quantum control spectroscopy of vibrational modes: comparison of control scenarios for ground and...

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Chemical Physics 350 (2008) 220–229

Quantum control spectroscopy of vibrational modes: Comparisonof control scenarios for ground and excited states in b-carotene

Jurgen Hauer, Tiago Buckup, Marcus Motzkus *

Fachbereich Chemie, Physikalische Chemie, Philipps-Universitat Marburg, Hans-Meerwein-Strasse, D-35043 Marburg, Germany

Received 14 September 2007; accepted 11 March 2008Available online 25 March 2008

Abstract

Quantum control spectroscopy (QCS) is used as a tool to study, address selectively and enhance vibrational wavepacket motion inlarge solvated molecules. By contrasting the application of Fourier-limited and phase-modulated excitation on different electronic states,the interplay between the controllability of vibrational coherence and electronic resonance is revealed. We contrast control on electronicground and excited state by introducing an additional pump beam prior to a DFWM-sequence (Pump-DFWM). Via phase modulationof this initial pump pulse, coherent control is extended to structural evolution on the vibrationally hot ground state (hot-S0) and lowestlying excited state (S1) of b-carotene. In an open loop setup, the control scenarios for these different electronic states are compared intheir effectiveness and mechanism.� 2008 Elsevier B.V. All rights reserved.

Keywords: Femtochemistry; Coherent control; Four-wave-mixing; Pulse shaping; Carotenoids; Nonlinear Raman spectroscopy

1. Introduction

Since the advent of ultrashort laser pulses, there hasbeen a growing interest in not only to analyze but also tomanipulate the course of quantum chemical events [1–4].A highly relevant sub-set of coherent control scenarios isthe selective excitation of molecular vibrational modes[5–10]. In the pathway approach to ultrafast photochemis-try, such structural movement may represent motion alonga reaction coordinate on a molecular potential energy sur-face [11]. Hence, control over vibrational degrees of free-dom can be the key step in the effort to determine theoutcome of a photochemical reaction. A challenging aspectof this promising attempt is posed by the fact that the deci-sive events in a molecular trajectory may take place onexcited-state potential energy surfaces.

The investigation and control of excited-state dynamicsis especially attractive in the case of biological chromoph-

0301-0104/$ - see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2008.03.021

* Corresponding author. Tel.: +49 6421 28 22541; fax: +49 6421 2822542.

E-mail address: [email protected] (M. Motzkus).

ores, due to the possible insight gained on light-steered bio-logical functions and potential technological applications[12–17]. One of the first studies of biomolecules withshaped pulses was the control of the fluorescence emissionof green fluorescent protein (GFP) with chirped pulses [12].By adapting the linear chirp of a femtosecond pulse to thewavepacket motion in the excited state, the stimulatedemission was controlled. More recently, the control ofwave-like motion in a complex system was shown in anadaptive-assisted quantum control of the energy flow inthe light-harvesting antenna complex (LH2) of Rhodo-

pseudomonas acidophila, a photosynthetic purple bacterium[13,18]. After excitation with a multipulse of the first one-photon allowed excited state (S2), the energy flow insidethe LH2 was steered into one of the available relaxationchannels in the antenna complex. The interaction of multi-pulse excitation and matter has the effect of generating a fil-ter in the frequency domain, optimizing molecularvibrational wavepackets with a period matching the sub-pulse separation and suppressing contributions from othermodes that are out of phase with the subpulse separation[5]. The observed optimal modulation period b = 210 fs

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Fig. 1. Time ordering of incident pulses in the discussed experiments. (A)DFWM-control with shaped pump and Stokes pulse (B) in Pump-DFWMan additional fs-pulse precedes the DFWM-sequence. Only the phase ofthe initial pump pulse is subject to modulation.

Fig. 2. Absorption spectra in comparison to excitation pulses for thediscussed experiments. (A) Absorption spectrum of b-carotene in cyclo-hexane (black line) and the resonant (red line) and non-resonant DFWMspectrum (blue line). (B) Absorption spectrum of b-carotene in cyclohex-ane (black line) and the initial pump (red line) and DFWM spectrum (blueline) used in the Pump-DFWM-experiment.

J. Hauer et al. / Chemical Physics 350 (2008) 220–229 221

was explained in the carotenoid as slow excursions alongthe bu asymmetric coordinate that induces a bending ofthe CCC backbone [19]. Selective excitation of the couplingbu mode facilitates relaxation through internal conversionfrom the S2 to S1 state, this way reducing the energy trans-fer to bacteriochlorophyll, the other available deactivationchannels in the complex. Experimental results suggest thatthe efficient selective excitation of these low-frequencymode wavepackets in the excited electronic state wasachieved through multiple selective Raman excitations inthe ground state of the carotenoid via impulsive Ramanscattering (IRS), enhanced by electronically resonant exci-tation. The proposal of a mechanism mediated by a vibra-tionally excited ground state raises important andfundamental questions, which will be addressed and elabo-rated on in this work. Following the concepts demon-strated on LH2, we deepen the understanding of theunderlying control mechanisms by investigating b-carotenewith two different spectroscopic techniques. b-Carotene is

chosen as a proto typical system since carotenoids are apart of the afore mentioned light-harvesting complexLH2. Carotenoids absorb energy in the blue-green regionof the visible spectrum and pass on this energy towardsthe chlorophylls via an intricate deactivation network[20]. We employ degenerate four-wave-mixing (DFWM,see Fig. 1A) to address vibrational modes on b-carotene’selectronic ground state.

In a second set of experiments, the valuable insightsgained by DFWM are applied to the excited state. This stepis necessary since the crucial points of the photochemistryto be controlled are between the lowest lying excited singletstates S2 and S1. Instead of detecting and controlling theoscillatory motion with DFWM, an additional excitationpump prior to the DFWM-sequence is phase-modulated(see Fig. 1B). In a concluding section, the control scenariosfor ground and excited states will be compared in theireffectiveness.

2. Experimental setup

The details of the experimental setups, namely fordegenerate four-wave-mixing [7] and pump-degeneratefour-wave-mixing (Pump-DFWM [21–24]), have been pub-lished elsewhere. In this section, only a brief summary ofthe experimental techniques is presented.

222 J. Hauer et al. / Chemical Physics 350 (2008) 220–229

2.1. Pulse shaping

The pulse train or multipulse was obtained by applyinga sinusoidal phase function / = a sin (bx + c) on a liquidcrystal modulator (LCM [25]). The period b was chosento coincide with an integer multiple of the period of thevibration to be excited. The best contrast between thesub-pulses is guaranteed if the amplitude parameter a isset to 1.23 [26]. The third parameter, the phase of the sinu-soidal function c, was kept constant with value 0. In allexperiments, the LCM was used in the 4-f arrangement.In the Pump-DFWM-experiment, a 128 pixel modulatorwas used, while in the DFWM setup a 640 pixel LCMwas employed.

2.2. Degenerate four-wave-mixing

In the DFWM-experiment, we used a non-collinearparametric amplifier (nc-OPA) pumped by a 2 kHz Ti:Sa-phire laser system to generate a temporal resolutionin situ of 22 fs [7]. The nc-OPA pulse was split into threefour-wave-mixing beams: DFWM-pump, Stokes and probe(Fig. 1A). Two excitation scenarios were investigated: (i)the DFWM-sequence is near-resonant with the S0–S2 tran-sition in b-carotene, with pulse spectra centered at 510 nm(blue1 line in Fig. 2A) and (ii) the DFWM-sequence is non-resonant with the first optically allowed transition, asensured by pulse spectra centered at 550 nm, depicted asthe red line in Fig. 2A. The DFWM-pump and Stokespulse were phase-modulated. The probe pulse remainedunaltered or Fourier-limited for near-resonant and non-resonant excitation. All beams were horizontally polarizedand focused in a folded BOXCARS geometry. TheDFWM-signal was recorded with a CCD-camera at severaldelays s of the probe pulse. b-Carotene was dissolved inHPLC-grade cyclohexane, without any further purifica-tion. The concentration was adjusted to obtain 0.7 OD atthe absorption maximum around 480 nm.

2.3. Pump-degenerate four-wave-mixing

In the Pump-DFWM-experiment, two separate singlestage nc-OPA were used to generate all four beams[22,24]. The initial pump was centered around 510 nm(Fig. 2B) with a temporal pulse width of 17 fs. The initialpump preceded the DFWM-sequence by a delay T(Fig. 1B). For purposes of coherent control, the beamwas phase-modulated as described in Section 2.1. Beforereaching the sample, the beam went through a synchro-nized chopper wheel, blocking every second pulse. Thisallowed for discriminating between transients with (‘‘InitialPump on”) and without (‘‘Initial Pump off”) the initialpump beam preceding the DFWM-sequence. The latter

1 For interpretation of colour in Figs. 1–7, the reader is referred to theweb version of this article.

was obtained by splitting the output of another nc-OPAinto three parts of equal intensity. The spectrum of theDFWM-sequence was centered around 560 nm (Fig. 2B)with a duration of 14 fs FWHM. One of the threeDFWM-beams serving as the probe beam was delayed bys. In order to guarantee photostability of the solution dur-ing the course of the experiment, the intensities of all inci-dent beams were kept as low as possible at the sample, i.e.40 nJ for the initial pump, 15 nJ for DFWM-pump andStokes and 3 nJ for the probe beam. All beams were hori-zontally polarized. The employed experimental arrange-ment allowed for three different detection methods: TheDFWM-signal was either detected in a photomultiplierafter an interferometric filter or spectrally dispersed andrecorded in a CCD-camera with 1024 pixels. In the thirdmethod of detection, not the DFWM-signal but the probebeam was recorded in a photodiode after the sample at achosen wavelength (data not shown). Since the initial pumpwas blocked periodically, transient absorption measure-ment were carried out simultaneously. This way, possiblesaturation or exceedingly big depletion effects [17,27] bythe DFWM-sequence were excluded. The sample was pre-pared similarly to the DFWM-experiment (Section 2.2).

3. Results and discussion

3.1. Control of ground-state dynamics

In a first experiment, the control of vibrational coher-ence is compared under two different excitation situations:near-resonant and non-resonant with the S0 ? S2 transi-tion, the first allowed one-photon transition from theground state in b-carotene [7]. The carotenoid has an effec-tive conjugation system of n = 10.5 double bounds similarto that of rhodopsin glucoside (n = 11), the native caroten-oid of R. acidophila in LH2. The DFWM-signal at 529 nmin both situations shows three main vibrational modes at1004, 1156 and 1532 cm�1 (Fig. 3). These are b-carotene’sground-state modes as known from frequency domainspectroscopy [20]. For the purpose of coherent control,the excitation pulses in the DFWM-sequence are shapedas described in Section 2.1, i.e. pump and Stokes show asubpulse spacing in agreement with a vibrational period.The wavepacket addressed in such a manner can be excitedexclusively over the others. The filtering of an arbitraryvibrational wavepacket works for the near-resonant excita-tion as well as for the non-resonant case, depending merelyon the subpulse separation.

Fig. 3 shows a comparison between vibrational spectraafter near-resonant (Fig. 3A) and non-resonant (Fig. 3B)shaped excitation compared to spectra obtained with Fou-rier-limited pulses of equal total energy. Importantly,amplitude enhancement of the vibrational wavepackets,i.e. of the respective peaks in the FFT-spectrum, is onlyobserved under near-resonant conditions. For the modearound 1004 cm�1 mode, the ratio between the shapedand unshaped FFT peak can reach a factor 5.7 (not

Fig. 4. Pump-DFWM as a method of detection for excited-state vibra-tions. (A) Energy level diagram for b-carotene. The probe delay s withinthe DFWM-sequence (red) is scanned for different values of the initialpump delay T (initial pump in blue). The transient for T = 1 ps is shown in(B). After subtraction of the slowly varying background, the molecularoscillations in (C) due to excited-state vibronic wavepacket motionbecome apparent.

Fig. 3. FFT-spectrum after resonant (A) and non-resonant (B) excitation.The red continuous line shows the intensity of the vibrational modes whena multipulse (b = 144 fs, corresponding to the fifth period of the1156 cm�1 mode) is used, while the black traced line corresponds to anexcitation with a Fourier-limited pulse (unshaped). Adapted from Ref. [8].


shown). If the DFWM-sequence is off electronic resonance(see Fig. 3B), the Fourier-limited case sets an upper bound-ary for vibrational amplitude not to be exceeded by coher-ent control. Hence, electronic resonance is an importantperquisite if the aim is to create a vibrational coherencethat is to be enhanced by phase modulation. This strikingdifference between resonant and non-resonant excitationunderlines the importance of electronic transitions for theenhancement mechanism of molecular vibrations.

Another aspect to be considered is the influence of phe-nomena related to coherence terms. The sub-pulse spacingb used for the data in Fig. 3 was b = 144 fs, which coincideswith the fifth multiple of the vibrational period of theaddressed mode at 1156 cm�1. The fact that the modecan still be controlled at higher harmonics of its fundamen-tal frequency is important for two reasons: first, with thesub-20 fs pulses used in the experiment, larger values of b

lead to pulse trains with clearly separated sub-pulses, whichresults in more pronounced control effects. Second, theemployment of large sub-pulse spacings requires a vibra-tional coherence time T2,vib larger than b. In other words:the vibrational wavepacket created by the first sub-pulsecan only be controlled by a multipulse if the subsequentsub-pulse arrives after a time b which is shorter than thewavepacket’s timescale of loss of phase relationship. Suchloss phenomena may be due to dephasing processes or

decoherence related to for example irreversible couplingto a thermal bath [28]. In the case of control of ground-state modes in b-carotene discussed here, the relevant timescale is identified directly from the transient data in thetime domain, where the wavepacket oscillations manifestas sinusoidal oscillations with a damping constant ofT2,vib. These time scales are mode specific and in the orderof 1 ps for all vibrations apparent in Fig. 3. For further dis-cussion, we note that the loss of phase relationship in awavepacket is its natural time limit for control purposesin this work. The duration of the pulse train cannot exceedthe dephasing time and still control the wavepacket in ameaningful way.

3.2. Control of excited-state dynamics

The previous section revealed that ground-state-wave-packets in b-carotene can be effectively controlled by mul-tipulse excitation. However, the system’s evolution on theexcited states is of greater importance for photo inducedprocesses, in particular for the dynamics of carotenoidsin photosynthetic light harvesting. In order to investigatethe influence of coherent control on the biologically rele-vant states of, e.g. b-carotene, the system has to be pro-moted to an excited state as depicted in the excitationscheme in Fig. 4A. Unlike in the previous section, DFWMwill now only be used as a method of detection. The addi-tional pulse prior to the DFWM-sequence will be subject tophase modulation. The resulting time ordering of the inci-dent pulses is summarized in Fig. 1B.

Prior to the discussion of the experiments with phase-modulated excitation, the general nature of the signals ina Pump-DFWM-experiment with Fourier-limited pulseswill be outlined. Special emphasis will be given to b-caro-tene’s vibrational modes and their behaviour in time. In asecond part, the aspect of coherent control of the observeddynamics will be addressed. In addition to the previous sec-

Fig. 5. Excitation scheme for a vibrationally hot ground state in Pump-DFWM via stimulated emission pumping (SEP-DFWM) in (A). (B)compares the Pump-DFWM-transients for early and later initial pumpdelays T (T = 60 fs and T = 400 fs, respectively). The FFT-spectra in (C)depend strongly on the chosen value for T. Note that the FFT-intensityfor T = 60 fs (red spectrum) is only 5% of the intensity at T = 400 fs.


tions of this work, not only sinusoidal phase functions butalso first order chirps (defined as the second time derivativeof the temporal phase d2//d(t)2) and their effect on popu-lation transfer will be discussed.

The experimental details of the scheme depicted inFig. 4A are described in detail elsewhere [24]. Briefly, theinitial pump beam in blue promotes the system from itsground-state S0 to its first optically allowed state S2. Asmentioned in Section 2.3, the initial pump beam is subjectto phase modulation while the DFWM-beams remain Fou-rier-limited. After the first excitation step (S0 ? S2), b-car-otene’s photochemistry is crucially determined by theultrafast internal conversion from S2 to S1 within 180 fsdepending on the solvent [20]. The DFWM-sequence isset resonant with the S1 ? Sn transition frequency around560 nm. This leads to two important points: (i) thePump-DFWM-signal will only be resonantly enhanced ifthe initial pump beam has already interacted with the sam-ple prior to the arrival of the DFWM-sequence. (ii) even ifthere was an interaction with the initial pump, the signalwill only be feasibly strong after the internal conversionfrom S2 to S1, since S2 absorbs in the infrared spectralrange [29]. These two points explain the slowly decayingbackground of the Pump-DFWM-transient in Fig. 4B, typ-ical for a resonant DFWM-signal [30]. Fig. 4B shows thedifference between the signal with and without the initialpump beam at an initial pump delay T = 1 ps. At thatpoint in time, all the population will have already relaxedfrom the initially addressed S2 to S1, resonantly excitedby the DFWM-sequence. The slowly varying part of thesignal is sufficiently described by A(k,T) exp [�s/Td(k,T)]with A(k,T) as a pre-exponential amplitude factor, depend-ing on the detection wavelength k and the initial pumpdelay T. The signal decays mono-exponentially for alldetection wavelengths k against the probe delay s with adecay time constant Td(k,T). After subtraction of theslowly varying signal contribution, the fast molecular oscil-lations in Fig. 4C remain, the Fourier-transform of whichleads to excited-state vibrational dynamics. By taking tran-sients in s at different initial pump delays T, the vibrationaldynamics of the system along the reaction coordinate canbe resolved in time. Hence, with Pump-DFWM one canunambiguously distinguish excited-state dynamics againstground-state activity by exploiting state specific resonances[23,24].

For the investigation of excited-state vibrational modesvia Pump-DFWM, two substantially different excitationscenarios have to be distinguished. The situation for initialpump delay times T > 180 fs is depicted in Fig. 4A. Forlarge values of T, the population excited to S2 has alreadyrelaxed to S1 as described above. For early initial pumpdelay times, however, the population on S2 can be pumpedback to a vibrationally hot ground state as depicted inFig. 5A.

The process describes in Fig. 5A has been termed stim-ulated emission pumping (SEP-DFWM [31]) and wasalready discussed for b-carotene [24]. When analyzing the

transients and FFT-spectra in Fig. 5B and C, the necessityof the proposed excitation mechanism becomes apparent.For an initial pump delay of T = 400 fs the populationhas already relaxed from S2 to S1. The FFT-spectrumshows the typical polyene modes including the S1 specificvibration near 1800 cm�1 [7]. When the spectrum is mea-sured at T = 60 fs, however, the initially excited-state S2

is still populated. This should lead to a weaker signal thanfor T = 400 fs since there is no resonance enhancement ofthe DFWM-signal from S2, which absorbs in the near IR[29]. Even though the FFT-intensity is expectedly lower,it cannot be attributed to S2 for the following reason:The vibrational life time of modes on S2 should not exceedthe life time of the electronic state (180 fs depending on thesolvent) [32]. However, when the transients at T = 60 fs areanalyzed, a vibrational lifetime above 1 ps is revealed (seetransients in Fig. 5B). In the frequency domain, this leadsto narrow frequency bands as can be seen in Fig. 5C.Due to their far too long life time, the vibrations atT = 60 fs cannot be attributed to S2. Fig. 5A shows a mech-anism explaining the long vibrational life times at smallvalues of T. Via a mechanism similar to SEP-DFWM, avibrationally hot ground state is populated. S2 serves as aresonant intermediate state. This is plausible, since theenergy difference between the initial pump centered around510 nm and the DFWM-sequence at 560 nm of 1700 cm�1

is small enough to excite a vibrationally hot ground state(hot-S0). A description of the spectroscopic properties ofhot-S0 based on an analysis of the slowly varying part ofa Pump-DFWM-signal has been given by Hauer et al. [24].

After establishing the electronic states contributing to b-carotene’s Pump-DFWM-signal, the discussion will nowturn to the coherent control of the vibrational modes onthe different energy surfaces. The results presented abovedemonstrate how excited-state vibrational dynamics areanalyzed by Pump-DFWM. The aim of quantum controlspectroscopy (QCS) [15,18] on such phenomena is to influ-

Fig. 6. Coherent control by pulse sequences with different sub pulsespacings b on b-carotene’s excited states. On hot-S0 in (A) as well as on S1

in (B) and (C), wavepacket selectivity is lost (see text for discussion),regardless of whether the pulse train was in phase (B) or out of phase (C)with the C@C stretching mode near 1530 cm�1. However, certain subpulsespacings enhance the population transfer from S0 to S2 and the successorstates.


ence them by coherent control in order to gain additionalinsight compared to the data after Fourier-limited excita-tion. Since there are two sets of beams in the experiment(initial pump beam and the DFWM-sequence), coherentcontrol can be implemented in two distinct ways. Onewould be to modulate the phase of the pump and theStokes pulse in the DFMW-sequence. This would lead toan excited-state analogue of the DFWM-experiment pre-sented in Section 3.1. The expansion of this method toexcited-state dynamic seems trivial. The other possibleapproach to implement coherent control in Pump-DFWMis to modulate the initial pump beam. In this scheme, theDFWM-sequence serves exclusively as a method of detec-tion with Fourier-limited pulses. Controlling the initialpump beam affects the population transfer from S0 andalso the wavepacket dynamics created on S2. Accordingly,the rest of the discussion is subdivided into two parts oncontrol of vibrational dynamics and population transfer,respectively.

Regarding control of vibrational dynamics, it wasshown in the previous sections that electronically non-res-onant excitation in contrast to the near-resonant case willonly lead to a filtering of Raman modes [5,33]. Only anelectronically (near)resonant multipulse can be expectedto yield FFT-spectra with greater intensities than a Fou-rier-limited excitation pulse of equal total energy [7,34].For coherent control on the excited state, the first questionis to which extent this simple and intuitive picture can stillbe applied. In Fig. 6, several sub-pulse spacings b are com-pared for control on S1 and hot-S0.

Since hot-S0 is populated via the short-lived S2 state, thetotal duration of the multipulse should not exceed 180 fs,which corresponds to the life time of S2. In order to obtaina clear hot-S0 related signal, the initial pump delay even hasto be drastically shorter than 180 fs in order to retain fea-sible population for the SEP-process on S2. Hence, the datain Fig. 6A were taken at an initial pump delay of T = 80 fs.The values for b were chosen so that all the sub-pulses caninteract with the sample before the DFWM-sequencearrives (2b < T = 80 fs). Due to these rigid constraints,the multipulses employed for control of hot-S0 are not asperfectly modulated as the pulse shapes used for ground-state control with b = 144 fs (see Section 3.1). The impactof these limitations on the experiment will be discussedbelow.

Like in the ground-state control scenario in Section 3.1,the sub-pulse spacing b was chosen to match the vibra-tional period of the strongest mode on hot-S0, namely theC@C stretching mode around 1530 cm�1 (see Fig. 5C).b = 22 fs corresponds to the first vibrational period of thismode and should lead to mode selective excitation andenhancement of this vibration if the same arguments asfor the control of ground-state-wavepackets apply.Accordingly, the respective pulse shape causes a strongerintensity in the FFT-spectrum (blue line in Fig. 6A). Apulse train out-of-phase with a vibrational mode isexpected to suppress it, as shown in Fig. 3. The excitation

pulse with b = 33 fs, corresponding to 1.5Tvib of the inves-tigated C@C mode in Fig. 6A still yields a peak of weaker


amplitude than an in-phase multipulse with b = 22 fs.Hence, multipulses are still a valid tool for control of vibra-tional modes on hot-S0. However, the spectral featureobtained with b = 33 fs is still stronger than under Fou-rier-limited conditions (magenta vs. black line inFig. 6A). We attribute this discrepancy to the less-than-optimal pulse trains that had to be used for control onhot-S0 due to the constraints outlined above.

Another interesting aspect of coherent control on hot-S0

is revealed by the green curve in Fig. 6A, taken with a sub-pulse spacing of b = 29 fs, which addresses the weakermodes in the range of around 1100 cm�1. The mode near1530 cm�1 should not be enhanced by a multipulse withb = 29 fs. On the contrary, the corresponding green curveshows the strongest enhancement of all tested sub-pulsespacings. This interpretational problem can be resolvedby considering the results of transient absorption studiesin Nile Blue [10] and a Rhodamine dye [35]. They revealedthat an in-phase multipulse not only enhances the FFT-intensity of a vibrational mode but leads to an improvedpopulation transfer to the electronically excited state.Applied on the Pump-DFWM-control results this meansthat the enhanced FFT-spectrum obtained with b = 29 fsis due to a higher population density on S2 and conse-quently hot-S0 after excitation with a multipulse. Theobserved mode amplification at b = 29 fs would then reflectthe dependence of the population transfer on the shape ofthe excitation pulse.

This idea is further substantiated when considering theresults from the control on S1 in Fig. 6B and C, taken atan initial pump delay T = 2 ps. The subpulse in Fig. 6Bwas chosen to coincide with the third multiple of theC@C stretch mode (sub-pulse spacing b = 65 fs). It has tobe noted that at T = 2 ps the interaction between the mul-tipulse and molecule is already over. Hence, at T = 2 ps theDFWM-sequence detects molecular dynamics exclusively,free from artefacts explainable by the modulated shape ofthe initial pump pulse. This is an important point to beconsidered since detection of the excitation pulse is a trivialeffect and must be distinguished from coherent control ofmolecular dynamics. The phase-modulated excitation isnot mode-selective and hardly enhances the vibration. Thislack of controllability is explained by considering the differ-ences between the successful control on the ground stateand the attempt on S1. In the first case (see Fig. 3), theground-state-wavepacket retains a stable phase relation-ship for more than 1 ps, enabling control with well-sepa-rated sub-pulses. For the scenario on S1, however, thewavepacket created by the initial pump beam undergoesinternal conversion from and S2 to S1, followed by vibra-tional cooling on a 400 fs time scale [20]. The latter processis commonly associated with decoherence and loss of phaserelationship, limiting the prospects of coherent control [28].We conclude that the wavepacket looses its phase relation-ship and hence its controllability due to dissipative propa-gation on S1 and/or by the non-adiabatic passage betweenS2 and S1.

The multipulse used for Fig. 6C is out of phase with themode around 1530 cm�1 with a sub pulse spacing b = 98 fs.In agreement with the arguments given on the loss of con-trollability on S1, this multipulse does not selectively sup-press vibrational modes. However, the overall intensity ofthe FFT-spectrum is increased compared to Fourier-lim-ited excitation (black line in Fig. 6C). This enhancementeffect is confirmed by comparing transient absorption datacollected at 560 nm detection wavelength with Fourier-lim-ited and phase-modulated pulses. The transient absorptionmeasurement was carried out simultaneously to the Pump-DFWM-experiment. It revealed an eleven percent increaseof excited-state population for both pulse trains used inFig. 6C. This is explained by the following argument: Sugi-saki et al. have recently reported that the methyl in-planerocking mode around 1004 cm�1 significantly contributesto the optical response of b-carotene [36]. The pulsesequence causing the FFT-spectrum in Fig. 6C is in-phasewith the third multiple of this vibration. Accordingly, thesub-pulse spacing showing the greatest effect in control ofhot-S0 (b = 29 fs, Fig. 6A) is also in-phase with the methylrocking mode. Hence, the increased spectral FFT-intensity(see red line in Fig. 6C) can be attributed to an increasedpopulation transfer to S2 and subsequently to S1 or hot-S0.

As mentioned above, effects due to the modification ofthe total excitation duration cannot explain the observedresults for the S1 state. The measurements were made foran initial pump delay T = 2 ps, which is much bigger thanthe total tailored initial pump duration. This assures thatthe observed changes in the FFT-spectrum are due toaltered molecular dynamics. On the other hand, for smallervalues of T as used for the control of hot-S0 dynamics, thiseffect may play an important role addressed in thefollowing.

The detection of dynamics on S1, the Pump-DFWM-sig-nal can be treated like an ordinary four-wave-mixing sig-nal. For smaller values of T, however, this simplificationis not valid. The response function must be treated to thefifth order perturbation expansion in order to correctlydescribe the process. Hauer et al. [24] discuss the corre-sponding Feynman diagrams for the creation of both pop-ulation and coherence on hot-S0 in detail. Briefly, thesimple picture of pulse trains driving molecular wavepacketmotion in or out of phase depending on the sub-pulse spac-ing b is obscured by the involvement of higher order pertur-bation terms. Factors like the Franck–Condon activity ofthe addressed modes or wavepacket propagation on S2

should be taken into account for an in-depth treatmentof control of hot-S0 dynamics. The control results shoulddepend on T, reflecting the position of the S2-wavepacketat the initial pump delay under investigation. Unfortu-nately, the short life time of the S2 state forbids a moreextensive test of this hypothesis. Additionally, the natureof hot-S0 and its possible relation to other low lying statesin carotenoids like S* [17,27,37,38] is still under debate.This discussion is out of the scope of this article but willbe addressed in a separate work.


In the above paragraphs, we examined the possibility tocontrol the excited-state vibrational dynamics of b-caro-tene by pulse trains. The outcome was that the dynamicscould only be controlled via a SEP-DFWM mechanisminvolving a vibrationally hot ground state. If the popula-tion has already relaxed towards S1, processes like vibra-tional cooling seem to obscure the control effectachievable by multipulses. If the methyl in-plane rockingmode around 1004 cm�1 is addressed by a pulse train, theobserved changes in the measured FFT-spectra on theshape of the initial pump beam were attributed to anincreased population transfer from S0 to S2. In order toclarify this point, we carry out an additional experiment,aiming exclusively at the enhancement of the excited-statepopulation. This is again performed in an open loop fash-ion. In contrast to the other experiments described in thiswork, the initial pump beam is not shaped into a multipulsebut its first order chirp is scanned while the Pump-DFWM-signal is recorded. The underlying physical process of con-trolling population transfer by chirped pulses has alreadyreceived some attention in literature [39,40]. In a prominentexample, Bardeen et al. [39] showed that a negativelychirped pulse preferably excites a vibrational wavepacketon the electronic ground state, adapting to the Stokes shifton the excited state. Hence, a chirp dependent increase ofpopulation transfer can give valuable information aboutthe curvature of the involved electronic states [40].

Since we emphasize on the effect of phase modulation onthe population transfer between S0 and S2, the fast oscillat-ing part of the signal representing molecular oscillations isneglected. Hence, a simple mono-exponential decay

Fig. 7. Coherent control of population transfer between ground and excited evarying part of the signal A(k,T) exp[�s/Td(k,T)] at T = 1 ps and 610 nm. The mComparison between the pre-exponential amplitude A(k,T) and a transient absbeam’s chirp. (C) shows that the maximal population transfer occurs for only san autocorrelation time of 18 fs.

A(k,T) exp [�s/Td(k,T)] (see Fig. 4) is fitted to theDFWM-transients. The pre-exponential amplitude A(k,T) is plotted as a measure for the excited-state populationagainst the initial pump’s first order chirp in Fig. 7.

Fig. 7 shows the slowly varying part of a Pump-DFWM-signal at a detection wavelength of 610 nm and an initialpump delay T = 1 ps. This delay ensures that the entireexcited-state population has already relaxed towards vibra-tionally cold S1. Fig. 7A clearly shows that the maximalexcited-state population is not obtained by a Fourier-lim-ited but by a pulse with a small amount of positive chirp,namely +80 fs2. Trivial effects like intensity modulationupon chirping were excluded by intensity measurementsafter the pulse shaper. Fig. 7B compares the chirp depen-dence of A(k, T) with the averaged transient absorption sig-nal, obtained by measuring the DFWM-probe pulse’sintensity in a photodiode [24]. Both plots in Fig. 7B werenormalized relative to the Fourier-limited value (/00 = 0)The similarity of the curves proves that A(k, T) is a mea-sure for the excited-state population, obtaining informa-tion equivalent to transient absorption. The difference inthe magnitude of the effect (1.4 for A(k, T) according toPump-DFWM and about 1.2 for transient absorption)are explained by the differing number density dependencesN of the methods [31]: FWM-processes scale with N2 andtransient absorption with N. Fig. 7C illustrates that theobserved effect is sensitive to marginal changes of the initialpump pulse’s phase. The maximal population transfer at+80 fs2 corresponds to an alternation of the pulse autocor-relation time of only 2 fs. The red curve shows autocorrela-tion measurements for the respective chirp values.

lectronic state in Pump-DFWM. (A) The chirp dependence of the slowlyaximal population transfer is reached for slightly positive chirp values. (B)

orption signal exhibiting the same trend upon variation of the initial pumplightly elongated pulses at sAC = 20 fs where the unmodulated pulse shows


One could assume that the above results are a reversal ofthe mechanism proposed by Bardeen et al.: the authorssuggested that negatively chirped pulses favour the excita-tion of ground-state modes, since the frequencies areoffered in an intuitively correct temporal sequence for sucha process. In a reversal of this argument, a positivelychirped pulse should lead to an increase of populationtransfer to the excited state because less population is re-pumped back to the ground state. The experimental condi-tions, however, are fundamentally different between thetwo studies: Bardeen et al. investigated LD 690 with 10 fspulses, revealing strong oscillations at around 590 cm�1.In such a case, up to six vibrational levels are excited simul-taneously. For b-carotene, however, the Stokes shift isexpected to be minimal since the oscillations are in a higherwavenumber regime (see Fig. 6C). Not more than twovibrational levels can be involved with the employed pulses.Hence, an adaptation to dynamic Stokes shift can beexcluded as a possible mechanism. In a time resolved study,Misawa and Kobayashi [41] demonstrated that a quantummechanical calculation of the wavepacket dynamics on twoanharmonic electronic surfaces leads to a more refined viewof the chirp dependence of population transfer. Theauthors showed that a negatively chirped pulses createswavepackets with spatially narrow distributions since thechirp compensates the dispersion among the frequencycomponents of the wavepacket. Hence, the overlapbetween excited and ground-state wavefunction is largerthan after Fourier-limited excitation, leading to more effi-cient stimulated emission from the excited state. For a pos-itively chirped pulse on the other hand, the excited-statewavepacket broadens readily and makes the dumping pro-cess unfavourable, leading to an increased excited-state sig-nal. This model also applies for the case of b-carotene. Theasymmetry of the population-related curve in Fig. 7B,which lacks an explanation in a dynamic Stokes shift pic-ture, is related to the shifted potential minima between S2

and S0 [41].

4. Conclusions

In this work, we present and compare different scenariosfor coherent control of vibrational modes on b-carotene’sground state (Fig. 3), hot ground state and first excitedstate (Fig. 6). Modulating the phase of the pump and theStokes pulse in a DFWM-sequence into a pulse trainallows for the selective excitation and, under near-resonantconditions, even the enhancement of molecular vibrations.If the coherence of the induced wavepacket is preserved,the basic features of this control mechanism still apply onthe excited state. However, this control effect is lost if thewavepacket’s phase relationship is affected by events alongthe molecular trajectory like coupling to a thermal bath. Asdiscussed above, some of the effects in Pump-DFWM con-trol can be attributed to a generally increased but not modespecific population transfer by a multipulse. The sensitivityof the population transfer against changes in the initial

pump’s phase was also confirmed in a scan of the first orderchirp. We also showed that vibrational modes on a vibra-tionally hot ground state in b-carotene are influenced bythe spectral phase of the initial pump pulse, resonant withthe S0 ? S2 transition. This proves the importance of long-lived vibrationally hot ground-state modes in b-carotene asrevealed by quantum control spectroscopy (QCS).

The investigation of the excited-state modes on b-caro-tene’s S1-state showed that the intuitive model based onthe accordance between the multipulse’s sub-pulse spacingand the vibrational period fails to explain the results whenthe wavepacket prepared in such a manner passes a conicalintersection and undergoes vibrational cooling. This under-lines the importance of processes associated to dephasingand decoherence in coherent control. However, controlover the system’s evolution during the process of vibra-tional cooling is of great interest. Future investigations willconcentrate on this promising aspect.

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