Signatures and control of strong-field dynamics in acomplex systemKristina Meyera,1, Zuoye Liua,b, Niklas Müllera, Jan-Michael Mewesc, Andreas Dreuwc, Tiago Buckupd, Marcus Motzkusd,and Thomas Pfeifera,e,1

aMax-Planck Institute for Nuclear Physics, 69117 Heidelberg, Germany; bSchool of Nuclear Science and Technology, Lanzhou University, 730000 Lanzhou,China; cInterdisciplinary Center for Scientific Computing, Universität Heidelberg, 69120 Heidelberg, Germany; dPhysikalisch-Chemisches Institut, UniversitätHeidelberg, 69120 Heidelberg, Germany; and eCenter for Quantum Dynamics, Universität Heidelberg, 69120 Heidelberg, Germany

Edited by Ronnie Kosloff, Hebrew University, Jerusalem, Israel, and accepted by the Editorial Board November 2, 2015 (received for review May 13, 2015)

Controlling chemical reactions by light, i.e., the selective making andbreaking of chemical bonds in a desired way with strong-field lasers,is a long-held dream in science. An essential step toward achievingthis goal is to understand the interactions of atomic and molecularsystems with intense laser light. The main focus of experiments thatwere performed thus far was on quantum-state population changes.Phase-shaped laser pulses were used to control the population offinal states, also, by making use of quantum interference of differentpathways. However, the quantum-mechanical phase of these finalstates, governing the system’s response and thus the subsequenttemporal evolution and dynamics of the system, was not systemat-ically analyzed. Here, we demonstrate a generalized phase-controlconcept for complex systems in the liquid phase. In this scheme, theintensity of a control laser pulse acts as a control knob to manipulatethe quantum-mechanical phase evolution of excited states. This con-trol manifests itself in the phase of the molecule’s dipole responseaccessible via its absorption spectrum. As reported here, the shape ofa broad molecular absorption band is significantly modified for laserpulse intensities ranging from the weak perturbative to the strong-field regime. This generalized phase-control concept provides a pow-erful tool to interpret and understand the strong-field dynamics andcontrol of large molecules in external pulsed laser fields.

phase control | transient absorption spectroscopy | complex molecules |liquid phase

Can we find universal concepts to understand and control theresponse of atoms and molecules in interactions with strong

laser fields? This question is at the heart of a vast number ofexperiments in time-resolved spectroscopy (1–30). The widerange of light sources spanning the spectral range from the X-ray(e.g., free-electron laser sources, synchrotrons) over the visible(conventional laser systems) to the far-infrared regime and cov-ering the temporal range from nanosecond down to attosecondtime scales created a wealth of new physics insight into quantummechanisms, however mostly of simple systems in the gas phase(1–4). In chemistry, the generation of femtosecond laser pulsesenabled the investigation of wave packet dynamics in molecules, asthe induced vibrations occur on these time scales. Experimentsfocusing on, for instance, dissociation reactions, atom transfer,isomerization, or solvation dynamics have led to a deeper under-standing of chemical bonds and their breakage dynamics and haveopened and established the field of femtochemistry (5, 6). The aimis not only to study the light−matter interaction, but to use theobtained understanding of the processes to control the dynamicsin complex molecules and, in the future, even to be able to controlchemical reactions (7–10). Shaping the amplitude and phase offemtosecond laser pulses has been used, for example, to controlthe shape of wavefunctions in atomic systems (11) or to controland optimize the single-photon and multiphoton fluorescence inatoms such as cesium (12) and complex systems, e.g., dye mole-cules (13). Shaped pulses are also used in time-resolved coherentanti-Stokes Raman scattering (14–16) or 2D spectroscopy (17, 18).Adaptive shaping of the pulses via feedback control even allows

the optimization of dynamical processes, e.g., the relative photo-dissociation yield of organometallic molecules (19), the relative two-photon fluorescence yield of dye molecules (20), and the energytransfer in light-harvesting molecules (21).However, the strong-field dynamics in complex systems, e.g.,

in the liquid phase, and its control have only recently moved intoscientific focus (22–27). The dynamics of complex systems wasthus far studied mainly in perturbative experiments such astransient absorption spectroscopy, which measures the evolutionof a system after absorbing a single or a few photons. Theseexperiments mainly measured population dynamics of excitedstates, without gaining access to the phases of the excitedwavefunction coefficients. Even the phase-sensitive method of2D/3D spectroscopy (28, 29), which evolved out of transientabsorption spectroscopy, probes the perturbative third- or fifth-order response of the system and has not yet been used to sys-tematically understand the strong-field response of a complexsystem. However, an important ingredient in approaching theultimate goal of controlling chemistry is to get access to thephase of quantum-state coefficients and to analyze systematicallythe phase of the system’s response. In recent work, the phase ofthe dipole response after excitation was measured and controlledin a simple system, namely gaseous helium (31, 32). Transientabsorption experiments were performed using extreme-UV atto-second pulses and 7-fs short visible to near-infrared (VIS/NIR)pulses, and the absorption was measured as a function of the timedelay. The intensity of the femtosecond pulse could be varied inaddition to the time delay. Thereby, the dipole response was

Significance

Using intense lasers to control complex molecules is a long-helddream in science. In this article, we develop a physics conceptfor measuring and controlling the quantum states of complexmolecules by strong laser fields. We show that, in particular,the quantum-mechanical phase of excited molecular states canbe manipulated by the intense laser, a key quantity for full(amplitude and phase) control of molecular quantum states.With the help of time- and intensity-resolved absorptionspectroscopy experiments, we apply this idea to the dynamicsof a large dye molecule in solution. The demonstrated phase-control concept thus represents a major leap toward the ulti-mate goal of laser chemistry.

Author contributions: K.M. and T.P. designed research; K.M., Z.L., N.M., and T.P. per-formed research; K.M., N.M., T.B., M.M., and T.P. analyzed data; K.M., Z.L., N.M., J.-M.M.,A.D., T.B., M.M., and T.P. wrote the paper; and J.-M.M. and A.D. performed calculationsconcerning the dye molecule IR144 (energy structure, polarizability, etc.).

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. R.K. is a guest editor invited by the Editorial Board.

Freely available online through the PNAS open access option.1To whom correspondence may be addressed. Email: tpfeifer@mpi-hd.mpg.de orkmeyer@mpi-hd.mpg.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1509201112/-/DCSupplemental.

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systematically investigated as a function of the laser pulse intensity,ranging from the weak perturbative to the strong-field regime.Modifications of the absorption line shapes of helium from Fano toLorentzian profiles and vice versa were observed with increasingVIS/NIR pulse intensity. These changes can be explained by aninduced phase shift of the dipole response that is caused by thefemtosecond pulse. Thus, the laser pulse intensity can be used as acontrol knob to modify the system’s response in a desired manner.In this work, we present the generalization of an atomic strong-field phase-control concept to complex systems in the liquid phase.

General Key IdeaWe developed a toy model to explain the observed line shapemodifications and to implement state-dependent interactionswith a strong laser field.In the following description, we consider the case of one single

transition. A first weak (probe) laser pulse with its oscillating electricfield induces a time-dependent dipole response in the system that isconnected to the absorption cross section σ via its imaginary part

σðωÞ∝ℑfdðωÞg∝ℑnFhedðtÞio, [1]

where the dipole dðωÞ is the Fourier transform of the temporaldipole response edðtÞ. The presence of a subsequent strong-field(pump) laser pulse causes a time-dependent energy EðtÞ of theexcited states. In the following, the pump pulse will be calledcontrol pulse, as we consider its action to be more general thanjust a single- or few-photon ”pump” or excitation step. Startingfrom the time-dependent Schrödinger equation

iZ∂ψðtÞ∂t

=EðtÞψðtÞ [2]

and using the ansatz

ψðtÞ∝ exp�−i�E0

Zt−ΔφðtÞ

��[3]

for the wavefunction (with the unperturbed energy E0), it can beeasily shown that the phase shift Δφ can be described by

ΔφðtÞ∝ 1Z

Z t

0

dt′ΔEðt′Þ. [4]

The energy shift ΔEðtÞ can be induced by a short intense laserpulse that follows a short excitation pulse and leads to a transientenergy shift of the excited states, e.g., due to the dynamic Starkeffect. The dipole response can generally be expressed by

edðtÞ∝ exp�−Γ2t− iðω0t−φÞ

�[5]

with the decay constant Γ, the angular frequency ω0 of the resonance,and an arbitrary phase φ, which is 0 for a Lorentzian spectral lineshape. Taking Eq. 1 into account, the following result is obtainedfor the absorption cross section:

σðωÞ∝ℑ

�−

e

1+ e2e iφ + i

11+ e2

e iφ�

[6]

with e= ðω−ω0Þ=ðΓ=2Þ. It can be clearly seen that a variation ofφ changes the imaginary part (and at the same time the real part,i.e., the dispersion) of the dipole response. Thus, shifting thephase of the temporal dipole response leads to a modificationof the spectral absorption profile.

A single, isolated transition, decaying exponentially in time,corresponds to a Lorentzian absorption line profile (Fig. 1A, blacklines). If the phase of this dipole oscillation is shifted immediatelyafter excitation, the absorption profile changes, for instance, for aphase shift of π=2, an asymmetric Fano profile is obtained (Fig. 1A,red lines). This was demonstrated recently for the helium atom(31). In complex molecular systems in the condensed phase, how-ever, additional vibrational (in the gas phase also rotational) de-grees of freedom superimpose the electronic transition, yielding aset of so-called (ro-)vibronic transitions (compare Fig. 1C). This setof energetically dense transitions ultimately determines the shape

Angular frequency

(

) Im

{d(

)} d(t)~

Time t

= 0 = /2

A

B

Angular frequency

(

) Im

{d(

)} d(t)~

Time t0

Rel. absorptionA

ngul

ar fr

eque

ncy

EE'

C

G

Fig. 1. Absorption line profiles and corresponding dipole response functions.(A) The absorption profile of a single, exponentially decaying excitation cor-responds to a Lorentzian line (black lines). If the phase of the temporal dipoleresponse is shifted, the absorption line is modified to an asymmetric, Fano-likeprofile, which is indicated here for a phase shift of π=2 as example. This phaseshift can be caused after excitation of the system by a laser-induced energy shiftof the excited states. (B) Complex systems (e.g., molecules) typically exhibitbroad absorption bands. The case of an absorption maximum (upper part, blackline) consisting of four single transitions is depicted to illustrate the mechanism.In the temporal domain, this case corresponds to four dipole responses thatcoherently add up to an overall decaying dipole response. A phase shift of oneof the dipole oscillations by π=2 modifies the overall dipole response (lowerpart, red line) significantly. In the spectrum, a minimum occurs due to this phaseshift. (C) Schablonski diagram representing the vibronic transitions between theground state G and excited states E. In the presence of an additional excitedstate E′, one of the vibrational levels E might couple to E′, which could be moresensitive to external light fields. Thus, as a consequence, the vibronic stateE would strongly shift in energy (ΔE) under the influence of a laser field, causinga Δφ=

RΔEðtÞ  dt phase shift after integration over the laser pulse.

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of the (UV/VIS) absorption spectrum. In addition, due to intra-molecular (and intermolecular, in solution) interactions, the excitedstates are typically short-lived, causing the dense absorption lines tooverlap spectrally, forming broad absorption bands. Bearing inmind the results obtained for single atoms, the question arising hereis: How will strong pulsed laser fields affect the band shape ofbroad, molecular absorption bands composed of a set of vibronictransitions?To illustrate absorption-profile modifications in complex mole-

cules, we consider the following scenario (compare Fig. 1B): Let abroad absorption maximum consist of four individual Lorentzianresonances. In the temporal domain, this situation corresponds tofour exponentially decaying dipole oscillations that coherently add upto an overall quickly decaying dipole response. Now, if the phase ofonly one transition’s dipole response is shifted by π=2, for example,the overall dipole oscillation changes significantly, and a clear mini-mum is visible in the spectral domain. As different excited states havedifferent coupling strengths (e.g., different Stark shifts) to an externalelectric field, for instance due to coupling to additional excited statesenabling a dynamic polarization (compare Fig. 1C), this model as-sumption of a selective coupling of one or just a few states out ofmany is realistic. It has to be pointed out again that we use stronglaser fields on purpose to strongly modify the quantum states.In the following, we present transient absorption measurements

in a dye molecule to provide clear evidence for this generalizedphase-control formalism in complex systems.

ExperimentWe performed transient absorption measurements with 7-fs shortlaser pulses in the VIS/NIR spectral range acting as both control(i.e., pump) and probe pulse. Further information about thecharacterization of the pulses is provided in Characterization ofLaser Pulses. In our experiment, we used a 0.125-mM solution ofthe dye IR144 in methanol as the sample. The absorption wasmeasured as a function of the time delay τ between control andprobe pulse. As a second parameter, we varied the fluence of thecontrol pulse and repeated the time-delay scans for differentfluence settings. In our measurements, we specifically focused onnegative time delays, that is, the probe pulse precedes the controlpulse, which is also referred to in the literature as perturbedpolarization decay. It also corresponds to the above-describedsituation of interest, where a strong laser pulse can have different

coupling strengths for individual excited states and can tran-siently modify their energies.The experimental setup is displayed in Fig. 2A. The control and

probe pulses are cut out from the incident 7-fs laser pulse by aspatial mask. The pulses are reflected off a split mirror, which isused to introduce the time delay τ between the two pulses. Then,the pulses are focused into the sample, which is a cuvette filled withthe IR144 solution. To mitigate spatial-volume averaging in thesample, the probe pulse is focused to a smaller spot size than thecontrol pulse. The dye molecule has a broad absorption maximumat a center wavelength of about 750 nm. Its structure is depictedin Fig. 2B. The energy of the probe pulse is kept constant at alow level of 21 nJ, which corresponds to a fluence of aboutð0.5± 0.1Þ · 10−4 J/cm2. The spectrum of the transmitted probepulse is recorded as a function of the time delay τ and also forvarying control-pulse energies or fluences.Fig. 3 shows time-delay scans for two different control-pulse

fluences. It can be clearly seen that for time delays close to 0 fs, theabsorption spectrum is strongly modified, even for low fluences.These modifications become more prominent, and, most impor-tantly, change the overall spectral shape, for higher fluences. Notethat OD (optical density) instead of ΔOD is shown, which meansthat the complete absorption spectrum, in particular on the nega-tive time-delay side, is massively reshaped by the interaction with astrong laser field. Since we focus on such strong modifications in theabsorption spectra, OD is chosen to represent the absolute ab-sorption spectrum instead of ΔOD, which is typically used to rep-resent small changes in perturbative (e.g., single-photon pump,single-photon probe) transient absorption spectroscopy at lowerintensities of pump and probe. At positive time delays, the signalrecovers on a timescale of roughly 50 fs, which can be attributed tothe lifetime of the excitation. This is in agreement with a number ofexperiments in which the dye IR144 was already studied, e.g., three-pulse photon echo spectroscopy, transient grating, and transientabsorption measurements (33, 34). However, these measurements,like most of the transient absorption measurements in complexsystems, focused on positive time delays, i.e., probing the dynamicsafter the system was excited by a perturbative (single-photon)control pulse, neglecting the perturbed polarization decay atnegative time delays. The perturbed polarization decay (35) is typ-ically regarded as a nuisance that is removed in data analysis (36). Incontrast, we focus on this negative time-delay axis in the following.

Neutraldensity

filter Iris 1 Iris 2

Variabledensity

filter

Split mirror

Focusingmirror

R = 1 m

Sample

Onlinemonitoring

DiffusorBeam splitter

N

N

CO2C2H5

N

(CH2)3SO3H

N+

CH3

CH3

CH3

CH3

(CH2)3SO3- N(C2H5)3·

IR144

Spectrometer

Mask

A

BFig. 2. Ingredients of the transient absorption spec-troscopy measurements. (A) Experimental setup. Thecontrol and probe pulses are cut out of the incident7-fs VIS/NIR laser pulses by a mask. The neutral andvariable density filters are used to adjust the intensitiesof the pulses. The time delay τ is introduced by the splitmirror. The two pulses are focused into the sample,which is a solution of the dye IR144 in methanol filledinto a standard cuvette (SpecVette CSV500 from OceanOptics, path length 500 μm). The transmitted spectrumof the probe pulse is detected by a spectrometer as afunction of the time delay and the control-pulse en-ergy. The online monitoring allows checking of thetemporal and spatial overlap of the two pulses duringthe course of themeasurement. (B) Molecular structureof the dye IR144. The dye exhibits a broad absorptionmaximum centered around a wavelength of 750 nm.

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To observe the strong-field response of the molecular system, wenow systematically analyze the perturbed polariation decay as afunction of laser fluence in Fig. 4 for fixed time delays τ. Thenegative time delays correspond to the case where the moleculesare first excited by the weak probe pulse and then exposed to theinfluence of the stronger control pulse. Significant modifications ofthe absorption spectra occur in a range of time delays of −20 fs to0 fs. The maximum of the absorption band shifts to higher fre-quencies. For smaller time delays, this shift becomes stronger, and aminimum occurs around 2.5 fs−1. To rule out the possibility that theobserved modifications are caused by the solvent, measurements inpure methanol are performed. The transient absorption measure-ments performed in the pure solvent and their results are presentedin Measurements in Pure Methanol.

Numerical Model and DiscussionThe question is whether the experimentally observed modificationsof the absorption spectra as a function of increasing intensity of thecontrol pulse can be explained by the generalized phase-controlmechanism as described above. To answer this question, we modifythe numerical toy model to implement state-dependent interac-tions with a strong laser field. As explained above, for the case of amolecule, there is not only one single transition to be taken intoaccount as in an atomic gas (31) but many possible transitions,which are overlapping in the spectrum. Thus, a single-excited-statedipole response has to be replaced by a sum over many dipoleresponses

PkedkðtÞ, one for each excited state. In contrast to the

atomic case, where the laser-induced phase shift was consideredinstantaneous compared with the lifetime of the excited state, inthe molecular system, it cannot be safely assumed that the lifetimeof the states is much longer than the exciting laser pulse. Corre-sponding to Eq. 4, the induced phase shift is given by

ΔφðtÞ∝ 1Z

Z t

0

dt′ΔEðt′Þ=Z t

0

dt′cIcontrolðt′Þ. [7]

Here, we consider the energy shift ΔEðtÞ induced by the dynamicalStark effect to be directly proportional to the control-pulse intensity

IcontrolðtÞ, and the constant c represents a generalized couplingstrength (e.g., proportional to the state’s polarizability α). The phaseshift thus increases linearly with laser pulse fluence (

RIðtÞdt). It is

explicitly time-dependent and accumulates during the entire pres-ence of the control pulse and while the dipole oscillation decays.To mimic the experiment, we estimated the molecular transitions

based on a particle-in-a-box model, as we could not find morequantitative information about the exact energy structure of the dyemolecule IR144 in the literature. We model the absorption spectraby 22 equidistant transitions ranging from 2.34 fs−1 to 2.76 fs−1,spaced by 0.02 fs−1 and equal in transition strength. Modeling theabsorption spectra by equidistant energy transitions corresponds tothe harmonic approximation that is usually used to describe mo-lecular vibrations. The assumed spacing of 0.02 fs−1 matches a typicallarge-scale vibration of π-conjugated systems (i.e., about 100 cm−1).The chosen spacing of the vibronic transitions was derived fromcalculations of the normal-mode vibrations in the electronic groundand first excited state and also agrees with previous measurementsof fluorescence and absorption spectra (37). A common lifetimeis assumed, which is expressed by a decay constant of the dipoleoscillation of 0.1 fs−1. This configuration of transitions approximatelyreproduces the measured experimental spectrum. The laser pulsesare described by a Gaussian spectrum with an angular center fre-quency of 2.6 fs−1. In analogy to the measurements, we model theabsorption spectra as a function of the control-pulse intensity forfour different time delays as displayed in Fig. 5. It turns out that onlyfour laser-coupled (phase-shifted) transitions, namely at frequencies2.34 fs−1, 2.36 fs−1, 2.46 fs−1, and 2.48 fs−1, are enough to reproducethe experimental observations. To find the best agreement, for eachof these four transitions, we used a coupling constant c of 2× 103rad·cm2·J−1, corresponding to a polarizability of about 3,400 a.u.,which agrees in order of magnitude with an isotropic polarizabilityon the order of 1,100 a.u. that was obtained from calculations. Withthese assumptions, the toy model mimics the observed features ofthe experiment, namely, the shift of the absorption maximum tolarger frequencies and the occurring minimum. A more detailedanalysis of the quality of the chosen parameters is provided in Choiceof Parameters and Their Impact on the Numerical Model. The modelbased on the generalized phase-control formalism is thus capableof qualitatively reproducing the experimental observations. The

-100-80 -60 -40 -20 0 20 40 60 80 1002.0

2.2

2.4

2.6

2.8

3.0

3.2

Ang

ular

freq

uenc

y ω

[fs-1

]

Time delay τ [fs]

OD [arb. u.]1.8

0.9

0.0

-100-80 -60 -40 -20 0 20 40 60 80 1002.0

2.2

2.4

2.6

2.8

3.0

3.2

Ang

ular

freq

uenc

y ω

[fs-1

]

Time delay τ [fs]

A B

Fig. 3. Time-delay scans for a control-pulse fluence of about 4.4 ·10−4 J/cm2 (A) and 18.2 ·10−4 J/cm2 (B). The positive time-delay range corresponds to thetypical pump–probe scenario. Negative time delays correspond to the perturbed polarization decay, where the system is first excited by the weak pulse(i.e., probe) and, afterward, the control pulse (i.e., pump) perturbs the absorption process. Significant modifications of the absorption spectra are clearlyvisible in the region around a time delay of 0 fs. For higher fluences, these modifications become even stronger.

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energy shifts and phase shifts in our model can, in reality, be causedby a number of coupling mechanisms that exist in molecules, e.g.,Stark effect, strong coupling of near-resonant electronic states, orRaman coupling of vibrational states (38–45). Typically, the higherthe pulse energy, the stronger are the energy shifts and, hence, thelarger are the phase shifts of the dipole responses (see Eq. 4). Thismodel assumption thus suffices to explain the strong intensity andtime-dependent spectral reshaping effects observed in the strong-field-controlled absorption spectra. The influence of possible effectslike cross-phase modulation and ionization of the medium can beexcluded. The details of the corresponding analysis are presented inFurther Possible Mechanisms: Cross-Phase Modulation and Ionization.Therefore, we have provided evidence that the concept of control-ling the phase of quantum states can be generalized to largemolecules in the liquid phase. The question of why only specificresonances experience the phase shift cannot be answered at this

point due to the lack of detailed information about the dyemolecule. With more such knowledge becoming available, e.g.,from quantum-chemical calculations, the general model de-veloped here should help to test our understanding of moleculesin strong fields, and thus pave a route to comprehensive controlof molecular excited states by intense laser fields (20, 46–49).The presented strong-field control mechanism goes beyond pre-

vious weak-field experimental approaches used in the liquid phase,exerted, e.g., by controlling the initial excitation step (20, 21, 30).While the previous schemes used shaped pulses (20, 21) or a pulsesequence (30, 50) to control the population and vibrational co-herence in excited states, here, strong fields are explicitly applied totransiently shift energy levels and thereby the phase evolution of theexcited states after their excitation. In the future, such strong-fieldcontrol may allow the time-dependent control of the entire potential-energy landscape, even for complex molecules in solution, directing

2.2

2.4

2.6

2.8

3.0

Ang

ular

freq

uenc

y

[fs-1

]

Fluence [10-4 J/cm2]5 10 15 20 25

Fluence [10-4 J/cm2]5 10 15 20 25

Fluence [10-4 J/cm2]5 10 15 20 25

Fluence [10-4 J/cm2]5 10 15 20 25

= -5 fs = -10 fs = -20 fs = -30 fs

1.8

1.35

0.9

0.45

0.0

OD [arb. u.]

Fig. 5. Simulation of the absorption spectra as a function of the control-pulse fluence based on the developed phase-control concept. The absorption band ismodeled by 22 transitions, equally spaced by 0.02 fs−1 and a common decay width of 0.1 fs−1. To mimic the measured spectra, only four transitions, namely at2.34 fs−1, 2.36 fs−1, 2.46 fs−1, and 2.48 fs−1, have to be taken into account to couple to the control laser pulse, i.e., only these dipole responses experience thelaser-induced phase shift. With these assumptions keeping the model as simple as possible, the measured observations can be reconstructed qualitativelyextremely well. The shift of the absorption maximum and the arising minimum at about 2.5 fs−1 are reproduced by the described toy model.

2.2

2.4

2.6

2.8

3.0

Ang

ular

freq

uenc

y

[fs-1

]

Fluence [10-4 J/cm2]

2.2

2.4

2.6

2.8

3.0

Ang

ular

freq

uenc

y

[fs-1

]

Fluence [10-4 J/cm2]5 10 15 20 255 10 15 20 25

Fluence [10-4 J/cm2]Fluence [10-4 J/cm2]5 10 15 20 255 10 15 20 25

Fluence [10-4 J/cm2]Fluence [10-4 J/cm2]5 10 15 20 255 10 15 20 25

Fluence [10-4 J/cm2]Fluence [10-4 J/cm2]5 10 15 20 255 10 15 20 25

= -5 fs = -5 fs = -10 fs = -10 fs = -20 fs = -20 fs = -30 fs = -30 fs

1.81.8

1.351.35

0.90.9

0.450.45

0.00.0

OD [arb. u.]OD [arb. u.]

Fig. 4. Measured absorption spectra showing optical density (OD) as a function of the control-pulse fluence plotted for fixed time delays τ= −5 fs, −10 fs,−20 fs, and −30 fs. At low time delays, strong features can be seen. First, the maximum shifts to higher frequencies. Secondly, at an angular frequency ofabout 2.5 fs−1, a minimum occurs with increasing fluence. These modifications remain visible even for larger time delays. The control pulse, i.e., the pump,that follows the excitation of the dye molecules leads to a significant perturbation of the absorption process with increasing intensity.

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molecular wave packets through light-induced transition states todesired final product states.

Conclusions and PerspectivesBy performing transient absorption experiments of the dyemolecule IR144 in the liquid phase, we have demonstrated thatthe phase-control model developed for isolated helium atoms(31) can be generalized to more complex systems. This enablesmeasurements of the intensity-dependent strong-field responseof systems ranging from simple atoms in the gas phase all the wayto condensed-phase systems, where decay and dephasing timesof excited states can be on the same order as the excitation andcontrol pulse durations. The presented model is completelygeneral, and its applicability certainly goes beyond the hereinused dye molecule IR144, which was only used as a represen-tative sample system. It can be adapted to any complex systemthat provides many resonances that spectrally overlap and formbroad absorption bands. In case the energy structure of thesystem is known in detail, quantitative studies come within reach.In addition, having a closer look at Fig. 1B reveals that, in the

temporal domain, the overall dipole response lasts for a longertime if a single transition is perturbed and phase-shifted. Theamplitude of the perturbed total dipole oscillation (red curve) is

larger at later times than in the unperturbed case (black curve).This means that by a simple phase control of a subset of transitions,as is described here, the overall coherence time of the dipoleresponse is extended. Manipulating such temporally extendeddipole responses by strong-field control of specific quantumstates may thus allow completely new routes toward coherentcontrol of larger molecules such as proteins or enzymes intheir natural aqueous environments.

Materials and MethodsThe optical density of the absorption spectra shown in Figs. 3−5 is de-termined by OD=−logðSp=S0Þ, where Sp is the measured probe pulse spec-trum transmitted through the sample and S0 is the reference laser spectrum,i.e., the unperturbed probe pulse spectrum without pump pulse and withoutsample. The concentration of the solution was chosen such that a trans-mission in the range of 7–10% was obtained, corresponding to an opticaldensity of about 1–1.2.

ACKNOWLEDGMENTS. We acknowledge financial support from the Deut-sche Forschungsgemeinschaft (Grant PF 790/1-1) and the European ResearchCouncil (Grant X-MuSiC-616783). J.-M.M. acknowledges funding from theHeidelberg Graduate School for Mathematical and Computational Methodsin the Sciences.

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