QUANTUM CHAOS : AN
EXAMPLE THROUGH THE FOURIER TRANSFORM OF A STIMULATED EMISSION PUMP-
ING SPECTRA OF C2H2 AT VERY HIGH VIBRATIONAL ENERGY. Journal de Physique Collo-
ques, 1987, 48 (C7), pp.C7-655-C7-657. �10.1051/jphyscol:19877158�. �jpa-00226980�
JOURNAL D E PHYSIQUE
Colloque C 7 , supplement au n ° 1 2 . Tome 4 8 , decembre 1987 C7-655
LASER SPECTROSCOPY AND QUANTUM CHAOS : AN EXAMPLE THROUGH THE FOURIER TRANSFORM OF A STIMULATED EMISSION PUMPING SPECTRA OF C2H2 AT VERY HIGH VIBRATIONAL ENERGY
J.P. PIQUE, Y. CHEN*, R.W. FIELD* and J.L. KINSEY*
Laboratoire de Spectrom6trie Physique, CNRS VA-08 et Celphyra, Universite Scientifique, Technologique et Kedicale de Grenoble, BP 87, F-38402 Saint-Martin-d'Heres Cedex, France
* Department of Chemistry and Georges Harrison Spectroscopy Laboratory, Massachusetts institute of Technology, Cambridge, MA 02139, U.S.A.
The spectra of polyatomic molecules a t high l e v e l s of v i b r a t i o n a l e x c i t a t i o n a r e extremely complex and a r e t e c h n i c a l l y d i f f i c u l t t o obtain because of very small Franck Condon f a c t o r s . Stimulated Emission Pumping (SEP) technique i s capable t o enormously simplify such*spectra by r e s t r i c t i n g the number of r o t a t i o n a l t r a n s i t i o n s and by forcing t h e population of an intermediate s t a t e to t h e ground s t a t e using high peak power l a s e r s . SEP spectroscopy i s b a s i c a l l y a v a r i a n t of Optical-Optical- Double-Resonance (OODR) spectroscopy (figure 1 ) .
In our experiment two l a s e r s (Pump and Dump) t r a n s f e r e d t2H2 molecules from an i n i t i a l thermally populated l e v e l v i a a s i n g l e rovi b r a t i o n a l level of an excited e l e c t r o n i c s t a t e t o t a r g e t r o v i b r a t i o n a l l e v e l s of t h e ground e l e c t r o n i c s t a t e . Large geometry mo- d i f i c a t i o n between fundamental and excited s t a t e s allows t h e access t o very high v i b r a t i o n a l energy (26500 cm-' from the ground s t a t e i s about 25 quanta of v i b r a t i o n in the trans-bend mode of C2H2 ! ) . In t h i s experiment we monitored the fluorescence decrease versus the tuning of dump t r a n s i - t i o n s .
Figure 1.
The enormous interest of getting such spectra is to study "quantum chaos" in poly- atomic molecules. According to one definition of quantum chaos, such spectra are intrinsically unassignable because of partial or complete loss of vibrational quantum numbers. Our goal is to show how structural and dynamical informations can be extracted directly from the Fourier Transform (FT) of such spectra. Unlike the spectrum, the FT is simple and gives very nice informations. An enormous interest of FT is to provide easily very short time resolution (few femtosecond ! ) .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19877158
JOURNAL DE PHYSIQUE
We show i n t h i s paper j u s t an example through the FT of a low resolution (0.3 cm-I) and ve long (1400 cm-l) SEP spectrum a t 26500
any
above the ground s t a t e (figure 2,. The intermediate single rovibronic s t a t e was excited with J r = l , Kt=l and two quanta of vibration i n the trans-bend mode v s . The SEP spectrum is nearly purely vibrational.26550 26600 26650 cm-
'
Figure 2.
The FT (figure 3) gives a time evolution DELAY TIME
with a resolution of 20 femtoseconds of an i n i t i a l wave packet :
I$>
=1
an(v) In> CORRELATION HOLEn
where In> a r e eigenstates and the expansion coefficients an a r e a dipole moment
(u)
function.
I I I I a
5 10 15 20 25
t ( p s )
Figure 3.
A rapid discussion of t h i s FT (for more d e t a i l see r e f . 1,2,3) give mainly three important informations :
i ) the i n i t i a l "delay time", a pure quantum e f f e c t , i s a d i r e c t measure of the non i n t e rable p a r t of the hamiltonian. This i n i t i a l decay i s exponential. A random
-bows
(figure 4) t h a t the corresponding time constant r obey the r e l a t i o n :? 1 = 2
n
p<v2>
where p i s t h e energy density and cV 2 > the second moment of the non integrable p a r t of the hamiltonian. T is the time t h a t the i n i t i a l system has t o wait t o see the chaos.
FT O F A R A N D O M M A T R i X E I G E N S P E C T R U M
a
l
I
I /
I I
! j
g I
-
!2 I C O R R E L A T I O N H O L E
. f
-
LS L O P E 4 2np
Figure 4.
<vz>
Figure 5.
ii) the correlation hole is a direct signature for quantum chaos. The rise of this hole on the long time side is related to fraction of phase space which is available.
iii) the recurrences after the correlation hole show that there is new periodic orbital which correspond to regular motion.
As we are well above the vinylidene isomer and to take into account of the large am- plitude motion needed to react from acety- lene to vinylidene, we propose a model with a sort of H-Rydberg molecule (figure 5) to explain these recurrences.
Figure 6.
To conclude, the FT is the revealer of complex spectra. Could you see these three informations directly on the s p e c t m ?
References
(1) L. Leviandier, M. Lombardi, R. Jost and J.P. Pique Phys. Rev. Lett. 56, 2449 (1986)
(2) J.P. Pique, Y. Chen, R.W. Field and J.L. Kinsey Phys. Rev. Lett.
58,
475 (1987)(3) J.P. Pique, Y. Chen, R.W. Field and J.L. Kinsey To be published.
