Preparation and monitoring of high-ground-state vibrational wavepackets byfemtosecond coherent anti-Stokes Raman scatteringIddo Pinkas, G. Knopp, and Yehiam Prior Citation: The Journal of Chemical Physics 115, 236 (2001); doi: 10.1063/1.1377028 View online: http://dx.doi.org/10.1063/1.1377028 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Analysis of time resolved femtosecond and femtosecond/picosecond coherent anti-Stokes Raman spectroscopy:Application to toluene and Rhodamine 6G J. Chem. Phys. 136, 064504 (2012); 10.1063/1.3682470 Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafastdetection of molecular Raman spectra J. Chem. Phys. 125, 044502 (2006); 10.1063/1.2219439 Time-resolved coherent anti-Stokes Raman-scattering measurements of I 2 in solid Kr: Vibrational dephasing onthe ground electronic state at 2.6–32 K J. Chem. Phys. 123, 064509 (2005); 10.1063/1.1990115 Vibrational polarization beats in femtosecond coherent anti-Stokes Raman spectroscopy: A signature ofdissociative pump–dump–pump wave packet dynamics J. Chem. Phys. 115, 8440 (2001); 10.1063/1.1412253 Time resolved coherent anti-Stokes Raman scattering of I 2 isolated in matrix argon: Vibrational dynamics on theground electronic state J. Chem. Phys. 114, 4131 (2001); 10.1063/1.1346643

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Preparation and monitoring of high-ground-state vibrational wavepacketsby femtosecond coherent anti-Stokes Raman scattering

Iddo Pinkas, G. Knopp, and Yehiam Priora)

Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel

~Received 20 October 2000; accepted 12 April 2001!

Femtosecond time-delayed coherent anti-Stokes Raman scattering is presented not only as a tool formonitoring but also as a viable method for the preparation of vibrational wavepackets with very highquantum numbers in the ground electronic state of molecules. We experimentally demonstrate aparticularly useful approach of using two separate time delays between the pulses for preparingvibrational wavepackets as high asv9538 @DEv57000 cm21# in bulk gas-phase molecular iodine.By means of an ultrashort laser pulse, we prepare a wavepacket in an electronic excited state,optimize the frequency and timing of a second pulse to efficiently generate the targeted ground-statevibrational wavepacket, and monitor the wavepacket by coherent scattering from a third pulse. Themethod is further used to probe interference effects in femtosecond four-wave-mixing signalsgenerated by molecular wavepackets. ©2001 American Institute of Physics.@DOI: 10.1063/1.1377028#

I. INTRODUCTION

Making and breaking of bonds is the basis for chemicalreactions. The direction and outcome of chemical reactions isusually determined by parameters such as temperature, pres-sure, and concentration of reactants or their solubility, but ifmore than one branch exists in a chemical reaction, explicitexternal control is not possible through the thermodynamicparameters. For a long time it was believed that with lasersone might overcome this hurdle, and that pumping enoughenergy into a specific bond will cause this bond to break ondemand. Early attempts to achieve mode- or bond-selectivechemistry with the goal of populating high-lying vibrationsincluded various infrared excitation schemes.1 However, suc-cess was rather limited, mostly due to the fact that selectivitymay be expected only for a time short compared to the in-tramolecular energy redistribution time. Therefore, excitationwith nanosecond lasers was not rapid enough, and by the endof a nanosecond excitation pulse the energy is already welldistributed to all accessible states. The introduction of muchshorter laser pulses has changed the situation, and the newfield of femtochemistry has emerged.2

In several detailed studies, Zare3 and Crim4 demon-strated cases where the preparation of a molecule in a spe-cific vibrational state led to selectivity in reaction products,and more recently, Houet al.5 demonstrated enhanced reac-tivity of highly vibrationally excited NO molecules on aCu~111! surface. In all these experiments, however, the timerequired for the preparation of the molecule was long on therelevant time scale of a single collision, and rarified gas con-ditions were needed. By virtue of their short duration, fem-tosecond pulses offer an alternative for the preparation ofvibrational wavepackets. Moreover, nonlinear optical tech-niques such as four-wave mixing are known to be useful, ina variety of experimental schemes, for the measurement of

populations and phases of coherently prepared states. In apioneering experiment, Hayden and Chandler6 demonstratedin 1995 femtosecond gas-phase coherent anti-Stokes Ramanscattering~CARS! for the measurement of mechanisms ofcoherence decay in samples of benzene and 1,3,5-hexatriene.Even earlier, Ruhman, Joly, and Nelson7 used ultrashortpulses for impulse excitation and monitoring of vibrationalstates in neat molecular liquids. More recently, Dantus andco-workers have extensively used degenerate three-pulsefour-wave mixing for coherent excitation and probing ofground and excited states in molecular iodine.8

The concept of using temporal shaping~amplitude andphase! of laser pulses for better control of chemical reac-tions, and in particular, the use of delay between two pulsesused for excitation, has been theoretically introduced byTannor and Rice.9 These authors have shown that withproper selection of the delay between a ‘‘pump’’ and a‘‘dump’’ pulse, one is able to affect the population in theground state, and thus hopefully control the outcome of thechemical reaction. In parallel, control by optimization in thefrequency domain10 was developed. More recently, and us-ing optimal control,11 Shenet al. theoretically discussed co-herent control of chemical reactions by pump–dump delay,12

and showed that by proper timing, they were able to transferpractically the entire population to the target state.

Experimentally, the preparation and monitoring ofground-state vibrational excitation is much more difficult,mostly due to the fact that the ground state does not fluo-resce, and is less open to direct observation by other means.As a result, most experiments of femtosecond preparation oftargeted states were carried out in molecular-excited elec-tronic states. Early on, Baumertet al.13 have seen ground-state vibrational excitations in pump-probe experiments. Intheir work, the ground-state population was cycled within thepump pulse, and the observed signal was florescence excitedby the probe in a multiphoton process~also involving highera!Electronic mail: prior@weizmann.ac.il

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 1 1 JULY 2001

2360021-9606/2001/115(1)/236/9/$18.00 © 2001 American Institute of Physics

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electronic states!. Pauschet al.,14 in recent experiments on amolecular beam of potassium dimers, have further used thepump–dump approach to generate vibrational wavepacketsin the ground electronic state of the molecules. The detectionof the ground-state population was done by three-photonresonant ionization. With the introduction of femtosecondlasers, time-resolved experiments were extended to this timerange, and several groups reported the utilization of ul-trashort pulses for the measurement and control of varioustime-dependent processes in small molecules.15–17

In a recent paper,18 we have combined the pump–dumpapproach with time-resolved CARS to prepare and monitorarbitrarily high-vibrational wavepackets in the ground elec-tronic state of molecular iodine, and have demonstrated vi-brational wavepackets up to a vibrational energy of 4500cm21. The method has inherent preparation and observationby light and is applicable also to condensed phases. In arelated experiment, Zanniet al.19 used femtosecond pump/dump to probe and reconstruct the ground electronic state ofI 2

2 within ultrafast photoelectron spectroscopy.

II. „TD…

2CARS

In the present paper, we report the successful experimen-tal preparation of molecules inspecificwavepackets in very-high-vibrational states in the ground electronic state, and theutilization of the ‘‘built-in’’ monitoring of these wavepacketsby femtosecond pulses. Using our recently introducedmethod of two-dimensional time-delayed coherent anti-Stokes Raman scattering~TD!2CARS,18 we are able to popu-late vibrations in the ground state up tov9;38. Althoughvibrational excitation in the electronic ground state wasachieved in previous CARS experiments,20 the ‘‘evolution’’time delay in~TD!2CARS adds a very important degree offreedom to the experiment, enabling the population of muchhigher vibrational-states and the observation of CARS evenfor a large detuning between the pump and Stokes pulses. Adetailed theoretical paper underlining these experiments willbe published separately.21

Starting from the electronic ground state at thermal equi-librium ~more than one vibration is significantly populated!,we generate a wavepacket in an electronically excited stateby means of an ultrashort laser pulse. Next, we allow thegenerated wavepacket to evolve in the electronic excitedstate, where the probability of transition to ground-state vi-brational levels changes as the wavepacket moves along theexcited-state potential surface. When the wavepacket reachesa place~bond length! where it is strongly coupled to thedesired ground-state vibration, we use a second ultrashortpulse to induce an electronic transition to the final wave-packet in the ground state. A third, delayed pulse, completesa CARS sequence, providing information on the generatedwavepacket. Whereas, in principle, the frequency of the thirdpulse will determine the output frequency~CARS is anenergy-conserving process!, in practice, it is easier to use thesame frequency as the pump. In general, the probe pulse canbe resonant or nonresonant with a higher bound electronicstate of the molecule. Such a resonance will naturally affectthe details of the detected signal but in either case, the signal

will provide information about the prepared wavepackets.The present approach of the unified generationandmonitor-ing of the wavepacket is very useful, since without the co-herent real-time detection of the ground state one is unable toverify the generation of the desired wavepacket or utilize itfor further experiments.

Figure 1 schematically shows the energy levels andpulse sequence for the process and the correspondingFeynman double-sided diagram. The given diagram repre-sents one of the 48 terms in the full expression of the third-order polarizationP(3),22 the term which in our case contrib-utes most to the signal. In general, all 48 diagrams should beincluded in any detailed calculation of the third-order sus-ceptibility, but for our resonantly enhanced pulse sequence,the selected diagram is the only one which contributes sig-nificantly to the process. The experimental details are givenbelow, and further theoretical details will be publishedelsewhere.21 In this diagram all the interactions take place onthe ket side of the diagram. The notation is thatB(11) indi-cates vibrational statev8;11 in the electronicB 3PO

u1 state

of iodine. In the experiment, three laser fields interact withan ensemble of molecules. The pump pulse att50 projectsthe ground-state wavefunction onto the excited state, creat-ing a localized vibrational wavepacket in the excitedB state.Next, the molecule evolves in theB state until the next laserpulse. The delay between the pump and the ‘‘Stokes’’ pulsesis the ‘‘evolution’’ time te . The Stokes beamvSt, chosen tomatch the Raman vibrational frequencyVR , brings the mol-ecule down to the desired vibrational region~for example,v9;27) in the electronicX 1Sg

1 ground state. The first twopulses are followed, after a variable time delay (tpr), by theprobe pulse of frequencyvpr ~in our case, equal tovpu),which scatters off the polarization generated in the groundstate by the first two pulses, and creates the signal beam atthe frequencyvout5vpu2vSt1vpr . As is well known, theprobability for generating very dissimilar wavepackets upona Raman process up to the excited state and back down to theelectronic ground state is very low. The introduction of theadditional evolution time overcomes this problem.

The geometry of the experiment is arranged for CARSphase matching such that the signals generated by all the

FIG. 1. (TD)2CARS time-ordering and energy-level scheme. On the right,the double-sided Feynman diagram, contributing most to the induced polar-ization.

237J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Monitoring wavepackets by CARS

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molecules in the interaction zone are added coherently. Sinceelectronic transitions are much faster than the nuclear mo-tion, they are described as vertical transitions between twoelectronic potential surfaces. Moreover, based on the semi-classical dynamic Franck–Condon model,23 we assume thatthe kinetic energy and linear momentum of the wavepacketdo not change during the transition. The transition is efficientwhen the overlap between the wavefunctions on the twoelectronic potential surfaces is maximal. The total energy ofthe wavepacket on the potential surface is the sum of itspotential energyV(B,X) and its kinetic energyEk . The opti-mal induced transition between two potential surfaces occurswhen the Stokes laser frequency matches the difference po-tential Vd5VB2VX . Therefore, the best transition for agiven excitation sequence does not necessarily take place atthe vibrational turning points. From these simplified consid-erations, it is clear that in order to achieve efficient transferto a selected final state, both frequency and timing should beoptimized.

The question of timing is addressed in detail in Fig. 2.The solid curve~scale on the right, cm21! depicts the energydifference between the two potential surfaces. The dashedcurves~scale on the left, fs! give the time when the center ofthe wavepacket for given excitation energies~wavelengths!reaches a specific bond length during the first half of a vi-bration period. The different excitation energies in Fig. 2@16 950 cm21 ~590 nm!, 18 868 cm21 ~530 nm!, and 19 608cm21 ~510 nm!# represent our experimental conditions. Asan example on how to use Fig. 2, consider our experimentalconditions, where we use a Stokes laser pulse oflSt

5800 nm (vSt512 500 cm21) to bring the molecule back tothe ground state. Figure 2, then, should be read as follows:

• Select the frequency for the Stokes laser on the rightscale. (vSt512500 cm21, in our case.!

• Move horizontally to the solid curve of the differencepotential.

• Move vertically to the dashed curve which represents

the wavepacket propagation in theB state for the givenexcitation frequency.~Indicated by a little arrow, point-ing down from the difference potential curve.!

• Read the optimal evolution time on the left scale of thediagram~bond length of;3.05 Å, and a delay of ap-proximately 50 fs!.

As one can see, in the region of Stokes laser energies~difference potential energy! above 10 000 cm21, the valueof te lies between 0 and 60 fs for the first cycle and is onlyslightly affected by the choice of pump frequencies between510 and 590 nm. This observation has been verified in ourexperiments. The optimalte does not change much if onechanges the Stokes frequency between 19 000 and 12 500cm21, and only for very high vibrational excitation whichcorresponds to very low Stokes frequency will the evolutiontime be significantly longer. However, the evolution delaytime is definitely essential for achieving a high degree ofexcitation of the desired vibrational wavepackets. Thus, it ispossible to leave the Stokes laser energy constant, keep theevolution time aroundte;60 fs, and progressively excitehigher-ground-state vibrations with the use of higher pumplaser energies. The best Franck–Condon overlap occurstwice during each vibrational period, and is recurring withthe periodicity of the vibrational period of the excited state,subject, of course, to the spreading of the wavepacket.

All the experiments presented in this paper were per-formed on iodine molecules in a vapor cell heated to 350 K~;10 Torr!. Thus, higher vibrational levels in the ground-state are significantly populated, and the nonlinear CARSprocess does not start from a single state, but rather fromseveral populated ground-state vibrations.

In general, the CARS signal for a given evolution timete

is proportional to the time-integrated-squared third-order po-larization induced in the molecule.24 The first laser pulsedetermines the beginning of the interaction and the integra-tion over t8 gives the integration time of the signal:

S~ te ,tpr!}E2`

`

uP~3!~ t8!u2dt8, ~1a!

with

^P~3!~ t !&5(i

bi^c i~0!~ t !umuc i

~3!~ t !&1c.c. ~1b!

Equation~1b! is a weighted sum of terms, each of whichis described by a Feynman diagram of the type given in Fig.1, and the weightbi is defined by the initial Boltzmannpopulation in that state.m is the total dipole moment operatorfor the transition andc (n) is the nth order wavefunction asgiven by Meyeret al.25 Equation~1b! shows how the differ-ent initial vibrations contribute to the signal. The treatmentof Meyeret al. is based on a wavefunction formalism, wherethe different initial states may be included weighted by theBoltzman factor.26 Pastirket al.27 based their calculation onthe density matrix formalism, and have included a largernumber of initial ground-state levels. For a general textbookderivation, see Mukamel’s book.24 The exact evaluation ofS(te ,tpr) is rather complicated and will be presentedelsewhere.21 Here, we give an intuitive explanation for the

FIG. 2. Stokes pulse timing optimization diagram. The solid curve repre-sents the difference potential curve, with the scale on the right~cm21!. Thedashed curves present the timing and location of the wavepackets preparedat given excitation energies during the first half cycle. The prescription ofhow to use this figure is given in the text.

238 J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Pinkas, Knopp, and Prior

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observed phenomena. To see the effect of the many initialstates, we insert Eq.~1b! into Eq.~1a! and obtain the follow-ing expression:

S~ te ,tpr!}E2`

` U(i

bi Pf i~ te ,t8!U2

dt8. ~2a!

The expectation value of the third-order polarizationstarting from one initial leveli is written asPf i(te ,t). Fordemonstration purpose, consider only two initial states num-bered 1 and 2, going to a final statef. S(te ,tpr) then becomes

S~ te ,tpr!}~b1!2E2`

`

uPf 1~ te ,t8!u2dt8

1~b2!2E2`

`

uPf 2~ te ,t8!u2dt8

1b1b2E2`

`

uPf 1~ te ,t8!Pf 2~ te ,t8!udt8

1b2b1E2`

`

uPf 2~ te ,t8!Pf 1~ te ,t8!udt8. ~2b!

Expression~2b! of the full CARS signal includes crossterms, in which the contributions to the polarization originat-ing from the different ground-state levels~here 1 and 2! areimportant. The full CARS signal given in Eq.~2a! above,consists of all such pairs originating from the participatinglevels. These terms will lead to a beating pattern in the sig-nal. Our experimental conditions are such that the laser spec-tral width covers 2–3 vibrational levels in the ground state,and 4–6 levels in the excited state. Moreover, the Franck–Condon factors of the different vibrational transitions differgreatly as one moves to higher-vibrational levels in theground state~see below!, and thus actual exact resonancesfor the two transitions simultaneously are not very commonwhen one excites to a bound state. It can be shown that theseterms vanish unless there is exact resonance for the two tran-sitions, which will occur automatically for excitation into acontinuum. In the latter case, one cannot distinguish betweenthe various initial states contributing to the coherent sum. Adetailed theoretical evaluation of the physical meaning of Eq.~1a!, including analysis of different initial vibrations withtwo independent time delays, leads to very interesting con-clusions about the nature of these interferences, and will bediscussed elsewhere.21

Clearly, if the transition probability for one of the tran-sitions involved in an interference is very small or zero, thatparticular cross term also vanishes. Expressed in a differentlanguage, if we separate thePf i into time-dependent andtime-independent parts,

Pf i}m j i * AFCFji * Pf j~ te ,t !, ~2c!

one can see that the cross terms disappear if the Franck–Condon factor FCFj i for the initial transition from a ground-state vibrationi to the excited-state vibrationj is zero.

III. EXPERIMENTAL RESULTS AND DISCUSSION

The two laser beams are derived from independentlytunable optical parametric amplifiers pumped by a femtosec-ond oscillator regeneratively amplified. The pulses were lessthan 50 fs in duration, and of order of 10mJ each~afterfrequency doubling or mixing to the visible spectral range!.The beams are brought to a joint focus in a three-dimensional forward propagating folded BOXCARSarrangement.28 The CARS emission is directional in thephase-matched direction. The signal is detected by a photo-multiplier tube followed by a gated boxcar integrator andsignal processing. All pulses are vertically polarized. Wemonitor the coherent polarization in the ground state by thedetection of the CARS signal generated by the probe beamas it scatters from that polarization. Full experimental detailswere given elsewhere.18

The method of~TD!2CARS enables the optimization ofthe timing and frequency of the Stokes pulse for best cou-pling to a specific ground-state vibration. The observationtechnique separates the ground- and excited-state dynamicsso that it is possible to follow the wavepacket dynamics inhigh-vibrational levels as they evolve. As an illustration, wefollow the evolution of a ground-state wavepacket aroundv957 during its oscillations in the excited electronic state.Figure 3 depicts the~TD!2CARS signal for different evolu-tion times (te) for vpu517 215 cm21 andvSt515 850 cm21

(VR51365 cm21!.The left panels show the time-domain transient signal as

a function of the probe delaytpr , and the right-hand sidedepicts its Fourier transform~FT! of these transients. Atte

close to zero, a coherent transient is observed attpr50, notshowing any contributions from ground- or excited-state vi-brations. As the evolution time delay is increased, a maxi-mum in the ~TD!2CARS signal is observed aroundte

560 fs(A). Further increase inte causes the population ofthe vibrational state to decrease, until it almost disappearsagain at 170 fs, and then reappears periodically with thevibrational period~approximately 340 fs!. Even thoughte

was optimal at 60 fs evolution, and the duration of our pulsesis ;35 fs, one can see the importance of the delay. Thepanels of the Fourier transforms show the same trend. Fol-lowing the intensity of the component close to 200 cm21 ~D!,one sees more clearly where the optimal evolution time be-fore applying the Stokes pulse is. When the second cyclearrives~B, E! the wavepacket in the excited state is broaderdue to some dephasing, and the choice of the time for theStokes pulse is wider, although generally the intensity islower. The intensity profile provides information on theB-state dymnamics. These have been measured by Kieferand co-workers as transients with negative time delay.20 Thesame applies to the third cycle~C, F!, where the optimalevolution time is around 740 fs.

Figure 4 depicts~TD!2CARS transients, obtained whilegenerating vibrational wavepackets in different regions in theground electronic state, under varying pump and Stokes laserfrequencies. In this and the following figures, we use thefollowing notation for the laser pulses involved(lpu/lSt/lpr /lout) in nm.

Figure 4~a! shows the wavepacket dynamics of the

239J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Monitoring wavepackets by CARS

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ground state with the~580/640/580/530! excitation schemeand the resulting Raman shift ofVR51626 cm21. The exci-tation with 17 240 cm21 generates a wavepacket in the ex-cited state atv8;13. In Fig. 5 we show the Franck–Condonfactors weighted by the Boltzmann factor for 350 K.29 In thiscase, the initial vibrations most contributing to the signal arev51 andv52. The vibrational energy of these states addsanother 213 or 425 cm21 to the resulting ground-state vibra-tion excitation energy. The peak in the relevant FT spectrum

appears at 203 cm21, which corresponds tov9;9 in theelectronic ground state. The transient was measured withte

;300 fs, which is;30 fs before completing a full cycle inthe excited state. The relatively longte was used in order toavoid any residual excited state or coherent spike contribu-tions to the signal, and to obtain a clearer ground-state sig-nal. According to Fig. 2, a Stokes frequency of 15 625 cm21

leads to an optimalte of ;30 fs in the first cycle.In Fig. 4~b! the excitation scheme is~585/722/585/478!

FIG. 3. (TD)2CARS transients for varying evolution times, showing the optimum timing of the Stokes pulse to be;60 fs during the first cycle in theB state~A, and corresponding FTD!. The next two Franck–Condon windows can be seen inB ~and FT inE!, andC ~and FT inF!.

240 J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Pinkas, Knopp, and Prior

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and, therefore, the Raman shift is 3243 cm21. The pumpenergy of 17 094 cm21 creates a wavepacket aroundv;12in the B state. In this scheme, the main participating levelsare v52, 1, and 0, with contributions fromv53 and 4 aswell, which allows the generation of ground-state wavepack-ets as high as 3880 cm21 abovev50, corresponding tov9

;20. The optimal evolution time delay waste;50 fs, whichis also in good agreement with the model presented in Fig. 2.Consider the fast FT spectrum in Fig. 4~b! showing a mainpeak at 190 cm21, which corresponds indeed tov9;20 inthe ground state,30 and two sidebands at620 cm21 from themain peak. Since the exciting pulses are very broadband~over 500 cm21 wide!, the generated wavepacket includesseveral ground-state vibrations~as many as five states in thepresent case!. These states oscillate at their own characteris-tic frequency, and if excited coherently, will display a beat-ing pattern between the components of the excited wave-packet. The main contribution at the mean excitation at190 cm21(v9;20) is modulated at the frequency corre-sponding to the difference between the characteristic fre-quencies of the various levels initially excited by the pulse,in this case, 20 cm21. These side peaks have their origin inpolarization beats between signals coming from the differentvibrational levels in the electronic ground state, as mentionedbefore, and will be observable as long as the four-wave-mixing signal is emitted before averaging occurs. Becausethe third pulse excites the molecule above theB-state disso-ciation, the lifetime of the last induced polarization is of theorder of the pulse duration, the signal is ‘‘prompt’’ on therelevant time scales, and the beating does not average out.Detailed theoretical calculations elaborating this point willbe presented elsewhere.

Next, in Fig. 4~c! we have a similar situation. The exci-tation sequence is~585/800/585/463! with VR54594 cm21.

FIG. 4. Four transients, obtained while generating vibrational wavepackets in different regions of theB state and the corresponding FT. The beating structurein cases~b! and ~c!, has its origin in contributions, coming from different initial vibrational ground states~see the text!.

FIG. 5. Boltzmann-weighted Franck–Condon factors for theB←X transi-tion of iodine at a temperature of 350 K. Exciting tov8537 in theB statewill mostly favor transitions fromv950, while exciting tov8515 willinvolve v950, 1, 2, 3, 4, and 5.

241J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Monitoring wavepackets by CARS

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Using the same pump frequency we were able to createwavepackets of 5230 cm21 abovev50 in the ground state.The FT shows the characteristic frequency of 180 cm21(v;28) and the two sidebands, as expected, at630 cm21.Compared to the previous figure@Fig. 4~b!#, the energy ofthe wavepacket plus the energy of the probe photon 17 094cm21 are even higher above the dissociation limit of theBstate, which causes a distinct beating pattern.

In the next step, the excitation energy was increased to19 050 cm21 ~525/800/525/390!. The FT spectrum depicts asingle peak at a frequency of 167 cm21, corresponding to thevibrational frequency ofv9;38 for iodine.30 Even thoughthe fingerprint of the wavepacket in the signal is clear, itsabsolute intensity is much weaker than in the previous cases.One reason for that might be the loss of the electronic reso-nance of the probe pulse with theB state of iodine. In the~525/800/525/390! scheme, the probe pulse reaches almost;6000 cm21 above the dissociation limit of theB state. Thisparticular case is considered in more detail in Fig. 6. Thereare two ways of reaching higher-vibrational levels~largerRaman shifts!. One way is to increase the energy of thepump photon, and the other is to decrease the energy of theStokes photon. Due to experimental reasons~at 800 nm, ahigh-power pulse is available from the regenerative ampli-fier!, it was more convenient to increase the energy of thepump photon, keeping the Stokes laser at 800 nm. This useof a higher-power pump power also explains the fact that theobserved signal level is not significantly reduced as we climbhigher and higher above the dissociation limit in theB state.Increasing the pump/probe frequency will reach higher andhigher above theB-state resonance while probing the wave-packet, and this will enhance the beating structure in thesignal. However, even at these higher frequencies, it is stillpossible to select a pump frequency such that the beatingeffect is minimized. This selection is based on the possibilityof selecting a transition where the FCF of one or more of thevibrational transitions is very small. With the increase of the

pump frequency, the first initial transition takes place atshorter internuclear distances, and then the most probableinitial state is thev50 in the ground state. At certain fre-quencies, the contributions from the other initial ground-statevibrations will be orders of magnitudes smaller and crossterms become vanishingly small. This situation occurs atlpu;525 nm. The 19 048 cm21 excitation generates a wave-packet aroundv9;36 in theB state. As we can see in Fig. 5,the main contribution comes from thev50 ground-statelevel. The contribution ofv52 is already ten times smaller.Thus, the contributions from higher-vibrational levels can beneglected at this point, and the signal should not show anybeating pattern. Figure 6~top! shows exactly this situation.At te of 50 fs, we see clear oscillation with a period of;200fs. The FFT depicts the frequency of 167 cm21, which can berelated tov9;38 in the ground state. In fact, we are depos-iting energy close to 7000 cm21 ~0.85 eV! into a ground-state vibration. Furthermore, at the bottom part of Fig. 6, weshow that even under these difficult conditions of excitationinto extremely high-vibrational levels in theB state, it is stillpossible to observe a signal from the ground-state wave-packet after a full cycle in the excited state~;530 fs!. Evenin these high-vibrational regions, the semiclassical descrip-tion used in the beginning of the paper still gives fairly goodapproximations for the optimal timing.

Time-resolved four-wave-mixing~FWM! spectroscopyprovides additional possibilities for the monitoring of wave-packet dynamics beyond the scheme discussed in the firstparts of this paper. We can change the time ordering of thequantum-mechanical-interaction pathways and vary thewavelength of the different lasers so that we enhance otherresonances and probe different processes.22,24,27As discussedearlier, for the way we used the~TD!2CARS approach, themain contribution to the detected signal is given by the dia-gram described in Fig. 1. Different configurations can beprobed by further increase of the pump pulse frequency with-out any other changes in the experimental setup or the detec-tion scheme, but realizing that different diagrams now con-tribute to the FWM signal. Figure 7 depicts the transientsignal for an excitation scheme of~510/800/510/375! and itsFT. The FT shows peaks at 31 and 36 cm21 and some othervalues in the 0–20 cm21 region. In order to understand thechange in the structure and periodicity of the signal, we mustconsider other electronic potential curves of the iodine mol-ecule. A simplified partial potential-energy diagram is givenin Fig. 8, which includes theX 1Sg

1 , the A 3P1u , and theB 3PO

u1 state~drawn as Morse potentials!. In addition, the

energy level of the state allowing two-photon absorption31 ismarked with the gray horizontal bar shown in Fig. 8. In allthe experiments discussed so far, we took only two elec-tronic states~X,B! into consideration. The 510 nm excitationpulse~;19 600 cm21! reaches theB state close to its disso-ciation limit and a two-photon excitation will be in near reso-nance with theOg

1(1S) state ~which dissociates into twoexcited I 2P1/2 atoms!. In addition, we should also considertheA3P1u state. TheA←X transition is relatively weak andis normally obscured by the much strongerB←X absorption.Thus, information about this state and its dynamics is notcommon. The minimum of its potential appears atTe

FIG. 6. Dynamics of a wavepacket created at 7000 cm21 abovev950 in theelectronic ground state. The lower part of the figure shows the same dynam-ics after a full cycle in theB state (te5530 fs).

242 J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Pinkas, Knopp, and Prior

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510 907 cm21 according to Appadooet al.32 and the depth is;1600 cm21. The 800 nm Stokes laser is strongly resonantwith this state, therefore, theA←X absorption is now com-parable to theB←X absorption. Under these conditions, adifferent description of the CARS process is needed. Unlikethe previous case, now the Feynman diagram in Fig. 8 pro-vides the dominant contribution to the observed coherent sig-nal, and the dynamics of the~510/800/510/375! experimentmay be described as follows: The pump pulse excites awavepacket in theB state of iodine aroundv8;50. Simulta-neously, the Stokes pulse excites a wavepacket in the iodineA state aroundv8;30 close to theA-state dissociation limit.A Feynman diagram can be completed if the Stokes pulseinteraction takes place on the bra side of the diagram, andtherefore, the stimulated emission occurs between theOg

1(1S) state and theA state on the ket side. The time-

delayed probe pulse is probing the generatedA- andB-statepolarizations using the close resonance to the ion-pairstates for enhancement of the process. The signal photoncompletes the process, connecting theOg

1(1S) state with theA state of the molecule. In this particular diagram, the time-delayed probe should show evidence of both theB- andA-state wavepacket dynamics. The strong peak at 31 cm21

~Fig. 7!, is related to the vibrational frequency of theB statearoundv8;50 and the peak at 36 cm21 fits theB-state fre-quency atv8;47. In the range of 60–70 cm21, we can see,with much lower intensity, the overtones of these frequen-cies. The peaks in the low region of the FT at;7 and;12cm21 probably reflect theA-state dynamics, but due to thestrong anharmonicity of theA state in the excited region, andbecause the broad linewidth of the lasers overlap many vi-brational levels, it is not possible to determine the exact fre-quency components. It should also be mentioned that thecontributions to the signal from the diagram in Fig. 1 arevanishingly small because of detuning from electronic reso-nance of the probe photon. Thus, the typical signature of thatdiagram at 160 cm21 could not be observed in the FT of thetime-delayed signal. Even though the process described byFig. 8 was weak in intensity, it still provides another optionfor probing vibrational wavepackets with a time-resolvedCARS-like excitation scheme, and shows the flexibility ofthe method of time-delayed coherent preparation and probingtechniques. In all the above, rotational effects are ignored,and thus, the low-frequency components cannot be analyzedin detail. To overcome this difficulty, experiments in cooledmolecular beams are required, or longer averaging times areneeded which will provide reliable higher-frequency resolu-tion. Moreover, while in the first set of experiments a singleFeynman diagram is the dominant contributor to the signal,21

here there might be more than one diagram, and a carefulanalysis is required.

IV. CONCLUSION

In summary, we have demonstrated a new approach,~TD!2CARS, to the efficient excitation and monitoring ofwavepackets in high vibrations in the electronic ground state.We applied the method to iodine vapor, and demonstratedthe excitation of wavepackets centered aroundv9;38, muchhigher than previously possible. By proper timing of the la-ser pulses, one can optimize the selective transfer to the spe-cific vibrational wavepackets, and follow their evolution bytransient CARS spectroscopy. Experiments, reaching the re-gion close to the dissociation limit of the ground state, oreven theA state by lowering the Stokes laser frequencydown to ;8000 cm21 and lower, are already in progress.~TD!2CARS is a good method to cover this region.

The built-in diagnostics is an essential ingredient of themethod, since otherwise it is impossible to probe the gener-ated wavepacket, or optimize its creation. The method enjoysall the advantages of a CARS technique, coherent emissionof a background-free signal, and time resolution which islimited by the laser pulses themselves. Moreover, as an all-optical technique, it is nonintrusive, and can be applied tocondensed phases, liquids, and solutions, and to any mol-

FIG. 7. 510/800/510/375 nm excitation scheme shows periodicities, whichcannot be related to the ground-state vibrations. In this case, the differentprocesses exhibitA- andB-state dynamics.

FIG. 8. Energy potential curves of theX, A, andB states of iodine~drawn asMorse potentials!. The Og

1(1S) state, which allows the two-photon transi-tion, is schematically given by the gray bar in the upper part of the figure.The arrows in the figure show the resonances of the process, which is de-scribed by the double-sided Feynman diagram on the right.

243J. Chem. Phys., Vol. 115, No. 1, 1 July 2001 Monitoring wavepackets by CARS

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ecule regardless of its specific electronic states. We havepresented a working prescription for using this method, and asimple analysis in terms of the difference potential betweenground and excited electronic states. Based on these results,we are presently continuing with further experiments to dem-onstrate our ability to use the selective excitation.

ACKNOWLEDGMENTS

The authors wish to thank Jim Faeder for many illumi-nating and deep discussions. The authors also thank D.Tannor and I. Averbukh for useful comments. The work wassupported in part by a grant from the Minerva Foundationand from Rita Marcus, New York.

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