polyatomic molecules in strong laser ﬁelds: nonadiabatic...

JOURNAL OF CHEMICAL PHYSICS VOLUME 117, NUMBER 4 22 JULY 2002

Polyatomic molecules in strong laser fields: Nonadiabaticmultielectron dynamics

M. Lezius,a) V. Blanchet,b) Misha Yu. Ivanov, and Albert Stolowc)

Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Dr., Ottawa,Ontario K1A 0R6 Canada

~Received 17 October 2001; accepted 1 May 2002!

We report the observation and characterization of a new nonresonant strong field ionizationmechanism in polyatomic molecules: Nonadiabatic multi-electron~NME! dynamics. The strongfield response of a given molecule depends on important properties such as molecular geometry andbonding, the path length of delocalized electrons and/or ionization potential as well as on basic laserpulse parameters such as wavelength and intensity. Popular quasi-static tunnelling models of strongfield molecular ionization, based upon the adiabatic response of a single active electron, aredemonstrated to be inadequate when electron delocalization is important. The NME ionizationmechanism greatly affects molecular ionization, its fragmentation and its energetics. In addition,multi-electron effects are shown to be present even in the adiabatic long wavelength limit. ©2002American Institute of Physics.@DOI: 10.1063/1.1487823#

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I. INTRODUCTION

Electric forces underlie almost all of chemistry. Precmanipulation with strong external electric fields might, thefore, seem a natural choice for exploring the control of mlecular dynamics. Laser fields in particular can be chostrong enough to modify the potential energy surfaces whgovern molecular dynamics. This goal appears increasinwithin reach due to femtosecond laser technologies whpermit the production of very high power, well-characterizyet variable coherent optical wave forms.1–4 Modern ampli-fied fs laser systems can easily produce focused intensitieexcess of 1015 W/cm2, corresponding to electric fields comparable to or stronger than the atomic Coulomb fie(;109 V/cm) which bind matter itself. Indeed, strong fieoptical processes in atoms such as tunnel ionization andgeneration of ultrahigh harmonics5–7 are now routinely ob-served in many laboratories. The ability to apply these strelectric forces with high precision and little energy has leto various applications in science and technology. Forample, intense fs lasers have found their way as novelization sources in mass spectrometry.8 There is also broadinterest in the fs laser machining9 of materials due to the highprecision and significantly reduced local heat depositionthis process. In particular, the fs modification of transpardielectrics promises to be a powerful method for writingtegrated optical circuitry.10

Intense laser fields are playing an increasingly importrole in molecular dynamics. Strong laser field control expements have recently demonstrated that, using pulse-shatechniques which adjust the phases of all colors withinlaser bandwidth, bonds in polyatomic molecules can be

a!Also at: Universita¨t Innsbruck, Institut fu¨r Ionenphysik, Technikerstr. 25A-6020 Innsbruck

b!Also at: Universite´ Paul Sabatier, IRSAMC 118 Route de Narbonn31400 Toulouse, France

c!Electronic mail: [email protected]

1570021-9606/2002/117(4)/1575/14/$19.00

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lectively broken11 and new bonds can be selectiveformed.12 The exact physical mechanisms which underthis control presently remain unclear. Another area undervestigation is in optical Coulomb explosion imaging whicmay emerge as a way of resolving the structural dynamicpolyatomic molecules.13 However, recent experiments on datomic molecules showed that very short pulses14 can lead tostrong electronic excitations in highly charged molecuions, making it more difficult to resolve the time-dependestructure in such studies. The physical origins of these etations are yet to be fully elucidated.

We shall be primarily concerned here with the electroresponse of polyatomic molecules to intense nonresonant~in-frared! laser pulses. Molecular systems often contain coplex electronic structures. A fundamental question is:many electrons are present, which ones are most stroaffected by the applied field and, therefore, would contribmost to any control schemes? When does the single acelectron dynamics which dominates the strong field respoof atoms give way to a richer multielectron responsepected in molecules? It is the purpose of the present worelucidate some of this complexity and to discuss importlimiting cases which arise when strong laser fields areplied to polyatomic molecules.

In addressing these questions, we begin by reviewingcurrent understanding of strong-field interactions in atoand small molecules, focusing on the underlying physiassumptions and their limits. There has been outstandsuccess in describing the detailed behavior of atoms in strinfrared laser fields.15–19 A simple physical picture hasemerged whereby, for sufficiently long wavelengths, tstrong field ionization of atoms is described by the tunnellof the most weakly bound electron~of binding energyI p!through an essentially static barrier formed by the supersition of the core potential~Coulomb electric field! with thelaser electric field. This static picture emerges when the e

5 © 2002 American Institute of Physics

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1576 J. Chem. Phys., Vol. 117, No. 4, 22 July 2002 Lezius et al.

tron can tunnel very quickly as compared to the time scfor the barrier to reverse~i.e., the laser period!. This physicalidea rests upon both the quasi-static and single active etron ~SAE! approximations, discussed in more detail beloThese in essence amount to:~i! Ignoring any electron exci-tation inside the potential well, based upon an adiabaticproximation; and~ii ! ignoring any multi-electron effects. Thquasi-static SAE picture has been extremely successfuatoms15,16and small molecules20 when the so-called Keldyshparameter21 is small:g!1 ~in practiceg,0.5!. The Keldyshparameter, discussed in more detail below, is related toratio of the tunneling timet t5A2I p/e to the laser periodvL

21 and can be defined as:21 g5t tvL . When the tunnelingtime is short compared to the laser period, we can consthe tunneling probability as varying parametrically with tamplitude of the applied strong field. As the tunnelling proability varies exponentially with barrier suppression, esstially all tunnelling events occur at the turning points~i.e.,maximal barrier suppression! of the field oscillation. It is forthis reason that a purely static calculation of the tunnelrates is successful.

Where and when should these two main approximatibreak down? The adiabatic approximation assumes thatime scale of electron motion inside the potential wellmuch faster than the laser period: The electrons are assuto adjust instantaneously to the time-varying electric fiE(t) of the laser. This is completely analogous to the familBorn–Oppenheimer approximation where the time scaleelectron motion is assumed to be much faster than that otime varying electric field due to nuclear motion. The comonly used figure of merit in strong field ionization studiis the Keldysh tunneling parameter. While the originKeldysh theory21 is not limited to tunnelling, it was derivedfor a zero-range potential and is, therefore, intrinsically uable to account for any electron dynamics inside the potenwell. Therefore, the limitg!1 should not be identified withthe adiabaticity of the electronic response: The Keldyparameter relates only to the electron motion under~tunnelling! potential barrier and completely ignores aelectron dynamics inside the well. Other Keldysh tyapproaches22,23 suffer from this same drawback. This cocern applies equally to the theory developed by PerelomPopov, and co-workers24 and its tunneling limit ofg!1 de-rived by Ammosov, Delone, and Krainov,25 now commonlycalled ADK theory. For single ionization of atoms closethreshold, it is generally accepted that ADK is highly sucessful. These theories include corrections to account forproper Coulombic shape of the binding potential but s~implicitly or explicitly! use the quasi-static~i.e., adiabatic!approximation for the electron dynamics inside the potenwell.

The adiabatic approximation is justified in rare gasoms because the time it takes for an electron to ‘‘traverseatom’’ is typically subfemtosecond, much less than the laperiod. This approximation will inevitably fail when the timscale of electron dynamics within its associated potentialproaches the laser frequency, as can be the case in patomic molecules.

The second standard approximation in the strong-fi

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atomic physics is the single active electron~SAE! approxi-mation. The SAE picture should fail when multiple electrowhich caneffectivelyrespond to the laser field~and interactwith each other! are present in the potential. The simpletype of multi-electron phenomena are the correlation effeobserved in multiphoton double ionization processes26 whichoriginate from rescattering phenomena and autoionizresonances.27 Nevertheless, for single ionization of atomshas been commonly accepted that the SAE approximatiojustified unless resonances with bound two-electron excstates are explicitly involved. SAE response is indeedcase in rare gas atoms: Even though they have multequivalent electrons in their outer shell, all doubly excitstates which can contribute to the strong field polarizabiare well above the ionization potential. The neglect of othelectrons and, hence, the couplings between them gresimplifies the problem. For He, Ne, Ar, and Xe, SAcalculations18,28 yield outstanding agreement witexperiments.15,16,19

In the strong field ionization of small molecules, the vbrational time scale has to be compared to the pulse duraand, in extreme cases, to the laser period itself. For examin H2 and in CH bonds the vibrational time scale is aboutfs, shorter than the duration of most femtosecond pulsBenchmark calculations of ionization rates of simple mecules such as H2

1 , H2 , and H31 show that the ionization

rates at intensities ofI;1015 W/cm2 can approach 10 fs.29 Insuch cases the electronic and vibrational responses manonseparable. In particular, even for short~few tens of fem-toseconds! pulses interacting with larger organic moleculea question will be whether or not the CH bonds are stroncoupled to the driven electron dynamics.

The additional aspect of vibrational dynamics leads tnumber of important, qualitatively new effects. If largamplitude vibrational dynamics is present during the lapulse, a new ionization mechanism obtains. When the bis stretched to a certain critical lengthRc , which is typicallysignificantly greater than the equilibrium bond length, efcient multiple ionization occurs.30–35 This phenomenon of‘‘enhanced ionization’’ has been extensively investigateddiatomic and small polyatomic molecules, see, e.g., R30–35.

For H21 , exact numerical simulations31 have shown that

the maximum in the ionization rate occurs when the lowunoccupied molecular orbital~LUMO! is Stark-shifted bythe instantaneous electric field of the laser to just aboveCoulomb barrier for the electronic motion. However, tLUMO, which acts as a doorway to ionization, must in adition be populated in order to enable this mechanism. Tis achieved when the electronic response to the laseroscillation becomes nonadiabatic. As the H2

1 bond stretches,the highest occupied molecular orbital~HOMO!–LUMOcoupling increases and the field-free energy gap decreaboth leading to a nonadiabatic electron response with resto the laser oscillation, thus populating the LUMO. In othmolecular systems the LUMO may not be the doorway stto ionization: In H2 the relevant doorway states are the iopair states.33

For sufficiently largeR>Rc , the same phenomenon ca

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1577J. Chem. Phys., Vol. 117, No. 4, 22 July 2002 Polyatomic molecules in strong laser fields

be described using an atomic picture.30 The coherent superposition of HOMO and LUMO, due to the nonadiabatic eletron response, corresponds to a dynamic electron localizaat one of the atoms. The tunnelling barrier at this atomcore, suppressed by the laser field, is additionally suppreby the Coulomb field of the other atomic core, leading togreatly enhanced ionization rate.30

We stress that population of the doorway states needbe resonant. This is confirmed by calculations31 showing thatthe enhancement structure in the ionization rate is assocwith conditions for dynamic electron localization~via nona-diabatic population of the Stark-shifted LUMO! and not withmultiphoton transitions that become resonant at certainues of the internuclear distanceR.

It is very important to note that the contribution of thenhanced ionization to strong field molecular ionizationpends greatly on the pulse duration. If the pulses areshort, vibrational excursions cannot reachRc before the fieldturns off and enhanced ionization will be absent. If the pulare longer than the time required to reachRc , then essen-tially all ionization events will occur atRc . @As discussed ina following section, we specifically used short 40 fs pulsesthe present study in order to minimize effects associated wenhanced ionization. We also kept intensities relatively lin order to avoid strong multiple ionization followed by thCoulomb explosion, resulting in significant fragment ioenergies36 and fast nuclear motions~significant even on 40 fstime scale!.#

As the system size increases from diatomic to poatomic molecules and clusters, the situation changes agThe zero-length scale approximation in the quasi-static tneling model was revised by showing that a longer molecintrinsically leads to a lowering of the barrier,37 as observedin the shape of the photoelectron spectra of field-ionizmolecules. A ‘‘correction’’ to the Keldysh parameter whicaccounts for the molecular ‘‘length’’ has been developed37

In the following, we will call this ‘‘length-corrected’’ quasi-static model, the molecular single active electron~MSAE!picture.

The MSAE model suggests that the larger the systthe more readily the tunneling limit obtains as comparedan atom of similar ionization potentialI p: The larger themolecule, the more efficient the strong-field ionization. Rcent experiments,38 however, suggest the opposite trend: Tintensity thresholds for efficient strong-field ionization, mesured for a large number of polyatomic molecules, are higthan those for atoms of similarI p . Our experiments reportehere confirm this trend, and the numerical simulationsscribed in the following section suggest that the originthese higher ionization thresholds lies in strong field-indupolarization of all delocalized electrons, even in the lofrequency limit.

As systems increase further in size, collective muelectron behavior should start to dominate their strong-firesponse. Experimental studies on fullerenes39–42 andmolecular,43 metallic,44 and rare-gas45–50 clusters revealed anumber of interesting phenomena: High ion kineenergies,45,48 efficient ionization rates,49 extreme ultraviolet~XUV ! photon,46 and x-ray generation,47 rapid fragmenta-

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tion, and high electron kinetic energies with multiple enerdistributions.50 For these larger aggregates, a ‘‘nanoplasma-based description appears appropriate.48,51 The ques-tion one would like to address is: What degree of systcomplexity is necessary to induce the transition from sinto multiple electron dynamics in strong, low-frequenfields? Our model calculations suggest that the onseplasma-like multielectron behavior could be related to fsaturation of nonresonant Landau–Zener-type electrotransitions between the ground and excited electronic staas discussed in detail below.

In a recent letter,52 we reported our observation ancharacterization of a new, general type of nonresonant strlaser field ionization which can exist in polyatomic moecules: Nonadiabatic multi-electron~NME! dynamics. In thefollowing, we present a full account of this work, includinadditional experimental results and a simple physical mowhich illustrates the essential physics.

This paper is organized as follows. We begin with a vesimple driven electron-in-a-box model in order to motivathe discussion and to illustrate the physical phenomenaconcern here. We then describe our experimental methodmaking the calibrated, absolute intensity measuremewhich were important in this study. In order to addresspotential failure of the adiabatic and SAE approximationspolyatomic molecules, we report our studies on unsaturahydrocarbons~the linear polyenes!, which have many delo-calized p electrons. Through systematic variation of thlength of the polyene and by studying its ionization and framentation patterns as a function of wavelength~from 1500 to400 nm!, we observed the transition from quasi-static tunning ionization to nonadiabatic multielectron behavior.

II. PHYSICAL MOTIVATION: A DRIVEN ELECTRON-IN-A-BOX MODEL

A very simple model for picturing phenomena relatedstrong field ionization dynamics is based on a smooth odimensional~1D! particle-in-a-box potential,U(x)

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11exp~ uxu2L/2a!. ~2.1!

We study both single and multiple electron laser-inducednamics in this model potential. For the multiple active eletron ~MAE! situation, we borrow an approach used in clusstudies.53 In the low-frequency limit, the main multi-electroeffect is the significant change in the~quasi-static! self-consistent Coulomb field experienced by an electron duethe displaced density~i.e., polarization! of the multi-electroncloud. Within this approximation, each electron is seconsistently initialized in its corresponding field-free sta~orbital! cn

(0) of the box. Each electron’s dynamics is dscribed by:~1! The effective one-electron field-free statioary potentialU(x) @in our case modelled by Eq.~2.1!#, ~2!the interaction with the laser field, and~3! the interactionwith the differential Coulomb potential due to the laseinduceddisplacementof the total electron densityDr

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S U0527.1 eVL513.2 Åa53.6 a.u.

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Such a crude model lacks many aspects of MAE behior and relies on the assumption that they are all includedthe field-free effective potentialU(x) which in principle maycontain any existing field-free electron correlations. We ephasize again that we use thedifferencein the self-consistenfield ~SCF!—Eq. ~2.2!. In spite of the highly simplified na-ture of our model, we expect that it will allow a qualitativunderstanding of the dynamics in the low-frequency limwhere the change in the SCF is the dominant effectshould allow us to see the onset of the departure fromquasi-static dynamics.

Some of the results of these calculations are presenteFigs. 1 and 2. The simulation considered four pairs ofp SCFelectrons, each pair occupying one orbital as per Pauli’s pciple. At time zero, before any field is applied, they haveexpected nodal structure. Driven by the field, each elecstarts to oscillate in the field and reacts to the displacemof the Coulomb field due to all other electrons. Althouonly the total electron density has a physical meaning inmodel, it is instructive to observe the evolution of each initorbital to verify that all electrons respond to the field@seeFigs. 1~a!–1~d!#.

An example of the time dependent evolution of a drivsingle active electron~SAE! is depicted in the top panel oFig. 1, showing the SAE electron density as a functiontime and coordinate. It evolves with increasing oscillationsR. When the density localizes close to the barrier, tunneis observed. Outside the potential, the density is dampedan absorbing boundary. As the electric field strengthcreases, the electron oscillations increase in amplitude, etually leading to ionization within about 1 1/2 optical cycleParts of the density are also scattered at the edges of theresulting in ‘‘splash’’-like excitation events.

At each laser wavelengthl the total ionization probabil-ity Wion(I ) was calculated as a function of laser intensity.frequency-dependent saturation intensityI sat(l) was definedas the limit when the probability of single or higher ioniztion is Wion(I )'0.9. For long wavelengths, the onset of ioization is very steep andI sat is not very sensitive to the exacform of Wion(I ). As shown in Fig. 2, we observe a stronfrequency dependence to the calculatedI sat, decreasing to-wards shorter wavelengths~higher frequencies!. For longwavelengths, theI sat is higher for the many-electron casthan for the single-electron case. We also show the resexpected for the quasi-static atomic tunnelling~obtained viathe ADK tunneling formula25! and the length-corrected mo

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lecular single active electron~MSAE! result.37 Of course,due to their inherent adiabatic approximation, both the ADand MSAE results are wavelength independent.

Our model shows that there are many-electron effeeven in the low frequency adiabatic~quasi-static! limit, sincethe calculatedI sat is higher for the many-electron case. Wbelieve that the reason for this is a dynamic shielding effcaused by the higher polarizability of the multi-electron sytem. Simply put, the dynamic polarization of allother elec-trons in the field essentially pushes them towards the potial wall. This adds additional electron–electron Coulomrepulsion to the potential barrier, making it harder for tactive electron to escape. The induced dipole moment, whwill depend on the total number of delocalized electronsthe system, can partially negate the externally applied fiand, therefore, increase the effectiveI sat. This observation isconsistent both with our experimental data~vide infra! andprevious observations38 and is currently under further investigation in our laboratory.

Very qualitatively, the electron density dynamics seenour calculations suggest a rough analogy with the splashof water in a periodically tipping bathtub of lengthL. In ourcase, it is the oscillating electric field that causes the pottial to periodically tip left and right~at the laser frequencyvL!, forcing the electron density to oscillate within the weIn the low frequency limit, the bathtub tips very slowly anthe surface of the water remains flat at all times~adiabaticdynamics!. As the amplitude~angle! of the tilt increases,water begins to pour over one edge or the other~tunnel ion-ization!. Depending on the degree of tilt~laser intensity!,more water may be lost~multiply charged cations! but thesurface of the water always remains flat~no electronicallyexcited cation states!. If the time it takes for water to pouover the edge~classical analogue of the tunneling time! ismuch less than the time to reverse the tilt~laser period!, thenthe ratio of these two times~the Keldysh parameter! is muchless than unity. This corresponds to the standard quasi-spicture. Independent of this~Keldysh! ratio, if the frequencyof the tipping motion now increases, the water no longremains flat due to the formation of waves~nonadiabatic dy-namics! and, as the amplitude increases, water is splasout of the bathtub~nonadiabatic ionization dynamics!. Fur-thermore, the waves can remain even after the tilting~laser!has been turned off~formation of electronically excited statewhich persist after the laser pulse is turned off!. When thelaser period matches the time scale of electron motion insthe potential well, there can be very large amplitude denoscillations.

The results of our calculations show that for increaslength ~or, equivalently, decreasing level spacings!, theexcitation–ionization dynamics appeared to change frquasi-static tunneling to a ‘‘splashing’’ dynamical behavioThe latter effect could potentially result in large energy asorption, even at low intensities and in the absence of fiefree resonances. The nonadiabatic departure from qustatic tunneling can occur even when the Keldysh paramg is less than unity, whether corrected or not for molecusize effects.37 It is important to note that the Keldysh parameter relates only to the tunneling motion through the fie

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FIG. 1. Top: AR2t probability density plot of a single active electron~SAE! in a 1D potential driven by a strong~40 fs! alternating electric field pulse~shownon the right!. Ionization events occur at the fourth, fifth, and sixth half-cycle of the pulse.~a! A R2t density plot showing the 40 fs time evolution of the firself-consistent field~SCF! coupled eigenstate in a 1D potential driven by the same field.~b!–~d! correspond to the second, third and fourth SCF eigenstaWhile only the total density~sum of all four graphs! carries physical significance, it is important to note that all orbitals are strongly and nonlinearly affby the electric field.

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induced potential barrier and that it completely ignores aelectron dynamics inside the well. We will further analyzbelow, the results of our simulations and the qualitatphysical picture that they suggest by using the LandaDykhne theory of nonadiabatic transitions.54 We stress thathere the term ‘‘nonadiabatic’’ refers to the driven electrmotion with respect to the oscillations of the electric fieduring the laser cycle. This should not be confused with

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non-Born–Oppenheimer coupling between the electronicvibrational motions, which can also cause laser-assisted etronically nonadiabatic transitions between laser-inducedtentials of the dressed molecule~see, e.g., review55 and/or56

for recent experiments!.The time scale of response in bound quantum system

given by the inverse level spacings in the problem. If eletronic level spacings are very large compared to the~near IR!

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photon energy, the electron can usually be considered tohave adiabatically with respect to field oscillations. Thisindeed the case for rare-gas atoms. However, for molecwith delocalized orbitals, the electronic level spacings vinversely with the ‘‘length of the molecule’’ and the adiabaapproximation can fail. If we allow for large amplitudnuclear dynamics, these types of nonadiabatic effects caseen even in the simplest diatomic molecule H2

1 where theefficiency of nonresonant electronic excitation and ionizatdepends greatly on the internuclear distanceR.31 In particu-lar, stretchingR from the equilibrium to a critical distancRc;4 Å not only maximizes the ionization rate of the Stashifted LUMO, but also greatly increases the probabilityefficient nonresonant population of this state~which acts asthe doorway to ionization!. The efficiency of nonresonannonadiabaticsg→su transition increases at largeR becausethe sg→su coupling increases withR and, simultaneouslythe electronic energy gap decreases.

Our simulations show that nonadiabatic electron dynaics becomes increasingly more pronounced in polyatomolecules with delocalized electrons as one increasesmolecular size. While the exact conditions for the onsetefficient nonresonant population of the excited statesdepend on the specific molecule, a Landau–Dykhne-tanalysis54 offers a simple semiquantitative estimate. Cosider a system with characteristic lengthL and field-freelevel spacing D0 , subjected to an oscillating fieldE5« sinvt. This situation is depicted in Fig. 3. For a lasfrequencyv!D0 , the levels will shift via the Stark shift athe field increases towards1« or 2«. In the purely adiabaticlimit, the populations always remains in their Stark shift

FIG. 2. Saturation thresholdsI sat, defined as 90% ionization, as a functioof wavelength obtained from simulations for a single active electron~SAE!and for multiple active electrons, MAE~eight SCFp electrons!. The eightSCF electrons initially populated the four lowest eigenstates of an elecin-a-box-type potential~see text!. Also indicated are the wavelength independentI sat expected from molecular single active electron models~MSAE!and from ADK theory. For a discussion, see the text.

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initial states without undergoing transitions to higher~orlower! lying states. However, as the laser frequency andthe Stark shift increases, the system will oscillate moquickly between1« and2«. ~For sufficiently strong fields,the Stark shift will no longer be quadratic, but will rathescale with the voltage«L applied across the length of thmolecule.! Landau–Zener type nonadiabatic transitions wbecome increasingly probable, allowing population to evotowards higher-lying~bound! electronic states. This proceswill be highly efficient and virtually insensitive to resonances if these nonadiabatic transitions are saturated withfew laser cycles: This situation implies a great energy broening of the manifold of electronically excited states anthus, the formation of an electronic quasi-continuum.

For a pair of electronic states separated byD0 andcoupled by the molecular dipole matrix elementm, the prob-ability PLZ of nonresonant Landau–Zener-type nonadiabatransitions during one-half a laser cycle is54

PLZ;exp~2pD02/4vLEm!. ~2.4!

Several comments are required before we discuss applthis expression to molecular systems. First, it assumesthe nuclear motion is negligible during a one-half of a lascycle. Second, the transition matrix element should be evated at the instantaneous molecular geometry: For very spulses, the equilibrium geometry should provide a suciently accurate estimate. Finally,D0 andm should be chosento correspond to the states most strongly coupled toground state. In general, the value of the dipole matrix ementsm will increase with increasingL, as is certainly thecase for charge-transfer and charge-resonant states, whmscales asL.57 Consequently, whenvLEL;D0

2, transitionswhich correspond to charge transfer across the moleculecome quickly saturated. This implies strong nonresonantsorption byall delocalized electrons involved in this coupling. ~We note that for many polyatomic molecules, threlatively unpolarizable electrons associated with C

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FIG. 3. Sketch of a one-dimensional multilevel quantum system of lengtL,average level spacingD0 and molecule transition dipole couplingd0 in astrong oscillating electric fieldE of frequencyvL . In the adiabatic lowfrequency limit, all states Stark shift smoothly withu«u and the populationsremain in their respective adiabatically field-dependent eigenstates. Asfrequency increases, Landau–Zener-type nonadiabatic transitions canat the avoided crossings with probabilityP. Such nonadiabatic strong fieldtransitions can lead to nonresonant excitation of many electronically excstates after only a few laser cycles.

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FIG. 4. A depiction of the experimental setup. A 0.mm 30 fs Ti:Sa oscillator is regeneratively amplifiedyielding 40 fs, 700mJ pulses. These were either usedirectly or pumped a short pulse OPA system, produing high power~.100 mJ! 40 fs pulses in the 1.2–2.4mm range. A restricted collection volume time-of-flighmass spectrometer~TOFMS! ensured that ions werecollected only from a cylindrical volume of constanaxial intensity. Ion signals and laser pulse energies wrecorded every shot. The sample inlet consisted oglass wool reservoir from where molecules were evaprated at ambient temperature and transported in an incarrier gas to the interaction region. For details, seetext.

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bonds are not much involved in this charge-transfercharge-resonant coupling, and therefore, the fact that tvibrational periods approach the period of infrared lafields is of small import here.!

The atomic analogue of such a nonresonant nonadiabresponse has been described theoretically58 and observedexperimentally59 in the strong field microwave ionization oatomic Rydberg states. In the MAE case, this represennonadiabatic multi-electron~NME! excitation mechanismwhich leads to acomplete failure of both the adiabatic~quasi-static! and the SAE pictures. This failure is intrinscally independent of the nature of the barrier and can oceven wheng,1, a case which is formally considered thtunneling limit. It is important to note that the greater tlengthL, the easier it is to reach the limitvLEL;D0

2. As aspecific example, with L513.5 Å, D054 eV, and l5700 nm, we find thatvLEL5D0

2 already at an intensityI'5.631012 W/cm2, a situation which corresponds to our eperimental results on the polyene all-trans decatetraene~seenext section! and, importantly, obtains inmanystrong fieldexperiments on molecules.

The creation of an electronic quasi-continuum via etreme broadening of excited states through highly efficinonadiabatic transitions suggests that the subsequent dmulti-electron dynamics might be qualitatively understoodterms of classical mechanics. From a classical perspecthe important classical parameters for electronic motionthe quasi-continuum are:~1! The electron oscillation amplitude aosc5E/vL

2 and ~2! the length of the delocalized electron path inside the moleculeL. There are two limiting casesaosc@L andaosc!L. Classically, whenaosc@L the electronis pushed by the field along the entire length of the molecand then scatters~splashes! off the edge of the potential wel~this occurs twice per full laser cycle!. The energy typicallyabsorbed~the work done on the electron! during each scat-

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tering event isEscat;EL. When Escat exceeds typical levespacings, electronically excited states are formed. WhenEscat

approaches the ionization potentialI p , these states will ion-ize over the barrier in the next optical half-cycle.

In the other limit of aosc!L, Escat;Up5E2/4vL2, the

average~ponderomotive! energy of electron oscillation in thelaser field. Since the ponderomotive electron drifts as weloscillates, it will soon hit the edges of the potential. WhI p,Up , the atomic Keldysh parameterg5AI p/2Up is lessthan unity, a situation that is usually interpreted as tunnling. However, ionization can now proceed via absorptionenergy;Up in one scattering~splashing! event, once againfollowed by over-the-barrier escape during the next lahalf-cycle. Such an ionization mechanism becomes the tcal case with increasing box lengthL. We conclude this dis-cussion by reiterating that the Keldysh parameter is not nessarily diagnostic of tunneling behavior.

III. EXPERIMENT

The experimental arrangement, illustrated in Fig. 4,described in detail elsewhere.38 Briefly, a mode-lockedTi:Sapphire laser oscillator produced'30 fs pulses at0.8 mm which were subsequently regeneratively chirppulse amplified~CPA!. The 30 nm bandwidth of the NRCdesign CPA system maintained a compressed pulse duraof 40 fs while delivering 700mJ per pulse at a repetition ratof 330 Hz in a near diffraction-limited spatial mode. The 0mm pulse was either used directly or it pumped a short-pufive-pass optical parametric amplifier~TOPAS!, generatingbroadly tuneable~1.2–2.4mm! high power infrared pulses o'40 fs duration. Additionally, via second harmonic genetion in 0.1 mm BBO crystals, high power 40 fs pulses coube generated at 0.4 and 0.6–1.2mm. These laser pulse chaacteristics were confirmed via autocorrelation, spectrome

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and frequency resolved optical gating~FROG!. After vari-able attenuation, pulse energies were monitored on a shoshot basis using an integrating sphere in order to binexperimental data with respect to intensity~vide infra!.

The central goal of this work was to study the intensand wavelength dependence of strong field molecular iontion processes. Importantly, in these studies we specificavoided the deleterious effects of spatial averaging overlength of the laser focus. The intense pulses were focuwith achromatic f30 optics into the interaction region ofrestricted collection volume time-of-flight mass spectrome~TOFMS, resolution of 300!. At 0.8 mm, the focusing geom-etry yielded aR527mm diameter beam waist and a Raleigh range of 3 mm, as measured with a CCD camera bprofiling system. The entrance electrode to the TOFMS ha500 mm slit aperture so that the Rayleigh range was signcantly longer than the width of the aperture. This ensuthat ionization events were collected only from a cylinderconstant axial intensity. The maximal Gaussian peak laintensity I 0 was 2.731015 W/cm2. This was independentlyconfirmed by studying the intensity dependence of heliionization. Gaussian spatial behavior at the laser focusfurther confirmed by scanning the focus with respect toentrance slit to the TOFMS drift region. The laser polariztion was directed along the TOFMS axis.

Low density gas, typically 1026 Torr pressure in order toavoid space charge effects, was introduced to the ionizaregion through a variable leak valve. We introduced sosamples using a weak flow of a carrier gas~e.g., He! througha glass tube packed with pre-cleaned glass wool. The sphase organic molecules used in these experiments~all-transDecatetraene,b-Carotene! were dissolved in hexane anevaporated on the glass wool before use, thus yielding a hexposed surface area. For the liquid phase organic molecused in these experiments~trans-Hexatriene and Cyclooctattreaene!, the vapor pressure was sufficiently high so as torequire this carrier gas technique. In all experiments,avoided heating the samples in order to eliminate any risthermal decomposition. A large aperture TOFMS, descripreviously,60 was used to determine the kinetic energylease amongst the ionization fragments. Again, the laserlarization was directed along the TOFMS axis. For all kineions observed here, the 0.759 aperture was nonvignettingExperiments consisted of measuring mass spectra as ation of laser pulse energy, via variation of an attenuator.each wavelength, laser pulse characteristics were determand the energy scans repeated. The energy scans wereverted to calibrated absolute laser intensity scans, descrbelow.

As discussed in detail by Hankinet al.,38 a cylindricalionization volume of constant axial intensity allows for thdevelopment of calibrated absolute intensity measuremthrough the definition of the saturation intensityI sat. Wehave used this method to make precise and accurate intemeasurements as a function of wavelength. The ionizasignal produced by a parallel Gaussian beam of peak insity I 0 is given by

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wheren is the concentration of the neutrals,l the length ofthe cylinder projected onto the detector,a the instrumentsensitivity andf is the ionization branching ratio.W(I ) isthe intensity dependent ionization rate andt is the effectiveduration of an equivalent square laser pulse. As long asW(I )increases sufficiently rapidly withI, a simple limiting behav-ior obtains. In theW(I )@1 limit, the above equation leads t

S~ I 0!5apR2nlf@ ln~ I 0!1 ln~ I sat!#, ~3.2!

whereI sat is defined to be the saturation intensity. It canseen thatI sat is the intercept of a linear extrapolation in a plof ion signal intensityS versus lnI. Importantly, I sat is amolecularproperty which indicates the ease of ionizationa laser field of given intensity and wavelength. For exampif the ionization rate followed a power law,W(I )5snI n, thequantity I sat would correspond to the constant intensitywhich 43% of the molecules are ionized. Therefore,I sat al-lows for the unambiguous characterization of the strong fimolecular response as a function of wavelength and molelar properties~e.g., length, shape etc.!. We note that we ex-pect this experimental definition ofI sat to be linearly propor-tional to the calculatedI sat discussed above in our driveelectron-in-a-box model.

A typical example of the determination ofI sat is shownin Fig. 5 for the case of singly, doubly and triply chargedecatetraene parent ions, irradiated with intense 1.45mmfemtosecond laser pulses.I sat is given by the intercept of thelinear extrapolation of a plot of signal versus the log of tlaser intensity. All values ofI sat reported in this paper weredetermined in this manner.

Absolute laser intensities were also obtained in the mner described by Hankinet al.38 Briefly, the experimentalionization rateS(I ) for atomic rare gases~here Xenon! canbe fit to the highly accurate ADK model of atomic tunnionization. Therefore, by fixing the measuredI sat for the Xe

FIG. 5. Determination of the saturation intensityI sat, a molecular propertyrelating to the response in a strong nonresonant field. A linear extrapolato the baseline definesI sat for the ion of interest. The calibrated absoluintensity scale is determined using the known saturation intensities forgas atoms such as Xenon which can be accurately fit to ADK tunnetheory.

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FIG. 6. Mass spectra of linear, fully conjugated atrans hydrocarbons of increasing length: Hexatriendecatetraene andb-carotene, using broadly tunable, intense 40 fs pulses, shown at characteristic wavelengof 800 and 1450 nm. Hexatriene shows the formationseveral charge states of the parent molecule with litfragmentation, characteristic of quasi-static tunnel ioization. The longer decatetraene shows a similar resat 1450 nm, forming singly, doubly and triply chargeparent ions. Importantly, its fragmentation patterns vawith wavelength, exhibiting a transition to completfragmentation by 800 nm. The much longerb-caroteneshows extensive fragmentation at all wavelengths stied. Absolute intensities were determined using atomXe as a reference standard, as discussed in the tex

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rare gas atom to its ADK value@ log(I)513.8#, as shown inFig. 5, the absolute intensity scale is determined. With tmethod, we estimate thatI sat has an absolute error of 30%and, in the comparison of different wavelengths, a relaterror of less than 20%.

IV. EXPERIMENTAL RESULTS

In order to study the effects of delocalized electron plengths on strong field ionization processes, we have chothree linear unsaturated hydrocarbons with similar electrostructures~delocalizedp systems! but different effectivelengthsL: Trans-hexatriene~7.2 Å!, all trans-decatetraene~13.5 Å! and b-carotene~32 Å!. In Fig. 6 we show strongfield ionization TOF mass spectra of hexatriene~HT!, de-catetraene~DT! andb-carotene~bC! at two different wave-lengths: 0.8 and 1.45mm. For HT, the mass spectra obtainwith I;1014 W/cm2 at 0.8 and 1.45mm are very similar.Both show large singly- and doubly-charged parent ionsnals with very little or no fragmentation. This shows that tdoubly ionized state of the HT cation is stable and thatsentially no electronically excited states of the cationformed.~It is well known that electronically excited statescations often undergo radiationless decay processes, leato fragmentation.61! Such a wavelength-independenfragmentation-free ionization pattern, which is expectedquasistatic tunnel ionization62 and adiabatic electron dynamics, is typical for HT over the whole range 0.8mm,l,1.6mm.

At I;1014 W/cm2 and l51.45mm, DT also yieldsmass spectra which are characteristic of quasistatic tuionization: Singly-, doubly-, and triply-charged parent iowith little fragmentation. By contrast, at 0.8mm DT frag-ments very strongly at a much lower intensity ofI;1013 W/cm2. There is a dramatic change in the naturethe strong field ionization dynamics in DT between 1.45 a0.8 mm. A new type of wavelength dependent ionizatiofragmentation mechanism is seen in the longer DT but nothe shorter HT. This wavelength dependence of the DT iization clearly demonstrates that any quasistatic picture fa

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The electron dynamics simply cannot be adiabatic. Thefore, we have observed the transition as a functionwavelength—or, equivalently, as a function of the molecu‘‘length’’—from quasi-static tunnel ionization to a nonadiabatic ionization dynamics. It is very important to note,discussed in a later section, that the differences in these mspectra cannot originate from optical resonances becadue to the large AC Stark shifts involved~;10 eV!, thediscrete level structure of the field-free molecule is irrevant. The 1.4mm mass spectrum demonstrates that eventriply charged parent ion is stable and therefore the extenfragmentation observed at 0.8mm is likely due to electroni-cally excited states of the~singly and multiply charged! cat-ion which fragment after the 40 fs laser pulse is over. Tgives us a first hint that a multi-electron excitation-ionizatimechanism is involved.

If the transition to nonadiabatic strong field ionizatiodepended on the molecular length, then we expected thstill longer molecule,b-carotene, should undergo nonadibatic ionization even at 1.5mm. In fact, at all intensities andwavelengths between 0.4 and 1.5mm, bC is completely frag-mented. This suggests an ionization process similar to thaDT at 0.8mm, but very different from that in DT at 1.45mmand HT at all wavelengths, is operative.

In sum, the results of Fig. 6 demonstrate a failure ofquasi-static tunneling model for molecular ionization asuggest the onset of a nonadiabatic excitation-ionizamechanism. The failure of the quasi-static approach is sto depend on important molecular properties such as deloized electron path lengths.

We consider two possibilities for the large energy asorption in the field which leads to the extensive fragmention of DT seen in Fig. 6 at 0.8mm. One is that a singleactive electron~SAE! experiences extensive above threshoionization–absorption~ATI !,54 reaching a superexcited staof the cation which subsequently decays, leading to theserved fragmentation after the laser pulse is over. The opossibility is that multiple active electrons~MAE! each ab-sorb energy from the laser field to form complex multip

ighAt

yl

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FIG. 7. Mass spectra of all-trans decatetraene at hand low laser intensities, using 700 nm, 70 fs pulses.the detection threshold intensity of 1012 W/cm2 ~yield-ing about 1 ion per 250 laser shots!, the fragmentationis as extensive as at 1013 W/cm2. The fragments showssignificant kinetic energy release. Inset: The methgroup part of the mass spectrum~12–15 amu!. Theforward–backward splitting corresponds to CH3 frag-ment average energies of 1.25 eV and highly directioemission, uncharacteristic of typical unimolecular dcomposition processes in photoexcited ions.

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excited states of the ion core which also decay after the lpulse is over. We expect these two processes to havedifferent intensity dependencies. The SAE ATI case shohave a very high order intensity dependence~i.e., one elec-tron must coherently absorb many photons! as comparedwith the MAE case.

In Fig. 7, we show DT ionization-fragmentation patterfor 70 fs, 0.7mm irradiation at intensities ofI;1012 and I;1013 W/cm2. It can be seen that even at this lowest laintensity where ionization signals can just be observ1012 W/cm2 @Fig. 7~a!, 1 count per 200–300 laser shots#, thefragmentation is as severe as at 1013 W/cm2 @Fig. 7~b!#where the ionization rate is much higher. The route to ioization for DT at 0.7mm appears the same at 1012 W/cm2 asat 1013 W/cm2. This result cannot be reconciled withmodel based on SAE above threshold ionization becausehighly nonlinear behavior of ATI with intensity would yieldmuch less fragmentation at the lower intensity. This resindicates that multiple active electrons are involved instrong field ionization. Therefore, we suggest that the nionization dynamics seen in DT at 0.8mm is a nonadiabaticmulti-electron~NME! excitation-ionization process.

It is interesting to analyze further the DT fragmenshown in Fig. 7~b!. In a linear TOFMS,63 it is possible todetermine the kinetic energyEkin released during the fragmentation from the ‘‘turn-around time’’ splittingDt seen infragment ion mass peaks:Dt5AmEkin /qFacc ~whereFacc isthe extraction field applied to ions of chargeq and massm!.We find that atI;1013 W/cm2 the kinetic-energy release ithe fragments is considerably larger than expected for simphotochemical bond cleavage in polyatomic molecules. Tinset in Fig. 7~b! demonstrates that the 13–15 amu~CHx ,x51 – 3! peak shapes correspond to an average kineenergy release of 1.25 eV. Furthermore, the clear doupeak structure shows that the dissociation is highly dirtional, in contradiction with simple bond rupture unimoleclar decay64 where isotropic emission is expected. As notabove, the large aperture mass spectrometer used in thissurement did not vignette the ion trajectories. Our analysithe peak shapes for theC2

1 andC31 fragments indicates av

erage~maximal! kinetic energies of 2 eV~4.2 eV! and 0.9 eV~3 eV!, respectively. While these kinetic energies are wbelow those typically observed in intense-field Coulombplosion (I;1015 W/cm2) of multiply charged molecular

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ions,36,43 they are much higher than those expected for tycal unimolecular decomposition of photoexcited ions.61 TheC–C sigma bond fission processes observed here are gally slow compared to a 40 fs laser pulse. In sum, thresults suggest that multielectron excitation leads to an etronically excited, multiply charged parent ion which subsquently fragments, partially assisted by some Coulombicpulsion.

Through the saturation intensityI sat ~as explained in SecIII !, it is possible to determine the intensity dependeionization/fragmentation of DT as a function of wavelengThis approach reveals further insight into the strong fimolecular response. In Fig. 8, we show the measuredI sat forHT ~80 amu!, DT ~134 amu! and the DT-fragments, at 0.and 1.5mm. We can see thatI sat for HT is wavelength inde-pendent, consistent with quasistatic tunnel ionization. It cbe seen that for the 0.8mm case, DT fragments~triangles! inthe 78–120 amu range, corresponding to singly charged9 ,C8 , C7 , and C6 fragments, have all approximately the samI sat of 1.131013 W/cm2. This value is very close to that othe DT parent ionI sat at 0.8 mm. This result once againpoints towards a NME excitation–ionization process, whthe fragmentation process cannot be separated from iontion.

For the case of the formation of some smaller fragmesuch as C2H5

1 , the saturation intensity (I sat'1.831013 W/cm2) remains relatively close to that of the pareion. Nevertheless, at 0.8mm, for fragments smaller thanC6Hn , the response appears more structured, dependinthe number of hydrogen losses for each carbon group.example, in the case of C2Hn

1 with n50¯7, I sat varies be-tween 1.831013 and 4.531013. It should be noted that forsuch small fragments only 1 to 2p-bonding orbitals are re-maining in the fragment. Therefore, C–C bond fission shobe energetically favorable compared to hydrogen atom loThe saturation intensity for DT double ionization is veclose to those of the fragments smaller than C6 which havelost more than one hydrogen. As the doubly- and tripcharged DT parent ions are themselves stable, this resultgests that the multiple hydrogen loss channels are caumainly by the formation of electronically excited, multiplycharged parent ions.

Although the fragmentation yield of DT at 1.5mm is

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very small as compared to the yield of multiply~21, 31!charged parent ions~see Fig. 6!, I sat can be determined fothese fragments nonetheless. In contrast to the destruionization seen at 0.8mm, at 1.5 mm I sat for the DT-fragments generally occurs at higher intensities thanI sat ofthe parent DT ion. ReachingI sat for the fragments requirequite high intensities. Additionally, the hydrogen loss chanels for each fragment group Cn appears to be less dominanWe also note that the fragment mass peak shapes are gally sharper at 1.5mm than at 0.8mm, suggesting that theris much less kinetic-energy release amongst the fragm~see Fig. 6!. We suggest that at 1.5mm most of the DTfragments are formed in a more typical statistical unimolelar fragmentation process which occurs long after the lapulse. This can still be reconciled with a quasi-static tunionization picture provided that the quantitative stabilitiesthe multiply charged parent ions are known. Unfortunateto the best of our knowledge, there exists no experimedata on the breakdown behavior of DT upon excitatioionization. A detailed study, using conventional techniqusuch as electron impact ionization, would help to clarify thsituation.

Figure 8 also includes some experimental results forI sat of HT, measured at 0.8 and 1.5mm. We find thatI sat

'5•1013 W/cm2 and is wavelength independent. From theobservations it is clear that at 0.8mm HT has reached itscorresponding long wavelength limit and that a furthercrease in wavelength does not significantly alter the strfield ionization response.

FIG. 8. Saturation intensitiesI sat for different fragment ions of massmi ofthe parent molecule decatetraene~DT!, obtained at two different wavelengths: 0.8mm ~triangles! and 1.5mm ~circles!. Also included are theI sat

determined for multiply charged parent ions~big symbols!, and forHexatriene~HT! at both 0.8mm ~black diamonds! and 1.4mm ~white dia-monds!. For a discussion, see the text.

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It is interesting to compare the strong field electronresponse of the quasilinear DT molecule to its cyclical coterpart cylcooctatetraene~COT!. Both molecules have thesame number of delocalizedp electrons, very similar num-bers of vibrational degrees of freedom and approximatelysameI p . Simple quasistatic tunneling models would therfore suggest that they ionize in similar ways. Figure 9 shoa comparison of the mass spectra of DT and COT un1013 W/cm2 irradiation at 0.7mm. While COT shows littlefragmentation and a very strong parent ion signal, DTalmost completely fragmented, with a broad distribution btween CHx and C7Hx . Again, the extensive kinetic-energrelease in the DT fragments suggests that electronicallycited multiply charged states of the cation are formed durthe laser pulse, consistent with NME dynamics. Althouunimolecular decay rates of ring compounds are generexpected to be slower than those of their linear analog~two bonds need to be broken!, these results show that COdoes not even form multiply charged ion states. This incates that the delocalized electrons in COT simply dointeract as strongly with the field as those of DT. The diffeences in fragmentation patterns between DT and COT casimply be due to different length-corrected MSAE Keldyparameters37 because we are unable to avoid fragmentatof DT even at the lowest ionization intensities. This ‘‘gemetric’’ comparison shows that the three dimensional shof the molecule is much more influential than simply ttotal number of delocalized electrons. The ring geometryCOT determines that the effective path length of a delocized electron in the direction of the laser field

FIG. 9. Time of flight mass spectra for all-trans Decatetraene~DT! andCylcooctatetraene~COT!, obtained using a 700 nm, 70 fs laser pulse. WhCOT shows little fragmentation and almost no doubly charged states,~with the same number ofp-bonds! fragments severely due to the muclonger delocalized electron path length in the direction of the laser field~seetext!.

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quite short~as compared with DT! and, therefore, it willinteract much less strongly, consistent with the observatio

In order to study the transition from adiabatic tunnelito NME ionization dynamics in further detail, we have ivestigated the wavelength dependence ofI sat for the DT case.The results of this extensive study are presented in Fig.For the case of adiabatic electron dynamics, implicit inquasi-static tunnel ionization models, theI sat is by definitionwavelength independent. Using the ionization potentialpropriate to DT, we have included in Fig. 10 the ADK atomtunnel ionization result~ADK, dashed line! and the predic-tion of the molecular single active electron~MSAE! tunnel-ling model, using the ionization potential and the lengthDT ~MSAE, dotted line!. The MSAE model corrects theatomic result by accounting for changes in the tunnellbarrier due to the molecular length.37 Wavelength independence is not observed, demonstrating the failure of qustatic models. Between 1.45 and 0.8mm I sat decreases by afactor of 4 to 5, which implies a very dramatic increase in t~highly nonlinear! ionization rate towards shorter wavelengths. We find that a wavelength-independentI sat(l) isachieved only in the long wavelength limit of these studiat around 1.45mm. This is fully consistent with the concomtant reduction in DT fragmentation at 1.45mm shown in Fig.6. As the wavelength decreases, the molecule becomes measier to ionize and, simultaneously, the fragmentation chnels grow extensively, completely dominating by 0.8mm~Fig. 6!.

Most importantly, the departure from quasi-static tunning can occur even when the Keldysh parameterg is lessthan unity, whether corrected or not for molecular seffects.37 For DT, the departure from adiabatic~wavelength

FIG. 10. The wavelength dependence ofI sat for all-trans decatetraene showa transition from quasi-static~wavelength independent! to NME dynamicsnear 0.8mm. I sat increases by;400% between 0.8 and 1.5mm, demonstrat-ing the failure of quasi-static models. The calibrated, absoluteI sat weredetermined using Xe as a reference standard. The expectations ofatomic tunnel ionization models~ADK, dashed line! and the length-corrected molecular single active electron model~MSAE, dotted line! areshown. I sat significantly exceed the expectations of both the ADK aMSAE results atl;1.4mm, due to multiple active electron effects.

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independent! behavior starts atg2;0.06 ~without molecularsize corrections which would further reduce its value!. Thisvalue is traditionally considered to be in the tunnelinggime. This clearly indicates that the Keldysh parameter cnot be used as a simple diagnostic of quasistatic tunnelbehavior in polyatomic molecules. A consideration of telectron dynamics inside the molecule becomes importa

It is also important to note that this transition from quastatic to NME ionization dynamics cannot be interpreted aconsequence of resonant photon absorption, as wouldnatural in the perturbative limit. Indeed, at these laser intsities, the voltageEL applied by the laser field across thmolecule approaches the ionization potentialI p;10 eV. Insuch cases, the AC Stark shifts ofdelocalizedmolecular or-bitals approachI p ~i.e., every optical cycle, the bound eletronic states sweep through;10 eV! and the discrete levestructure which governs energy absorption in weak lafields becomes irrelevant.

Figure 10 dramatically illustrates the transition froquasi-static to NME dynamics. Interestingly, it also demostrates the importance of multi-electron effects even inlong-wavelength limit where quasistatic behavior obtainscan clearly be seen that the experimental long-wavelenlimit I sat is significantly higher thanboth the ADK andMSAE values. We believe that this increase in the quastatic I sat must be due to multi-electron effects that originain the dynamic polarization of all delocalized electrons in tstrong field. As a consequence, via Coulomb interactiothese polarized electrons repel the active electron and etively increase the tunnelling barrier for the ‘active’ electroand therefore leads to a larger value ofI sat. We are presentlycarrying out an experimental investigation into the nonrenant~IR! strong field ionization of neutral metal clusters. Ametal clusters have a short length but many equivalent higpolarizable electrons, they represent ideal systems forinvestigation of these dynamic multielectron polarizationfects in the long-wavelength limit. The results of these stuies will be reported in a future publication.

V. CONCLUSION

The quasi-static model of strong field ionization, highsuccessful in atomic physics, is based upon two fundameassumptions. The first is the adiabatic approximation thattime scale of electron motion inside the binding potentwell is much faster than the laser period, allowing the neglof any electron dynamics inside the atom and/or molecuoften justified by the small size of rare gas atoms. The sond is that only a single active electron~SAE! is operational,justified because the doubly excited states which contribto the polarizability lie above the ionization potential in ragas atoms. Our studies were motivated by two conceFirstly, that as the path lengths of delocalized electrons glonger in molecules, the adiabatic approximation may fand the driven electron dynamics inside the molecule wbecome important. Secondly, that the neglect of multiactive electrons~MAE! is not easily justified in moleculesas doubly excited states often exist below the ionizatpotential.

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We studied the nonresonant strong field ionization oseries of linear unsaturated hydrocarbons~HT, DT, andbC!as a function of intensity and wavelength, using mass sptrometry. We specifically used short;40 fs laser pulses inorder to avoid~i! domination by vibrationally induced dynamic electron localization effects~such as enhanced ionization! or ~ii ! field-induced alignment effects during the inteaction. This allowed us to emphasize the purely electroresponse to the field. A restricted collection volume TOFMensured that observed ion signals originated from a cylinof constant axial intensity. This allowed us to make cabrated absolute intensity measurements as a functionwavelength, based on the saturation intensityI sat. We ob-served and characterized a new type of strong field molecbehavior: Nonadiabatic multi-electron~NME! excitation-ionization dynamics.

We observed that the onset of NME ionization depenon the time scale~path length! of delocalized electron motionas compared with the laser period. In HT behavior consiswith quasistatic tunnel ionization was observed at all walengths. In DT we observed the transition as a functionwavelength from quasistatic tunnel ionization to NME ioization. In bC NME ionization was observed at all wavelengths. Our study showed that the saturation intensityI sat inDT varied by over 400% in the 0.8–1.5mm range, demon-strating a complete failure of the adiabatic approximatiThe inherently multi-electron nature of the interaction wcorroborated by studies of~i! intensity effects on fragmentation patterns and~ii ! kinetic energy distributions amongst thfragments. We emphasized that the popular Keldysh pareter, often used as a diagnostic of tunneling behavior,comes meaningless when electron dynamics inside theecule become important.

The SAE assumption in the~adiabatic limit! quasi-statictunneling of molecules has also been questioned. Even inlong wavelength quasistatic limit for DT~around 1.5mm!,multi-electron effects were observed. The experimentalI sat inthis limit was higher than the atomic ADK expectation asignificantly higher than the length-corrected molecusingle active electron MSAE expectation. We suggest tthis is due to the dynamic polarization of all electrons in tmolecule which, via Coulomb repulsion, effectively increaing the tunnelling barrier for the active electron.

In order to gain an intuitive picture of NME dynamicwe developed a very simple driven electron-in-a-box modsimilar to that used in clusters studies.53 While most qualita-tive features of the physics were reproduced, supportingpicture, a time-dependent multi-configuration Hartree–Foor density functional model needs to be developed in ordeproceed further. We note that our physical model is also csistent with and is supported by another recent experime65

The emergence of NME ionization dynamics in delocized electron systems will have important consequencesmany applications of intense laser pulses. A recently pposed mechanism of strong-field control in polyatommolecules12 is based on effective broadening of all statemaking them energetically accessible without tuning to fiefree resonances. We believe that the highly efficient nonrenant nonadiabatic multielectron processes described in

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paper are a clear manifestation of and a physical mechanfor such broadening. In fs-mass spectrometry, NME dynaics can lead to almost complete fragmentation of the paion, even at threshold ionization intensities. In fs laser mchining, dynamic polarization effects will directly affecdamage thresholds. Conceptually, NME ionization dynambridges the gap between atomic strong field ionization athe panoply of strong field phenomena observed in larmolecules, clusters and solids. In intense field coherent ctrol, the nature of the driven electron response willstrongly affected by NME dynamics. Below the ionizatiothreshold, NME should allow for the highly efficient excitation of various multi-electron states which are inaccessivia conventional means. This may lead to new avenuesthe control of unimolecular reaction dynamics. Consquently, we expect that an area of future investigation willthe effects of pulse shape~e.g., chirp! on intense field NMEdynamics and its potential or lack thereof for the opticcontrol of molecular processes.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge valuable contributiofrom P. Arya and M. Barnes for the synthesis of all trandecatetraene and D.M. Rayner, D.M. Villeneuve, andHankin for technical assistance. We have benefited grefrom stimulating discussions with many colleagues includP.B. Corkum, S. Hankin, D.M. Rayner, D.M. VilleneuveM.Z. Zgierski, and H.G. Muller. M.I. acknowledges stimulating discussions with R. Levis and A. Markevitch. M.Land V.B. thank the NSERC Visiting Fellowships Program ffinancial support. M.L. also thanks the Austrian Fund for tAdvancement of Science~FWF!.

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polyatomic molecules in strong laser ﬁelds: nonadiabatic...

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