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Chemical Physics Letters 421 (2006) 523–528

Enhancement of Raman modes by coherent control in b-carotene

Jurgen Hauer a,b, Hrvoje Skenderovic a,c, Karl-Ludwig Kompa b, Marcus Motzkus a,b,*

a Max-Planck-Institut fur Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germanyb Fachbereich Chemie, Physikalische Chemie, Hans-Meerwein-Strasse, D-35043 Marburg, Germany

c Institute of Physics, Bijenicka 46, 10000 Zagreb, Croatia

Received 22 December 2005; in final form 13 January 2006Available online 6 March 2006

Abstract

The enhancement of vibrational modes by phase-shaped femtosecond laser pulses is studied under resonant and non-resonant con-ditions in an open loop coherent control experiment using non-linear Raman spectroscopy. Applying multipulse sequences matching theperiodicity of single vibrations, the modes of b-carotene solvated in cylcohexane were not only specifically excited, but under resonantconditions also enhanced compared to the Fourier-limited case. This effect is attributed to an increased population transfer to the excitedstate and stronger coherences created and demonstrates the feasibility to selectively amplify ground state Raman modes by coherentcontrol.� 2006 Elsevier B.V. All rights reserved.

1. Introduction

The capability to modulate femtosecond laser pulses inphase and amplitude has stimulated numerous experimentsaiming at the control of quantum phenomena [1–4]. Suc-cessful control schemes for specific product channels andfor molecular states were demonstrated in a variety of sys-tems [5–11]. However, in many of the studies the shapedlaser pulse suppresses unwanted pathways and thereforemerely acts as a filter. Examples where the desired targetstate is reached with higher efficiency than in the Fourier-limited case are rare. To explore the underlying mecha-nisms of coherently controlled quantum phenomena it isimportant to understand if an optimal shaped laser pulsecan overcome the limitations defined by a Fourier-limitedlaser pulse as it has been shown for example by the STI-RAP control scheme in frequency domain [12].

One promising mechanism in time domain exploits pulsesequences, which selectively excite Raman transitions andare generated by simple periodic modulation of spectralphases [13–18]. For example optimal control experiments

0009-2614/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2006.01.115

* Corresponding author. Fax: +49 6421 28 22542.E-mail address: motzkus@staff.uni-marburg.de (M. Motzkus).

on energy flow in a biological complex identified multipulsestructures by a closed loop set-up which selectively excitedlow-frequency modes leading to an enhancement of theratio of internal conversion vs. energy transfer [10]. Recentoptimal control studies on the resonant one-photon transi-tion of a dye in solution by Prokhorenko et al. [19] showedthe possibility of increasing transition probabilities byapplying multipulses and revealed an 8% increase in trans-ferred population compared to the Fourier-limited pulse.In a recent experiment using four-wave-mixing (FWM)[13,16,17,20,21] Nagasawa et al. [22] were able to enhancelow-frequency oscillations in a dye-doped polymer at 10 Kby setting appropriate time delays between two of the threeDFWM-pulses.

In this Letter, the effects of pulse trains with specific timeseparations between the subpulses were studied with specialemphasis on electronic resonance conditions during theexcitation process. We will show that resonant excitationis a mandatory condition to enhance Raman transitionsin complex molecular systems. The molecule under investi-gation is all-trans-b-carotene, which plays a crucial part inphotosynthetic light harvesting. The kinetics of b-carotenehave been studied extensively [23], including the coherentdynamics of the high frequency modes in the electronicground state S0 [24,25].

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2. Experimental section

The laser system used was a Ti:Sapphire based femtosec-ond laser at 2 kHz repetition rate, delivering 190 fs pulses at700 lJ. It pumped a non-collinear parametric amplifier(NOPA) with an output of typically 10 lJ at 510 nm or14 lJ at 550 nm (Fig. 1). The NOPA-pulse was subsequentlyspilt into the three FWM-beams: pump, stokes and probepulse. To shape the spectral phase of the first two pulses, a4f-pulse-shaper with a 640 pixel spatial-light-modulator(SLM) [26] was used. In the case of transform-limited pulses,a temporal resolution of 22 fs was achieved as determined byan instantaneous DFWM- signal in glass. This transient-freesignal is equivalent to a v(3) FROG [27]. By the same means, itwas confirmed that the temporal shape of the pulse adjustedin the SLM was maintained after passage through the sam-ple. Therefore, reshaping of the pulse could be excluded.

A 250 lm cell was filled with all-trans-b-carotene inHPLC-grade cyclohexane, which was used as received(Sigma–Aldrich). Optical densities of about 0.7 at 480 nmwere used in order to obtain feasible signals at excitationin the red wing of the S0! S2 transition of b-carotene(see dashed line in Fig. 1).

The spectrum in Fig. 1 shows the first optical allowedelectronic transition in b-carotene (S0! S2) with the char-acteristic electronic sub-structures [23]. The two Gaussiancurves represent the pulse spectra used for resonant(dashed) and non-resonant (dashed-dotted) excitation. Inour experimental set-up, shortest pulse durations around16 fs were achieved near 550 nm (non-resonant excitation).Pulses with a centre wavelength of 510 nm performed reso-nant excitation, providing both clear overlap with theS0! S2 transition of b-carotene and short pulse durationof below 20 fs. The criterion of short pulses is crucial forthe detection of high frequency Raman modes in aDFWM-experiment [28]. The typical pulse energy was30 nJ for the pump and the stokes pulse and 14 nJ for theprobe pulse in the case of resonant excitation. In the non-

Fig. 1. Absorption spectrum of b-carotene in cyclohexane (solid line) andspectra of resonant (dashed) and non-resonant (dashed-dotted) excitationpulses.

resonant case, the energies of the pump and the stokes pulsewere doubled in order to achieve a feasible level of signal.

To obtain the desired pulse trains for pump and stokesin the DFWM-sequence, a sinusoidal phase functionuPulseTrain was applied on the SLM.

uPulseTrain ¼ a sinðbxÞ ð1ÞIf the period 1/b coincides with the vibrational frequencyspacing of a Raman mode X or an integer multiple thereof,this mode will be exclusively excited over all the othervibrations also addressed by a Fourier-limited pulse. Asshown by Weiner et al. [15], the excitation probability fora mode addressed by a non-resonant pulse train is alwayslimited by the excitation probability in the Fourier limitedcase. Nonetheless, it is shown in the present work that res-onant pulse trains allow for an enhancement of Ramanmodes in comparison to a transform-limited pulse.

The parameter a was set to 1.23. According to Zeidleret al. [29], this value guarantees that the pulse amplitudebetween the sub pulses goes to zero, which is crucial forthe coherent control effect. This choice of a = 1.23 also lim-its the number of sub pulses with feasible intensity to three.The actual spacing between the sub pulses was verifiedprior to every experiment.

It is important to note here that for selective excitation,the temporal spacing between the peaks of a pulse traindetermined by b can match either the Raman period 1/Xor an integer multiple of the same. This is a crucial factas the duration of an unshaped pulse in the DFWMsequence is sub 20 fs. The period of the shortest groundstate mode under investigation is only 21.9 fs, which wouldmake the construction of a matching pulse train impossible(see Table 1). For the mode at 1524 cm�1 corresponding tothis fundamental period, an excitation with a pulse trainspacing of 109 fs was sufficient, matching the mode’s fifthharmonic. An excitation with such a pulse train also guar-antees for selective excitation as its period is already wellseparated from those of the other two ground state modes.

Besides the capability of selective excitation of one outof the three modes, it was also possible to excite two modessimultaneously while suppressing the third. For example, aperiod of 66 fs allowed for excitation of the modes at 1004and 1524 cm�1. The mode at 1156 cm�1 (T = 28.8 fs) is thestrongest under Fourier limited conditions. A 66 fs pulsetrain matches the 2.3 multiple of the mode’s fundamentaland is therefore out of phase with it, which results in a sup-pression of this mode.

The probe pulse was kept transform-limited. To obtainthe transient data, the time delay s between the first two

Table 1Pulse train spacings used to selectively excite single ground state modes(italized) and 1524 and 1004 cm�1 simultaneously (underlined)

Energy (cm�1) T (fs) 2T (fs) 3T (fs) 4T (fs) 5T (fs)

1524 21.9 43.8 65.7 87.6 109.5

1157 28.8 57.6 86.4 115.2 144

1004 33.2 66.4 99.6

Under T the fundamental periods.

Fig. 2. (a) DFWM-signal as a function of wavelength and delay time s under resonant excitation. The coherence spike around s = 0 is not shown. (b)Cutoff of the 2D transient dataset at a specific detection wavelength.

Fig. 3. (a) FFT-spectrum after non-resonant excitation with unshaped pulses. (b)–(d) Excitation with appropriate multipulses leads to exclusivepreparation of one mode. (e) comparison of Raman intensities after shaped and unshaped excitation pulses with equal energy.

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Fig. 4. (a) FFT-spectrum after resonant excitation with unshaped pulses. A solvent mode is marked with an asterisk. (b)–(d) FFT spectra after excitationwith multipulses. (e) comparison between a) and (c). In contrast to non-resonant excitation, the resonant multipulses enhance Raman modes compared toa Fourier-limited pulse of equal energy.

526 J. Hauer et al. / Chemical Physics Letters 421 (2006) 523–528

pulses and the probe pulse was varied in steps of 2 fs. TheDFWM signal was recorded with a CCD-camera at eachstep, leading to a signal described by

IðsÞ /Z

dtjP 3ðt; sÞj2 ð2Þ

Only positive delays s were considered. To predeterminethe signal’s direction by phase matching, the folded BOX-CARS geometry was chosen. This also allowed for minimi-zation of stray light.

3. Results

Fig. 2 shows a 2D-contour plot [30] of a typical resonantsignal, resolved in wavelength and time. For this and all

consecutive measurements, the arrival time of the pumpand the stokes pulse is set to be equal. The transients eval-uated below (see Fig. 2b) are slices of such a 2D-plot, takenat certain detection wavelengths. Regardless of whether themolecule is excited resonantly or non-resonantly, the signalis characterized by a fast rise of 160–200 fs around s = 0(not shown in Fig. 2), known as a coherent artefact [31],which is omitted in all further discussions.

The vibrational modes, whose control is the aim of theexperiment, are shown in Fig. 2b. In the transients, theyappear as fast oscillations superimposed on the slowlydecaying DFWM-signal. After subtraction of this back-ground, a Fourier transformation with zero padding andWelsh’s apodization of the transient data directly lead tothe characteristic vibrational modes of b-carotene.

J. Hauer et al. / Chemical Physics Letters 421 (2006) 523–528 527

3.1. Non-resonant excitation

Fig. 2b shows a typical resonant DFWM-transient. Asan important difference, non-resonant transients exhibitweaker oscillations [32]. The Fast Fourier Transform(FFT) spectra of the non-resonant transients with excita-tion at 550 nm are shown in Fig. 3a. The phase of all pulseswas left unshaped. At 529 nm detection wavelength, threevibrational modes at 1004, 1156 and 1532 cm�1 can be seen.These are the ground state modes of b-carotene as knownfrom frequency domain spectroscopy [23]. If the first twopulses in the DFWM-sequence are phase shaped, one ofthese modes can be excited exclusively over the others, asseen in Fig. 3b–d. The multipulses show excellent filteringcapabilities. Undesired modes can be totally suppressed.

A direct comparison of Raman intensities after shapedand unshaped non-resonant excitation is given in Fig. 3e. A pulse train matching the fifth harmonic of the stron-gest mode seen with transform-limited pulses was chosen.The shaped and the unshaped beams had equal energiesof 60 nJ. The shaped spectrum shows only the desiredmode. Its intensity however, is less than 60% of that inthe Fourier-limited (unshaped) case. In agreement withtheory [13], the Fourier-limited case is the upper boundaryfor all transition probabilities. The multipulse filters out thedesired mode but does not enhance it. Theoretically, theintensities of the shaped and unshaped mode are expectedto be equal when a matching pulse train is applied. The rea-son why the signal is even less is the limited number of pix-els in the SLM. Only less than ideal pulse trains, which donot perfectly match the vibrational frequency, are realisa-ble yielding transition probabilities below the Fourier-lim-ited case.

3.2. Resonant excitation

Like under non-resonant conditions, adequately spacedpulse trains allow for full control over the detected ground

Fig. 5. Comparison between unshaped (left) and shaped (right) resonant rawentire fitting window of 4 ps is shown. (b) In the shaped case, only the desired

state modes. Fig. 4 a shows an FFT-spectrum after reso-nant excitation with Fourier-limited pulses.

The oscillations are again in perfect agreement with fre-quency domain data. In analogy to Fig. 3, 4b–d were takenafter excitation with a multipulse matching the period ofthe respective mode. Like in the non-resonant case, thepulse trains show excellent filtering capabilities. Alldetected ground state modes can be selectively excitedwhile the others are suppressed completely. Fig. 4e showsthe most striking difference between multipulse excitationon and off resonance. In the former case, Raman intensitiescan be enhanced in comparison to a Fourier-limited pulseof equal energy.

4. Discussion

In order to gain information on the amplitudes of theformed vibrations and to quantify the success of theemployed control scheme, the following simple and intui-tive formula 3 was applied to fit the transients. It is basedon the assumption that each mode oscillates and decaysexponentially with independent decay constants for eachvibration.

SðtÞ ¼Xn

i¼1

Aie�t=si sinðxit þ /iÞ ð3Þ

The parameters of the above sum of damped sine func-tions were fit to the whole transient data set of 4 ps via a glo-bal analysis based on an evolutionary algorithm [29], n isthe number of modes taken into account, each with an oscil-latory amplitude Ai. The frequencies xi were taken from thecorresponding FFT-spectrum, /i are corrective phase termsand si are respective vibrational dephasing times. Ten runsof the evolutionary algorithm were averaged for each tran-sient. The parameters obtained showed a scatter of less thanfive percent between the runs. The measured transient dataand the Fourier spectra were reproduced satisfactorily ascan be seen in Fig. 5. The transients also differ qualitatively.

data taken at 484 nm and the fit according to Eq. (3). Only a part of themode is present.

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After Fourier-limited excitation (unshaped data in Fig. 5),slow mode beatings are still observable. The shaped tran-sient shows the desired mode only.

The pulse-sequences were set to coincide with the vibra-tional period of the modes at 1004, 1156 and 1532 cm�1.According to the model given in Eq. (3), the ratio of theintensity of the shaped modes (s) and the unshaped ones(u) decreases with the mode’s wavenumber. A similar effectwas reported in Ref. [22]. Under resonant conditions, s/ufor the mode at 1004 cm�1 is 5.73. For 1156 cm�1 it is5.5 and 2.5 for 1532 cm�1. In the case of non-resonant exci-tation carried out at 550 nm, no such enhancementoccurred. The s/u-ratio was 0.6.

This important difference between resonant and non-res-onant excitation strongly suggests that the excitation bymultipulses increases the population transfer between thetwo electronic states involved compared to an unshapedpulse. We add further proof to this assumption in a tran-sient absorption experiment [33], where we show that mul-tipulses allow for a more effective population transfer tothe excited state of a dye molecule and create strongervibrational coherences than a Fourier limited pulse ofequal energy.

5. Conclusions

In summary, we introduced a DFWM-experiment, inwhich we were able to excite vibrational modes selectivelyby coherent control. The quantitative analysis showed thatthe intensity of the modes in the case of shaped excitation(multipulses) exceeded the intensity after a Fourier-limitedpulse by a factor of up to 5.7. We attribute this to strongervibrational coherence and enhanced population transfer tothe excited state and back to the ground state by the phase-modulated pump and stokes pulses. The possibility ofselecting and enhancing vibrational modes by multipulsesopens a wide range of opportunities to study the role ofcertain molecular oscillations in photochemical reactions,even on electronically excited states [28].

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