Attosecond electron dynamics in complex molecular systems

(1)

Politecnico di Milano

DEPARTMENT OF PHYSICS

“Attosecond electron dynamics in

complex molecular systems”

Supervisor: PhD Thesis by:

Prof. Mauro Nisoli Andrea Trabattoni

The Chair of the Doctoral Program: Mat.: 785033 Prof. Paola Taroni

(2)

(3)

“... Il linguaggio dell’Universo ... ” Pino Mascolo

(4)

(5)

INTRODUCTION

In 1981 Zewail and coworkers published a pioneering work on quantum coher-ence effects in the vibrational states of anthracene [1], paving the way for the study of ultrafast dynamical processes in isolated molecules. In the same years the laser sources were experiencing a dramatic development thanks to the ap-pearence of the first subpicosecond dye lasers (1974) [2] and, few years later, the achievement of pulses with a duration down to 6 fs (1987) [3]. The great results on both sides converged in the development of ultrafast spectroscopy and femtochemistry [4], providing an “ultrahigh-speed photography” at the atomic and molecular level. Nowadays this research field is really well estab-lished and gives a direct access to dynamical processes of great importance in physics, chemistry and biology [5].

From quantum mechanics we know that femtosecond temporal scale is intrin-sically related to the nuclear motion, for this reason a typical experiment with femtosecond resolution is able to investigate in real time the evolution of a reaction, the breaking of a chemical bond, the fragmentation of a complex system after the perturbation of the initial quantum state, down to the vibra-tional oscillation in diatomic molecules (the ground state vibravibra-tional period of H2is in the order of 10 fs). Electron dynamics occurs on a faster temporal

(8)

scale ranging from a few fs down to a few hundreds as (1 as = 10−18_{s), for this}

reason in order to track the electronic motion in matter shorter light pulses are required.

In 1987 and 1988 two indipendent experiments were able to produce coherent extreme ultraviolet (XUV) radiation by exploiting the interaction between a strong IR laser field and the atoms of a rare gas [6, 7]. The result was a series of odd harmonics of the fundamental wavelength, corresponding to a train of subfemtosecond bursts. Only few years later this process was fully underestood and called High Harmonic Generation (HHG) [8–11]. Since then, great effort was made to investigate more in detail the HHG process, until the first experimental demonstration of attosecond pulses generation, performed in 2001 by Paul and coworkers, who were able to generate a train of 250 as pulses [12]. During the same year a single attosecond pulse with a time dura-tion of 650 as was successfully isolated from a train of attosecond pulses [13]. These results paved the way for the birth of attosecond physics.

In the last two decades a strong effort was made to characterize attosecond sources and to apply this technology to the investigation of ultrafast elec-tronic dynamics in matter. The main problem the community has to face is the low intensity of attosecond sources, since the convertion efficiency of HHG process is quite low (in the order of 10−6_{), resulting in XUV energies usually}

in the range between hundreds of picojoules up to few nanojoules. This level of energy, and correspondent intensity, is tipically too low for initiating non linear processes in matter, thus for performing pump attosecond-probe experiments (for high energy XUV sources and recent results concerning XUV-pump XUV probe experiments, see for example [14, 15]). For this rea-son the common solution is to combine the XUV pulses with a VIS/NIR laser field, with an attosecond-pump femtosecond-probe configuration. This setup can still preserve a temporal resolution in the attosecond timescale and in the last years gave important results in investigating ultafast electron dynamics in atoms, and recently even in simple molecules [16–21]. Despite these posi-tive results, attosecond physics still didn’t show the capability of investigating

(9)

Introduction complex systems, for example biomolecules, where ultrafast electron dynamics are expected to play a fundamental role in many biological processes such as catalysis, respiration, DNA damage by ionizing radiation and photosynthesis. I dedicated my PhD activity to the ELYCHE (ELectron-scale dYnamics in CHEmistry) project, in the high energy attosecond lab of Politecnico di Mi-lano - department of Physics, with the aim of applying attosecond tools to the investigation of purely electronic dynamics in complex systems, such as multielectron molecules, nanoparticles and molecules of biological interest. In the first part of my PhD we installed and developed the attosecond-pump VIS/NIR probe beamline in the ELYCHE laboratory. A strong effort was made to compress the laser pulses down to 4 fs of duration and use them for the generation of isolated attosecond pulses (IAP).

In the last two years of my PhD I applied these tools in some important pump-probe experiments. First we investigated ultrafast relaxation process in multielectron diatomic molecules. We concentrated on the N2 molecule,

that is the most abundant species in the Earth’s atmosphere, with the goal of understanding the interaction of molecular nitrogen with extreme ultra-violet (XUV) radiation, that is of crucial importance to completely disclose the atmospheric radiative-transfer processes. By performing a Velocity Map Imaging (VMI) experiment, we were able to disclose the ultrafast dissociative mechanisms leading to the production of N atoms by XUV photoionization, and to observe a predissociation quantum interference between the electronic states of the molecular cation. We also managed to extract information about the slope and shape of nitrogen (in particular N+2 ions) potential curves, a sort

of “real-time mapping” of molecular electronic states.

Then we tried to push our invstigation to more complex systems with the aim of studying ultrafast electronic dynamics in molecules of biological interest. We perfomed a mass spectrometry experiment on Phenylalanine (one of the essential amino acids) and analyzed the temporal evolution of molecular frag-mentation after XUV ionization. We were able to measure a charge oscillation

(10)

in the yield of immonium dication fragment, providing for the first time an experimental demonstration of charge migration in a biological molecule. The thesis is organized as follows:

• The first chapter treats some background concepts concerning attosec-ond technology applied to molecular physics. Particular attention is dedicated to the description of Polarization Gating (PG) technique for the generation of isolated attosecond pulses and the temporal charac-terization of such pulses. Then the applications of attosecond tools to the investigation of molecular systems are introduced.

• The second chapter is dedicated to the experimental setup we developed. Particular attention is devoted to the generation and characterization of isolated attosecond pulses and VIS/NIR probe pulses. Concerning the characterization of the probe pulses, we carefully investigated the tem-poral duration and the carrier-envelope phase (CEP) stability. Then we performed Attosecond Streak Camera (see the section 1.1.2) experiments to fully characterize the temporal structure of attosecond pulses. • The third chapter describes the investigation of ultrafast electronic

dy-namics in N2molecules. The experiment of photoionization is presented.

Numerical simulations are introduced and results analyzed, discussing the possibility of experimentally mapping N+₂ electronic states.

• The fourth chapter reports about the measurement of charge migra-tion in the aminoacid Phenylalanine. The experimental setup is first presented. After that the experimental results are discussed according with the numerical simulations.

• The conclusion consists in a summary of the principal results described in the thesis and a discussion upon the possible future perspectives.

(11)

BIBLIOGRAPHY

[1] Wm. R. Lambert, P. M. Felker and A. H. Zewail, “Quantum beats and dephasing in isolated large molecules cooled by supersonic jet expansion and excited by picosecond pulses: Anthracene”, J. Chem. Phys. 75, 5958 (1981);

[2] C. V. Shank and E. P. Ippen, “Subpicosecond kilowatt pulses from a mode-locked cw dye laser”, Appl. Phys. Lett. 24, 373 (1974);

[3] Fork, R. L.; Brito Cruz, C. H.; Becker, P. C.; Shank, C. V., “Compression of optical pulses to six femtoseconds by using cubic phase compensation”, Optics Letters, Vol. 12 Issue 7, pp.483-485 (1987);

[4] Peter M. Felker and Ahmed H. Zewail, “Purely rotational coherence effect and timeresolved subDoppler spectroscopy of large molecules. I. Theoreti-cal”, J. Chem. Phys. 86, 2460 (1987);

[5] Ahmed H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond”, J. Phys. Chem. A 104, 5660-5694 (2000);

[6] A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIn-tyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of

(12)

vacuum-ultraviolet radiation in the rare gases”, JOSA B, Vol. 4, Issue 4, pp. 595-601 (1987);

[7] M Ferray, A L’Huillier, X F Li, L A Lompre, G Mainfray and C Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases”, J. Phys. B: At. Mol. Opt. Phys. 21, L31 (1988);

[8] M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields”, Phys. Rev. A 49, 2117 (1994);

[9] J. L. Krause, K. J. Schafer and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime”, Phys. Rev. Lett., 68, 3535-3538 (1992);

[10] K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff”, Phys. Rev. Lett., vol. 70, pp. 1599-1602 (1993);

[11] P. B. Corkum, “Plasma perspective on strong field multiphoton ioniza-tion”, Phys. Rev. Lett., vol. 71, pp. 1994-1997 (1993).

[12] P. Paul, E. Toma, P. Breger, G. Mullot, F. Aug, P. Balcou, H. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation”, Science, vol. 292, pp. 1689-1692 (2001);

[13] M. Hentschel, R. Kienberger, C. Spielmann, G. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosec-ond metrology”, Nature, vol. 414, pp. 509-513 (2001);

[14] Eiji Takahashi, Yasuo Nabekawa, Tatsuya Otsuka, Minoru Obara, and Katsumi Midorikawa, “Generation of highly coherent submicrojoule soft x rays by high-order harmonics”, Phys. Rev. A 66, 021802(R) (2002); [15] P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris

and D. Charalambidis, “Extreme-ultraviolet pumpprobe studies of one-femtosecond-scale electron dynamics”, Nature Physics 7, 781784 (2011);

(13)

Bibliography (Introduction) [16] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy”, Nature, vol. 419, pp. 803-807 (2002);

[17] M. Uiberacker, T. Uphues, M. Schultze, A. Verhoef, V. Yakovlev, M. Kling, J. Rauschenberger, N. Kabachnik, H. Schroder, M. Lezius, K. Kompa, H.-G. Muller, M. Vrakking, S. Hendel, U. Kleineberg, U. Heinz-mann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms”, Nature, vol. 446, pp. 627-632 (2007); [18] M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M.

Hof-stetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nico-laides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission”, Science, vol. 328, no. 5986, pp. 1658-1662 (2010);

[19] E. Goulielmakis, Z. Loh, A. Wirth, R. Santra, N. Rohringer, V. Yakovlev, S. Zherebtsov, T. Pfeifer, A. Azzeer, M. Kling, S. Leone, and F. Krausz, “Realtime observation of valence electron motion”, Nature, vol. 466, pp. 739-743 (2010);

[20] J. Mauritsson, T. Remetter, M. Swoboda, K. Klnder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lepine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique”, Phys. Rev. Lett., vol. 105, p. 053001 (2010);

[21] G. Sansone, F. Kelkensberg, J. Perez-Torres, F. Morales, M. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lpine, J. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M.

(14)

Ivanov, M. Nisoli, F. Martin, and M. Vrakking, “Electron localization fol-lowing attosecond molecular photoionization”, Nature, vol. 465, 763-766 (2010);

(15)

CHAPTER

1

ATTOSECOND PHYSICS

The motion of an electron or a nucleus inside a molecule can be simply seen as a dynamical process which occurs with a precise time-dependent probability distribution. There exist three requirements in order to study the motion of such a system [5]. First, we need to clock the dynamics by defining the zero-time, with a precision that should approach the resolution of the experiment. Second, the dynamics must be synchronized, since a huge amount of events are typically recorded and create the statistics necessary to map and solve the process. Third, coherence must be induced in the molecule in order to obtain localization.

A pump-probe experiment is able to satisfy each of these requirements. The pump pulse excites the molecule coherently creating a quantum wavepacket with electronic and nuclear degrees of freedom and initiating the dynamics. The probe pulse provides the shutter speed for freezing the molecular motion, defining the clock. By varying the delay between the pump and the probe pulses a series of “snapshots” of the dynamics are obtained.

(16)

resolution of the experiment. This is not a trivial task and doesn’t come simply from a careful characterization of pump and probe pulses. Paradoxically, the resolution of an ultrafast pump-probe experiment on a molecular target is estimated by taking into account the physical process under study. With the aim of investigating ultrafast dynamics of nuclei and electrons inside a molecule, we know that the motion of these elementary particles is governed by the laws of quantum mechanics. The characteristic timescale can be found by considering a system with two eigenstates φ1, φ2with correspondent energy

eigenvalues E1, E2. The wavefunction ψ of the system is described by:

|ψ(t)i = a1e− i ~E1t_|φ 1i + a2e− i ~E2t_|φ 2i (1.1)

where a1, a2 are amplitudes that describe the coherent superposition of the

two eigenstates. This analysis is absolutely general but the two states can be thought as two rotational, vibrational or electronic states of a molecule. The time evolution of the wavefunction |ψ(t)i results from the difference in the evolution of the amplitudes of the two states, in particular in the value of phase. This time-dependence can be probed by a measurement of the inter-ference of the two states. The operator ˆA that represents such a measurement is described in the basis of the eigenvectors of the hamiltonian in the form:

ˆ A = " c1 c12 c∗ 12 c2 # (1.2)

The expectation value of ˆA gives the measurement of the interference between φ1 and φ2:

hψ| ˆA |ψi = c1| a1|2+c2| a2|2+2R(c12a∗1a2)cos∆E

~ t+ −2I(c12a∗1a2)sin

∆E ~ t

(1.3)

with ∆E = E2− E1. When c12 6= 0 and a1, a2 6= 0, Eq. 1.3 displays an

oscillatory dynamics with a period of T = h/∆E. This motion can be seen as the result of the beating between the two waves corresponding to the two

(17)

Isolated attosecond pulses eigenstates. The beating can be observed when there is a non-zero amplitude in both eigenstates and the eigenstates of ˆA are different from the eigenstates of the hamiltonian that describe the system. From this simple analysis it can be deduced, for example, that rotations of a molecule occur on picosecond (1 ps = 10−12_{s) timescales. Chemical reactions are usually thought as processes}

in which it is the atomic motion in molecules to drive the transformation from the initial to the final state. The fastest chemical reactions evolve on femtosecond timescales and can be studied in time-resolved experiments using femtosecond laser pulses [5]. An example of femtosecond nuclear motion is the vibration of a molecule. The fastest molecular vibration in nature is that of a H+2 molecular ion. The energy splitting between the two lowest vibrational

levels is 270 meV, that corresponds to a vibrational period of 15.2 fs. As shown in the next sections, even purely electronic dynamics inside a molecular system can strongly affect the temporal evolution of the system from the initial to the final state. Energy splittings between electronic states are typically on the order of ≃ 1 eV, which corresponds to an electronic motion occuring in the attosecond timescale. Therefore attosecond pulses are required to capture electronic motions inside a molecular system.

1.1 Isolated attosecond pulses

At the end of the 80’s, two indipendent experiments were able to produce coherent extreme ultraviolet (XUV) radiation by exploiting the interaction between a ultraintense IR laser field (1013_{− 10}14 _W/cm2_{) and the atoms of a}

rare gas target [6,7]. The XUV spectrum so obtained displayed unprecedented characteristics beyond the well known perturbative regime: after a significant intensity drop in the lowest harmonics, the spectrum was characterized by a plateau of odd harmonics of the fundamental wavelength, with approximately constant intensity. The plateau then ended at a sharp cut-off beyond which no harmonic emission was found. Furthermore, the photon spectrum that results from this process can extend well above the ionization potential (Ip)

(18)

of the atom. It was found that the XUV cutoff satisfies a universal rule and lies at approximately Ip+ 3Up for all wavelengths, targets and driving laser

intensities [9] (Up is the ponderomotive energy).

After the initial experimental results, numerous theoretical efforts led to a deep understanding of this new non-perturbative process, that was dubbed High Harmonic Generation (HHG). Quantum calculations, based on the time-dependent Schr¨odinger equation for a single electron interacting with the fun-damental laser field, reproduced the principal observations of HHG experi-ments. Such calculations have helped to determine, for example, the cutoff law for HHG [8]. Explanations were also found in terms of a classical model for the interaction between the electrons and the generating field [9–11]. A few years after the first experimental demonstration of HHG, several pro-posals suggested the generation of attosecond pulses based on HHG [22–24], since the XUV bandwidth produced by HHG is large enough to support such short pulses. Although it was long expected that HHG could produce at-tosecond pulses, it has taken almost a decade before it could be confirmed experimentally [12], with the first observation by Paul and coworkers of a train of attosecond pulses. Nowadays HHG is a really well enstablished tech-nique, and great achievements were reached in the generation of attosecond pulses in this way. In particular, in 2001 Hentschel et al. demonstrated the generation of isolated attosecond pulses (IAP) [13], paving the frontier for the temporal resolution in ultrafast pump-probe experiments. This result was of great importance, since for many applications it is crucial to reduce the pulse train to a single attosecond pulse. This is particularly important, for exam-ple, in order to investigate the sub-femtosecond evolution of single coherent wavepacket by using the pump-probe technique. Several approaches for effi-ciently generating IAPs have been proposed and demonstrated in the years. All of them, anyway, are based on the ability of properly confining the HHG process, in order to create a gate in the driving field and select a single burst from the train of attosecond pulses.

(19)

Isolated attosecond pulses

1.1.1 Gating methods

Isolated attosecond pulses produced by HHG have been experimentally demon-strated exploiting a number of experimental techniques; these include spectral selection of half-cycle cutoffs [25, 27, 29] as in amplitude gating [30, 31] and ionization gating [18,24,28,32], temporal gating methods such as polarization gating (PG) [24, 25] and double optical gating (DOG) [26–28], and spatio-temporal gating with the attosecond lighthouse effect [29].

It is worth noting that, in general, the generation of broadband isolated at-tosecond pulses requires a series of challenging technological tools. One of these is to have CEP(Carrier-Envelope phase)-stable driving pulses. By defin-ing the electric field of the generatdefin-ing pulses as:

E(t) = A(t)ei(w0t+ϕ) _(1.4)

(where A(t) is the complex envelope of the electric field and w0 is the carrier

frequency of the pulse), the term ϕ represents a temporal offset between the maximum of the envelope (assumed at t = 0) and the maximum of the carrier wave of frequency w0. The term ϕ is usually indicated as Carrier-Envelope

phase (CEP). Nowadays several methods exist to lock the CEP value in the laser pulses, as described in chapter 2. The generation of isolated attosecond pulses, in general, requires a “light switch”, a method that can effectively turn on the HHG process during only a single half cycle of the driving electric field, with the carrier-envelope phase (CEP) of the driving laser tuned so that only electron trajectories originating from a single ionization event produce attosecond pulse generation. To date, the most efficient light switches are based on the polarization gating technique.

This method is based on the fact that the generation of attosecond pulses is really sensible to the driving laser field polarization, as explained by the semiclassical recollision model [11]. Indeed the HHG efficiency strongly drops when the driving electric field is elliptically or circularly polarized [30, 31]. The efficiency of attosecond pulse generation decreases by ≃ 50% when the ellipticity is increased from 0 to only 0.1, and by about an order of

(20)

magni-tude for an ellipticity of 0.2. Therefore, a proper manipulation of the driving laser polarization, producing linear polarization only in a subcycle temporal window of the pulse, allows for the selection of only a single attosecond burst. This is possible by using a system of two birefringent (quartz) plates, a first thick retardant plate and a zero-order quarterwave plate [24, 32–34]. This system ensures a reliable modulation of the laser ellipticity and a 100% trans-mission of the incoming pulses.

The polarization gating setup is described in Fig. 1.1: the incoming pulse,

Figure 1.1: A schematic diagram of Polarization Gating (PG) method. The inco-ming pulse, that is linearly polarized with an angle α = 45◦ _{with respect to the}

neutral axis of the first quartz plate, is projected on the two axes of the plate, pro-ducing a pair of cross-polarized twin pulses. Transmission through a second plate, that is a zero-order quarterwave plate with the neutral axis at β = 0◦ _(“narrow

gate”) with respect to the original laser polarization, changes the circular polariza-tion into linear polarizapolariza-tion, and conversely, producing a temporal linearly-polarized gate close to the principal cycle of the driving field. Another configuration exists, where α = 45◦ _{and β = 45}◦_{, and it is dubbed “large gate”.}

that is linearly polarized with an angle α = 45◦ _{with respect to the neutral}

(21)

produc-Isolated attosecond pulses ing a pair of cross-polarized twin pulses. Since each pulse propagates inside the plate with a different group velocity (due to the difference in the refrac-tive index), a delay δ between the two is created, resulting in an alteration of the original overall polarization. The overlap between the two projections, indeed, produces circular polarization, whereas the tails are still linearly po-larized. The delay depends on the thickness of the plate and the refractive indexes at the carrier frequency of the pulses. Transmission trough the zero-order quarterwave plate (with the neutral axis at β = 0◦ _{with respect to the}

original laser polarization) changes the circular polarization in linear polariza-tion, and conversely, producing a temporal linearly-polarized gate close to the principal cycle of the driving field. This configuration, in which the neutral axes of the two plates are oriented, respectively, with α = 45◦ _{and β = 0}◦

re-spect to the polarization of the incoming laser pulses, is called “narrow gate”. Another configuration exists, where α = 45◦ _{and β = 45}◦_{, and it is dubbed}

“large gate”.

Concerning the narrow gate configuration, it is possible to find a relation be-tween the duration τg of the polarization gate, the duration T of the driving

field and the delay δ accumulated by the two projections of the incoming pulses inside the retardant plate. Let us consider a Gaussian driving pulse, linearly polarized along z, with a temporal duration T (FWMH):

Ez(t) = EA(t)cos(w0t + ψ)

EA(t) = E0e(−(t/σ)

2₎

σ = T /p2ln(2)

(1.5)

After the first plate, with the ordinary and extraordinary axes along the x and y directions, the driving pulse can be written as:

   Ey(t) = √ 2 2 EA−cos(w0t − π 2 + ϕ) Ex(t) = √ 2 2 E + Acos(w0t + ϕ) (1.6)

(22)

where: _   EA−= EA(t − δ/2) EA+= EA(t + δ/2) (1.7) After the second plate (the zero-order quarter waveplate) with the ordinary and the extraordinary axes along the z and w directions, the field can be written as:    Ez(t) =1₂EA−cos(w0t − π + φ) +1₂EA+cos(w0t − π₂ + φ) Ew(t) = 1₂EA−cos(w0t −π₂ + φ) +1₂EA+cos(w0t + φ) (1.8)

By using trigonometric identities and changing the reference frame from (z,w) to (x, y), it is possible to obtain the following expression:

   Ey(t) =1₂[EA−+ E + A]sen(w0t + φ −π₄) Ex(t) = 1₂[EA−− E + A]cos(w0t + φ −π₄) (1.9)

We can see that in the center of the pulse (i.e. around t = 0) the x component of the field is zero, i.e. the field is almost linearly polarized along the y axis. The ellipticity ǫ is defined as:

ǫ = E − A − E + A E− A + E + A = 1 − exp(− 2δt σ2) 1 + exp(−2δt σ2) (1.10) This parameter gives information about the polarization of the driving field: if ǫ = 0 the pulse is linearly polarized, if ǫ = 1 the pulse is circularly polarized. In order to investigate the polarization gate, we are interested only in the temporal range where the field is almost linearly polarized, i.e. | −2δt/σ2_|<<

1, which yields:

ǫ ≈ δt

σ2 (1.11)

Therefore the temporal gate is: τg =

ǫthrT2

(23)

Isolated attosecond pulses Usually the threshold ellipticity ǫthris defined as the ellipticity value for which

the HHG efficiency is decreased to the 50% of the maximum value (obtained for ǫ = 0). Considering that τg < T0/2 (where T0 is the optical cycle of

the driving field), it is possible to extract a good estimation also about the duration of generating pulses. According with [34], T < 2.5 T0. Therefore

few-cycle (CEP-stabilized) driving pulses are required in order to confine the HHG process in a temporal polarization gate and efficiently generate isolated attosecond pulses.

1.1.2 Characterization techniques

The generation of isolated attosecond pulses requires methods for accurate temporal characterization of attosecond XUV fields, a problem that has long obstacled the development of attosecond science. Nevertheless, during the past years, a number of proposals has been demonstrated [12,13,30,35–38] to characterize the temporal structure of attosecond pulses [39, 40].

Today, femtosecond metrology tools allow for the full characterization of utral-short laser fields in the visible or near-infrared range. To do this, it is necessary to use at least one time-nonstationary filter [41], e.g. an amplitude gate, and usually the pulse to be measured itself is turned into a time-nonstationary filter, by means of a nonlinear effect. However, in principle nonlinear ef-fects are absolutely not required for ultrashort pulse characterization. Be-cause attosecond light pulses usually have available low intensities, the use of nonlinear effects for their characterization is still challenging. Therefore, generally attosecond measurement methods rely on a different approach. In particular, attosecond XUV fields can efficiently ionize atoms by single-photon absorption. This ionization generates an attosecond electron wavepacket in the continuum, which is a replica of the attosecond field when it is far from any resonance. The phase and amplitude of the XUV field are transferred to the photoelectron wavepacket. A characterization of this wavepacket, that is analogue to the characterization of ultrashort light pulses, gives a direct information on the temporal structure of the XUV attosecond field. To this

(24)

end, near-infrared or visible laser fields constitute ideal time-nonstationary filters, by acting as ultrafast phase modulators on the electron wavepacket. The first step for characterizing the attosecond pulses is to write a relation between the XUV radiation and the correspondent electron wavepacket. Let’s consider the ionization of an atom by an attosecond field alone (in the sin-gle active electron approximation). By applying the first-order perturbation theory, at times large enough for the attosecond field to vanish, the transi-tion amplitude av from the ground state to the final continuum state |vi with

momentum v is given by: av = −i

Z +∞

−∞

dtdvEXUV(t)exp[i(W + Ip)t] (1.13)

where W = v2_{/2 is the energy of the final continuum state (in atomic units).}

EXUV is the XUV electric field, dv is the dipole matrix element for the

tran-sition from the ground state to the final state |vi and Ip is the ionization

potential of the atom. Eq. 1.13 directly connects the attosecond field and the correspondent electron wavepacket generated after ionization.

The two spectra might differ in phase because of a possible phase dependence of dv on v, which can be expected to occur, for example, near resonances in

the continuum. If this phase dependence is negligible (or known) the spectral phase of the attosecond pulse can be directly deduced from the spectral phase of the electron wavepacket. Under these conditions, the electron wavepacket can be treated as a perfect replica of the attosecond field.

By considering also the presence of the VIS/NIR field, acting as an ultrafast phase modulator, strong field approximation (SFA) [8] can be used in addi-tion to the single active electron approximaaddi-tion. It consists of neglecting the effect of the ionic potential on the electron motion after ionization. However, when the photoionization is induced by an XUV field of central frequency wX,

the requirement wX >> Ip already ensures that the ionic potential can be

neglected for continuum states. Within these approximations, at times large enough for the attosecond field and the laser field to vanish, the transition amplitude av(τ ) (where τ is the delay between XUV and VIS/NIR fields) to

(25)

Isolated attosecond pulses the final continuum state |vi with momentum v can be written as:

av(τ ) = −i Z +∞ −∞ dtdp(t)EXUV(t − τ)exp[i(Ipt − Z +∞ t dt′p2(t′)/2)] (1.14) p(t) = v −A(t) is the instantaneous momentum of the free electron in the laser field, A(t) being the vector potential of this field in the Coulomb gauge, such that EL(t) = −∂A/∂t. The exponential in the integral of Eq.1.14 accounts

for the phase of the ionization/phase-modulation process, which is the sum of the phase Ipt accumulated in the fundamental state until time t, and of

the phase subsequently accumulated in the continuum. Within SFA, this last term is the Volkov phase, i.e. the integral of the instantaneous energy of a free electron in the laser field, p2_(t′_{)/2, from the ionization time t to the}

observation time. By rewriting Eq. 1.14 as: av(τ ) = −i

Z +∞

−∞

dte[iφ(t)]dp(t)EXUV(t − τ)e[i(W +Ip)t] (1.15)

φ(t) = − Z +∞

t

dt′_{(v · A(t}′_{) + A}2_(t′_)/2) _(1.16)

it is evident that the main effect induced by the VIS/NIR field is a temporal phase modulation φ(t) on the electron wavepacket generated in the contin-uum by the XUV field. Because of the scalar product v · A in Eq. 1.16, the phase modulation of photoelectrons needs to be defined for a given di-rection [13, 30, 35]. There exist many experimental implementations of this principle. One of these is the Attosecond Streak Camera method [35]. It is a photoionization experiment in which an isolated attosecond pulse ionizes a gas target (usually consisting of a rare gas jet). The photoelectrons are col-lected by an electron time-of-flight spectrometer, that is able to measure the kinetic energy accomulated by the charge particles. A VIS/NIR pulse, usu-ally linearly polarized, is able to drive the photoelectrons in the continuum after photoionization and thus to be used as phase modulator. In this case the VIS/NIR pulse is also dubbed streaking pulse. In the Fig. 1.2, a typi-cal streaking effect by the driving phase-modulator field on the photoelectron

(26)

Figure 1.2: A typical streaking spectrogram. The streaking pulse drives the pho-electron spectrum (vertical axes), according with the value of the delay between the attosecond pulse and the streaking pulse.

spectrum is reported.

In the case of a linearly polarized streaking field, and in the slow-varying envelope approximation [42], the phase term of Eq. 1.16 can be written as:

φ(t) = φ1(t) + φ2(t) + φ3(t), φ1(t) = − Z ∞ t dtUp(t), φ2(t) = ([8W Up(t)]1/2/wL)cosθcoswlt, φ3(t) = −(Up(t)/2wL)sin(2wLt) (1.17)

Up(t) = E02(t)/4w2Lis the ponderomotive potential of the electron in the laser

field at time t (E0(t) is amplitude of the laser field). The observation angle θ

is defined as the angle between v and the laser polarization direction. φ1(t)

(27)

Isolated attosecond pulses φ2(t) and φ3(t) oscillate at the laser field frequency and its second harmonic,

respectively. We emphasize that around θ = 0, the amplitude ∆φ of the phase modulation can be large even at moderate laser intensities, due to the W1/2

factor in φ2(t).

It is important to observe that the streaking pulse has to be fast enough to work as a proper non-stationary filter, therefore the maximum value of | ∂φ/∂t | should be a significant fraction of that of the unknown attosecond field, which will typically range from a few eV to several tens of eV. This can be easily calculated from Eq. 1.17.

1.1.3 FROG-CRAB retrieval

Among the variety of methods for the retrieval of the temporal structure of isolated attosecond pulses, such as Attosecond Spider [39] or phase retrieval by omega oscillation filtering (PROOF) [43], Frequency Resolved Optical Ga-ting for Complete Reconstruction of Attosecond Bursts (FROG-CRAB, or simply CRAB) is a very well established technique and offers the advantage of accurately recostructing arbitrary attosecond fields [44].

FROG-CRAB is inspired from frequency-resolved optical gating (FROG), a widely used technique for the full characterization of visible pulses [45]. In a FROG measurement the pulse to be characterized is decomposed in temporal slices due to a temporal gate G(t), and then the spectrum of each slice is recorded. This provides a two-dimensional set of data, called a spectrogram or FROG trace, given by:

S(w, τ ) =| Z ∞

−∞dtG(t)E(t − τ)e iwt

|2 (1.18)

where E(t) is the field of the unknown pulse and τ is the delay between the gate and the pulse. The gate may either be a known function of the pulse, as in most implementations of FROG, or an unrelated, and possibly unknown, function (blind FROG) [46]. Various iterative algorithms can then be used to extract both E(t) and G(t) from S(w, τ ). The principle of FROG-CRAB

(28)

can be derived by comparing the Eq. 1.15 and 1.16 with Eq. 1.18, in partic-ular the spectrum S(w, τ ) with the photoelectron spectrum | a(v, τ) |2_{. This}

comparison shows that, by scanning the delay τ , the dressing laser field can be used as a temporal phase gate G(t) = eiφ(t) _{[47] for FROG measurements}

on photoelectron wave packets generated by attosecond fields.

The full characterization of the wave packets provides all the information on the temporal structure of the XUV attosecond pulses as well as the unknown gate fields, as for a blind-FROG measurement. Therefore the iterative Prin-cipal Component Generalized Projections Algorithm (CPGPA) [46, 48, 49], developed for the optical blind FROG, can be used to retrieve the amplitude and phase of the pulses (see Appendix A).

1.2 Attoseconds for molecular physics

Isolated attosecond pulses hold great potential for time-resolved measure-ments on unprecedented timescales. The first attosecond experimeasure-ments on atomic systems studied continuum electron dynamics and made use of the principle of the Attosecond Streak Camera, described above. This method, indeed, can be used not only for the characterization of attosecond pulses, but also to investigate the photoionization processes occuring in the gas target. These measurements are named Streaking Spectroscopy experiments, and are particularly suitable to study photoionization time delays [16, 18].

Applying attosecond science to molecular physics, instead, the observables change, moving towards charge localization, molecular dissociation, or charge transfer processes [21, 52–54].

1.2.1 From H

2

to multielectron diatomic molecules

For H2 (or D2) single ionization, one of the simplest molecular excitation

processes, the ionizing pulse usually removes the outermost electron of the highest occupied molecular orbital (HOMO) from the neutral molecule and launches a wave packet on the potential curves of the cation (many alternative

(29)

Attoseconds for molecular physics to direct ionization exist, such as the population of an autoionization state of the neutral molecule). After ionization many processes can occur in the molecule. For example, if the populated curve is dissociative (2pσ for hy-drogen), the wavepacket proceeds monotonically outward, producing, at large internuclear distance R, one charged and one neutral fragment. On the other hand, if the potential energy curve (PEC) of the parent has a potential well in the Franck-Condon (FC) region (1sσ), the wave packet will oscillate in the well.

In the first attosecond pumpprobe experiment on the hydrogen molecule, an isolated attosecond pulse was used to excite neutral H2molecule, both

ioniz-ing and excitioniz-ing the molecule [21]. Then a probe pulse, that is a co-polarized few-cycle NIR pulse interacted with the excited molecule or molecular ion, driving the localization of the one remaining bound electron in the H + H+

dissociative ionization channel that was monitored. The momentum-matched neutral H atom and charged H+ _{moved in opposite directions. Depending}

on the XUV-NIR time delay and the kinetic energy of the detected H+

frag-ment ion, this fragfrag-ment ion moved preferentially upward or downward along the XUV/NIR polarization axis, resulting in a preferential localization of the single remaining bound electron downward or upward.

In the case of multielectron molecules, even diatomic, the interpretation of any excitation/ionization process in a pump-probe experiment becomes very complex. First of all, expecially in the case of broadband pump pulses, a huge amount of charge states of the parent molecular ion can be created and, for each of these, wave packets are launched on many different PECs, simultaneously and coherently. After that the molecule begins to stretch and the wave-packet propagates along the PECs. If the distance in energy among nuclear and electronic states are comparable, the overall molecular dynamics is strongly affected by the coupling between electronic and nuclear degrees of freedom, causing the breakdown of the Born-Hoppeneimer approximation [55] (this is true also for H2 molecule). In this perspective any adiabatic picture

(30)

is not valid anymore, and procedures of diabatization on the electronic states have to be considered in the theoretical calculations. The broadband excita-tion, furthermore, can open many channels for the evolution of the molecular dynamics, leading for example to the dissociation of the molecule, or the pop-ulation of autoionizing states, or even to Coulomb explosion. On the other hand the presence of the probe pulse gives more than a “real-time picture” of the molecular dynamics, since it can actively alterate the propagation of the wavepackets along the PECs and affect the overall dynamics itself. One of the principal effects induced by the probe is the coupling between different states with an energy gap that is favorable for one-to-few photon transitions, and this can induce population transfers before fragmentation.

The action of the probe pulse on the potential curves can be easily defined and investigated by introducing the Floquet picture [56], that in general describes a quantum system interacting with a coherent electromagnetic radiation. By defining the interacting Hamiltonian as:

H =X i 1 2mi[pi− qi cA(ri, t)] 2_{+ V (r} i) (1.19)

where A is the vector potential of the electromagnetic radiation, the Floquet theorem states that any solution ψ(r, t) of the Schr¨odinger equation written using this Hamiltonian (that has the same time-periodicity of A) can be expressed in the form:

ψ(r, t) = e(−iEt/~)φ(ri, t) (1.20)

where φ has the same periodicity of H and A. Therefore it can be written as a Fourier expantion: ψ(r, t) = e(−iEt/~) ∞ X n=−∞ e(inwt)_φ n(ri) (1.21)

where w is the frequency of the electromagnetic radiation. The integer n refers to the number of photons absorbed (or emitted) by the system. Coming back to the molecular potential curves, the result of this periodic absorbtion process

(31)

Attoseconds for molecular physics is a periodic deflection of the PECs and the appearance of possible crossings, as reported in Fig. 1.3. This can cause the coupling between different

elec-Figure 1.3: Dressed potential energy curves. (a) Unperturbated configuration. (b) One-photon absortion induces a dressing process in the state 2, resulting in a crossing with state 1. This can produce population transfer between state 1 and state 2.

tronic states (during the propagation of the wavepacket along the potential curves) and consequent population transfers, that can ultimately affect the dynamics of the parent molecular ion.

The broadband excitation/ionization by XUV radiation and the conseguent interaction of the molecule (molecular ion) with the probe pulse can ultimately lead to important information about real-time dynamics of the system after the initial perturbation. The insight provided by this approach, in principle, could even provide a real-time mapping of the quantum paths the excited molecule (molecular ion) goes trough before fragmentation, giving an exper-imental signature of the “real” potential energy curves of the system (see chapter 3). In particular the possibility of directly accessing different chan-nels of molecular dissociation allows one the control over the overall process of fragmentation, that is a fundamental issue in light-matter interaction physics.

(32)

1.2.2 Charge motion in complex molecular systems

A chemical rearrangement occurs when atoms in a molecule change their spe-cific positions. For this reason the time scale in chemistry is traditionally considered as the time scale for the dynamics of atoms. Actually, many ex-periments recently demonstrated that the breakdown of Born-Oppenheimer approximation is really common in complex molecules. For example, it is known that the photostability of DNA bases is based on photoprotection mechanisms, involving ultrafast relaxation around conical intersections [57]. Also in this case, anyway, it is still the nuclear motion to drive the dynamics. This type of electron dynamics mediated by nuclear rearrangement is usually called charge transfer.

In 1995 and 1996 Weinkauf and coworkers performed some pioneering exper-iments in which they induced the photoionization of a chromophore (trypto-phan, phenylalanine or tyrosine) on the C-terminal end of a peptide chain [58, 59], and observed that the fragmentation pattern was dominated by species related to the N-terminal end whenever this amino acid (glycine or leucine) had a lower ionization potential than the chromophore. This observation sug-gested the presence of a purely electronic charge transfer from the N-terminal to the chromophore named charge migration. A new idea was rising, i.e. the creation of an electronic wavepacket could bypass the rearrangement of the nuclei and then be used to control chemical reactivity. Subsequent theoret-ical works demonstrated that the prompt ionization of large molecules may produce ultrafast charge migration along the molecular skeleton, which can precede any nuclear rearrangement [60–63](Fig. 1.4). This purely electronic dynamics, evolving on an attosecond or few-femtosecond temporal scale, can determine the subsequent relaxation of the molecule. This behavior play a crucial role in many biological and chemical processes, such as vision, photo-syntesis and radation damage of biomolecules.

According to Cederbaum and Zobeley [62], this charge migration may rely on the existence of a coherent superposition of hole states, leading to coherent hole propagation within the molecular ion. In this case, the ionization of the

(33)

Attoseconds for molecular physics

(a) (b)

Figure 1.4: (a) Migration of hole charge in glycine. At t = 0 the the charge is located on the left-hand side of the molecular skeleton. The charge migrates to the right-hand side of the molecule. At t = 3.5 fs the charge is mainly located on the right-hand side of the molecule. Figure adapted from [61]. (b) Snapshots of the densities of the hole as a function of time for a hole created on the HOMO of TrpLeu3. The hole migrates to the N end in 0.75 fs and it returns to the origin after

1.5 fs. Figure adapted from [60].

molecule must involve a mechanism that coherently produces a superposition of cationic states. In the independent-electron picture, the ultrafast removal of an electron from an orbital creates a stationary hole that can be assigned to a well-defined peak in the photoelectron spectrum (Koopmans’ theorem). This is dubbed a one-hole (1h) configuration. When electron correlation con-tributes to the molecular dynamics (for a molecule containing N electrons), the wavefunction resulting from the removal of one electron by photoioniza-tion (thus representing N-1 electrons) is not an eigenstate of the caphotoioniza-tion, and it

(34)

corresponds to a non-stationary state that can be described as a coherent su-perposition of several cationic eigenstates. Several cases can be distinguished. First, situations exist where only 1h configurations play a role in the dynam-ics. This configuration is called “hole mixing” and can produce oscillations in the population of “Koopmans-like” hole states [63]. Another situation occurs when second-order (or even higher order) configurations become important in the dynamics, for example when the hole formation by single-electron re-moval is accompanied by the generation of a second hole by a shake-up process (2h1p). The result is a photoelectron spectrum displaying a satellite peak, in addition to the peak corresponding to the main 1h configuration. Also in this case the coherent superposition of states leads to charge migration (that is, oscillations in the population of the two holes in the 2h1p configuration). Higher-order processes are also possible when many hole configurations play a role in the dynamics. In this case, the molecular orbital picture breaks down, and the main 1h character is completely redistributed over many possi-ble configurations; consequently, there is no main 1h line in the photoelectron spectrum. The coherent preparation of many cationic states again drives the hole density to rearrange in an ultrafast timescale. In fact, the possible existence of a “universal” timescale of about 50 as has been suggested [64], corresponding to the contribution of an infinite number of hole states to the ionization mechanism. Hole migration has been theoretically investigated for several systems. Hennig and coworkers studied N-methylacetamide and found ultrafast hole motion from one end of the linear molecule to the other within a few femtoseconds [65]. A similar effect was found for DNA bases (glycine), with different isomers showing different timescales for charge propagation [66]. Another important example was given by Remacle and Levine, who studied hole migration in small peptides [60]. It is important to observe that the occurrence of hole migration requires a number of conditions. In order to pre-pare a non-stationary cationic state, the electron should be removed quickly enough to avoid rearrangement of the electronic density during the ionization process. This non-adiabatic or “sudden” ionization allows the (N-1)-electron

(35)

Attoseconds for molecular physics state to be written as a superposition of cationic eigenstates. This means that the photoelectron should be ejected with a sufficiently high velocity (for in-stance, by using a high-energy photon). Furthermore, in order to have charge migration through the molecular structure, at least one of the eigenstates formed in the photoionization process must be delocalized. In addition, the timescale of hole migration must be short compared to that of diabatic vi-bronic couplings, which lead to a loss of coherence. Finally, to be observable in a time-resolved measurement, the dynamics must be triggered by a suffi-ciently short coherent event.

For all these reasons attosecond pulses are excellent candidates in order to solve this type of phenomena, since they could provide the necessary tempo-ral resolution to track charge migration in real time.

(36)

(37)

BIBLIOGRAPHY

[1] Ahmed H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond”, J. Phys. Chem. A 104, 5660-5694 (2000);

[2] A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIn-tyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases”, JOSA B 4, 4, 595-601 (1987);

[3] M Ferray, A L’Huillier, X F Li, L A Lompre, G Mainfray and C Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases”, J. Phys. B: At. Mol. Opt. Phys. 21, L31 (1988);

[4] M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields”, Phys. Rev. A 49, 2117 (1994);

[5] J. L. Krause, K. J. Schafer and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime”, Phys. Rev. Lett., 68, 3535-3538 (1992);

(38)

[6] K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff”, Phys. Rev. Lett. 70, 1599-1602 (1993);

[7] P. B. Corkum, “Plasma perspective on strong field multiphoton ioniza-tion”, Phys. Rev. Lett. 71, 1994-1997 (1993).

[8] P. Paul, E. Toma, P. Breger, G. Mullot, F. Aug, P. Balcou, H. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation”, Science 292, 1689-1692 (2001);

[9] M. Hentschel, R. Kienberger, C. Spielmann, G. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosec-ond metrology”, Nature 414, 509-513 (2001);

[10] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy”, Nature 419, 803-807 (2002);

[11] M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hof-stetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nico-laides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission”, Science 328, 5986, 1658-1662 (2010);

[12] G. Sansone, F. Kelkensberg, J. Prez-Torres, F. Morales, M. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lpine, J. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Ivanov, M. Nisoli, F. Martn, and M. Vrakking, “Electron localization following attosecond molecular photoionization”, Nature 465, 763-766 (2010); [13] G. Farkas and C. Toth, “Proposal for Attosecond Light-Pulse

Genera-tion Using Laser-Induced Multiple-Harmonic Conversion Processes in Rare-Gases”, Phys. Lett. A, 168, 447-450 (1992);

(39)

Bibliography (Chapter 1) [14] S. E. Harris, J. J. Macklin and T. W. H¨ansch, “Atomi–Scale Temporal Structure Inherent to High-Order Harmonic-Generation”, Opt. Commun., 100, 487-490 (1993);

[15] P. B. Corkum, N. H. Burnett and M. Y. Ivanov, “Subfemtosecond Pulses”, Opt. Lett.,19, 1870-1872 (1994);

[16] A. Baltuˇska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. H¨ansch and F. Krausz, “Attosecond control of electronic processes by intense light fields”, Nature 421, 611-615 (2003);

[17] M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, C. Vozzi, M. Pascol-ini, L. Poletto, P. Villoresi, and G. Tondello, “Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra”, Phys. Rev. Lett. 91, 213905 (2003);

[18] C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos and J. W. G. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval”, Nature Phys. 3, 52-57 (2007). [19] R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuˇska, V.

Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher and F. Krausz, “Atomic transient recorder”, Nature 427, 817-821 (2004);

[20] T. Witting, F. Frank, W. A. Okell, C. A. Arrell, J. P. Marangos and J. W. G. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking”, J. Phys. B. 45, 074014 (2012);

[21] A. Jullien, T. Pfeifer, M.J. Abel, P.M. Nagel, M.J. Bell, D. M. Neumark and S.R. Leone, “Ionization phase-match gating for wavelength-tunable isolated attosecond pulse generation”, Appl. Phys. B 93, 433442 (2008);

(40)

[22] Mark J. Abel, Thomas Pfeifer, Phillip M. Nagel, Willem Boutu, M. Jus-tine Bell, Colby P. Steiner, Daniel M. Neumark, Stephen R. Leone, “Iso-lated attosecond pulses from ionization gating of high-harmonic emission”, Chem. Phys. 366, 9-14 (2009);

[23] I. Thomann, A. Bahabad, X.Liu, R. Trebino, M. M. Murnane and H. C. Kapteyn, “Characterizing isolated attosecond pulses from hollow-core waveguides using multi-cycle driving pulses”, Opt. Express 17, 4611-4633 (2009).

[24] F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields”, Nature Photon. 4, 875-879 (2010);

[25] I. J. Sola, E. Mevel, L. Eloug, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.P. Caumes, S. Stagira, C. Vozzi, G. Sansone and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating”, Nature Phys. 2, 319-322 (2006);

[26] Hiroki Mashiko, Steve Gilbertson, Chengquan Li, Sabih D. Khan, Ma-hendra M. Shakya, Eric Moon, and Zenghu Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers”, Phys. Rev. Lett. 100, 103906 (2008);

[27] Ximao Feng, Steve Gilbertson, Hiroki Mashiko, He Wang, Sabih D. Khan, Michael Chini, Yi Wu, Kun Zhao, and Zenghu Chang, “Generation of iso-lated attosecond pulses with 20 to 28 femtosecond lasers”, Phys. Rev. Lett. 103, 183901 (2009);

[28] Hiroki Mashiko, M. Justine Bell, Annelise R. Beck, Mark J. Abel, Philip M. Nagel, Colby P. Steiner, Joseph Robinson, Daniel M. Neumark and Stephen R. Leone, “Tunable frequency-controlled isolated attosecond pulses characterized by either 750 nm or 400 nm wavelength streak fields”, Opt. Express 18, 25887-25895 (2010);

(41)

Bibliography (Chapter 1) [29] H. Vincenti and F. Qu´er´e, “Attosecond lighthouses: how to use spa-tiotemporally coupled light fields to generate isolated attosecond pulses”, Phys. Rev. Lett. 108, 113904 (2012);

[30] 36. Budil, K. S., Sali`eres, P., L’Huillier, A., Ditmire, T. and Perry, M. D., “Influence of ellipticity on harmonic generation” Phys. Rev. A 48, R3437-R3440 (1993);

[31] 37. Max M¨oller, Yan Cheng, Sabih D. Khan, Baozhen Zhao, Kun Zhao, Michael Chini, Gerhard G. Paulus, and Zenghu Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity”, Phys. Rev. A 86, 011401(R) (2012);

[32] G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, L. Poletto, P. Villoresi, V. Strelkov, I. Sola, L. B. Elouga, A. Za¨ır, E. Mvel, and E. Constant, “Shaping of attosecond pulses by phase-stabilized polarization gating”, Phys. Rev. A 80, 063837 (2009);

[33] Marceau, C., Gingras, G. and Witzel, B., “Continuously adjustable gate width setup for attosecond polarization gating: theory and experiment”, Opt. Express 19, 3576-3591 (2011);

[34] V. Strelkov, A. Za¨ır, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével and E. Constant, “Single attosecond pulse production with an ellipticity-modulated driving IR pulse”, J. Phys. B 38, L161-L167 (2005); [35] J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B.

Corkum, “Attosecond Streak Camera”, Phys. Rev. Lett. 88, 173903 (2002); [36] Markus Kitzler, Nenad Milosevic, Armin Scrinzi, Ferenc Krausz, and Thomas Brabec, “Quantum Theory of Attosecond XUV Pulse Measure-ment by Laser Dressed Photoionization”, Phys. Rev. Lett. 88, 173904 (2002);

(42)

[37] P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte and G. D. Tsakiris, “Direct observation of attosecond light bunching”, Nature, 426, 267 (2003);

[38] Armin Scrinzi, Michael Geissler, and Thomas Brabec, “Attosecond Cross Correlation Technique”, Phys. Rev. Lett. 86, 412 (2001);

[39] F. Qu´er´e, J. Itatani, G. L. Yudin, and P. B. Corkum, “Attosecond Spec-tral Shearing Interferometry”, Phys. Rev. Lett. 90, 073902 (2003);

[40] H. G Muller, “Reconstruction of attosecond harmonic beating by inter-ference of two-photon transitions”, Appl. Phys. B, 74, S17 (2002);

[41] I. A. Walmsley and V. Wong, “Characterization of the Electric Field of Ultrashort Optical Pulses”, J. Opt. Soc. Am. B 13 (11), 2453-2463 (1996); [42] Paul N. Butcher, David Cotter, “The elements of nonlinear optics”,

Cam-bridge University Press, (1991);

[43] Chini, M., Gilbertson, S., Khan, S. D. and Chang, Z., “Characterizing ultrabroadband attosecond lasers” Opt. Express 18, 13006-13016 (2010); [44] Y. Mairesse and F. Qu´er´e, “Frequency-resolved optical gating for

com-plete reconstruction of attosecond bursts”, Phys. Rev. A 71, 011401(R) (2005);

[45] R. Trebino, “Frequency-Resolved Optical Gating”, Kluwer Academic, Boston (2000);

[46] D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort pulses from a single spectrogram in a single shot”, J. Opt. Soc. Amer. B, vol. 14, pp. 935943 (1997);

[47] M. D. Thomson, J. M. Dudley, L. P. Barry, J. D. Harvey, “Complete pulse characterization at 1.5 µm by cross-phase modulation in optical fibers”, Optics Letters, Vol. 23 Issue 20, pp.1582-1584 (1998);

(43)

Bibliography (Chapter 1) [48] Daniel J. Kane, “Real-Time Measurement of Ultrashort Laser Pulses Using Principal Component Generalized Projections”, IEEE J. Quantum Electron. 4, 2, (1998);

[49] Daniel J. Kane, “Principal components generalized projections: a re-view”, J. Opt. Soc. Am. B, Vol. 25, No. 6 (2008);

[50] K.W. DeLong, D.N. Fittinghoff, R. Trebino, B. Kohler,and K.R. Wilson, Opt.Lett. 19, 2152 (1994);

[51] K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, J. Opt. Soc. Amer. B 11, 2206 (1994);

[52] M. F. Kling, Ch. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, Th. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, M. J. J. Vrakking, “Control of electron localization in molecular dissociation”, Science 312, 246-248 (2006);

[53] L. Belshaw, F. Calegari, M. Duffy, A. Trabattoni, L. Poletto, M. Nisoli, J. Greenwood, “Observation of Ultrafast Charge Migration in an Amino Acid”, Journal of Phys. Chem. Lett. 3, 24, 37513754 (2012);

[54] F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Green-wood, F. Martin, M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses”, Science 346, 6207, 336-339 (2014);

[55] L. J. Butler, “Chemical reaction dynamics beyond the Born-Oppenheimer approximation”, Annu. Rev. Phys. Chem. 49, 125-171 (1998); [56] F.H.M. Faisal, “Theory of Multiphoton Processes”, Plenum (New York)

(1987);

[57] M. N. R. Ashfold, B. Cronin, A. L. Devine, R. N. Dixon, and M. G. D. Nix, “The role of πσ∗ _{excited states in the photodissociation of}

(44)

[58] R. Weinkad, P. Schanen, D. Yang, S. Soukara, and E. W. Schlag, “Ele-mentary Processes in Peptides: Electron Mobility and Dissociation in Pep-tide Cations in the Gas Phase”, J. Phys. Chem. 99, 11255-11265 (1995); [59] R. Weinkauf, P. Schanen, A. Metsala, and E. W. Schlag, M. Burgle and H.

Kessler, “Highly Efficient Charge Transfer in Peptide Cations in the Gas Phase: Threshold Effects and Mechanism”, J. Phys. Chem. 100, 18567-18585 (1996);

[60] F. Remacle, and R. D. Levine, “An electronic time scale in chemistry”, PNAS 103, 18, 6793-6798 (2006);

[61] A. I. Kuleff, J. Breidbach, and L. S. Cederbaum, “Multielectron wave-packet propagation: General theory and application”, J. of Chem. Phys. 123, 044111 (2005);

[62] L.S. Cederbaum, J. Zobeley, “Ultrafast charge migration by electron cor-relation”, Chem. Phys. Lett. 307, 205210 (1999);

[63] J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications”, J. of Chem. Phys. 118, 9 (2003); [64] J. Breidbach, and L. S. Cederbaum, “Universal attosecond response to

the removal of an electron”, Phys. Rev. Lett. 94, 033901 (2005);

[65] H. Hennig, J. Breidbach, and L. S. Cederbaum, “Electron correlation as the driving force for charge transfer: charge migration following ionization in N-methyl acetamide”. J. Phys. Chem. A 109, 409-414 (2005);

[66] A. I. Kuleff, and L. S. Cederbaum, “Charge migration in different con-formers of glycine: the role of nuclear geometry”, Chem. Phys. 338, 320-328 (2007);

(45)

CHAPTER

2

EXPERIMENTAL SETUP

2.1 Attosecond beamline

The laser installed in the ELYCHE laboratory is the FEMTOPOWER PRO V CEP, a commercial system developed by Femtolasers. It consists of a Ti:Sa oscillator (Femtosource Raimbow) and a 2-stage Ti:Sapphire multi-millijoule (mJ) amplifier. It provides IR pulses (at the wavelength of ≃ 800 nm) with an energy of 6 mJ, 25 fs of duration and a repetition rate of 1 KHz. The laser pulses are Carrier-Envelope Phase (CEP) stabilized [1], thanks to two differ-ent stabilization stages. The first one (Menlo Systems XPS800), consisting of a f0− f interferometer, is installed just outside the oscillator cavity and

it’s able to phase lock the offset frequency at a 1/4 of the oscillator repetition frequency. The second CEP-stabilization stadium (Menlo Systems APS800) is a f −2f interferometer installed at the end of the laser system, and compen-sates for the slow CEP drift introduced by the 2-stage amplifier. The 2-stage CEP stabilization system provides a single-shot phase stability with an RMS of ≃ 190 mrad. Few-femtosecond pulses were required by our experiments, so

(46)

(a)

(b)

Figure 2.1: A schematic view of the attosecond-pump femtosecond-probe beamline. In the interaction area several detection systems have been installed, alternatively: Velocity Map Imaging spectrometer, TOF spectrometer, KEIRA mass spectrometer. The beamline is split in the figure for a better view.

the hollow-core fiber compressor [2] was installed at the output of the laser system and used to compress the pulse duration from 25 fs down to 4 fs. The laser beam is focused into the hollow fiber made of silica by a 1750 mm

(47)

fo-Attosecond beamline cal length mirror, as described in section 2.3.1. After the fiber another focal mirror collimates the radiation into a chirped-mirror compressor made of 11 dielectric multilayer mirrors with a 450 nm - 970 nm bandwidth acceptance. Fig. 2.1 shows a scketch of the experimental setup after the chirped-mirror compressor.

An ultrabroad band beamplitter divides the pulses entering the pump-probe interferometer. 70% of the incoming energy is used for the attosecond-pump arm, 30% for the probe, in order to maximize the photon flux of attosecond pulses. On the pump arm, the VIS/NIR pulses pass through the two plates for the Polarization Gating (PG) [3, 4] (see section 1.1.1) and a pair of glass wedges, that are used to finely tune the spectral dispersion of the pulses. A 50 cm focal length mirror focuses the beam into the vacuum chamber where high harmonics generation occurs. Here the gas cell for HHG is mounted on a XYZ motorized translational stage, that allows one to properly align the cell with respect to the laser focus position. In order to select the short trajectories in HHG, the cell was positioned few millimeters after the laser focus position [5–7]. The XUV radiation enters the recombination chamber where metallic foils are used to filter out the fundamental radiation and the low-order harmonics, and then reaches the central hole of a drilled mirror, where recombination between pump and probe pulses occurs.

On the probe arm, the VIS/NIR pulses pass through a pair of wedges (also in this case they were used to optimize the pulse compression by controlling the dispersion) and a coarse delay line mounted on a micrometric translation stage. It was used to roughly approach the temporal overlap between the pump and the probe. A 75 cm focal length mirror focuses the laser beam into the recombination chamber. After the focus the beam inpinges the pump-probe delay line mounted on a piezoelectric translation stage by Piezosys-tems Jena. The resolution of the translation stage is 1 nm, corresponding, in the temporal domain, to a delay resolution of ≃ 3 as. The VIS/NIR probe pulses recombine with attosecond pump pulses on the drilled mirror and both reach a 80cm focal length toroidal mirror. This is a grazing incidence optics,

(48)

coated of gold, that is able to reflect ≃ 85% of XUV incoming radiation (for s-polarization), and all the VIS/NIR radiation, and focalize the beams into the interaction chamber. Here several detection systems were used, accord-ing with the experiments. An electron time-of-flight spectrometer was used to characterize the attosecond pulses by streaking measurements and to per-formed straking spectroscopy experiments (see section 2.2.1). We also used a Velocity Map Imaging (VMI) spectrometer to investigate ultrafast electron dynamics in diatomic molecules (see section 2.2.3) and a mass spectrome-ter to study charge transfer processes in complex biological molecules [8](see the KEIRAlite spectrometer described in section 2.2.2). After the interaction area, a XUV spectrometer is installed to monitor the spectral properties of attosecond pulses. The XUV spectrometer consists of a toroidal mirror and a grating. The toroidal mirror has a 800 mm entrance arm and two exit arms, 700 mm (horizontal plane) and 1519 mm (vertical plane). The grating, in-stead, that is positioned at 1050 mm after the toroidal mirror, has a 350 mm entrance arm and a 469 mm exit arm (in the horizontal plane, no focaliza-tion on the vertical plane). 469 mm after the grating, a MCP+phosphorus screen+CCD camera detection system is able to record the XUV spectra at different integration time values, down to (sampled) single-shot measure-ments.

2.2 Detection systems

2.2.1 Electron time-of-flight spectrometer

An electron time-of-flight (TOF) spectrometer (Kaesdorf ETF 10) was in-stalled in the interaction area for streaking experiments (see section 1.1.2), to collect photoelectrons produced by the interaction between a gas target and the attosecond pulses. The spectrometer is optimized for a distance of 3 mm between the ionization zone and the entrance cone, so we aligned the TOF spectrometer in order to have the laser focus centered at this height with respect to the cone. The gas source consists of a stainless steel nozzle with

(49)

Detection systems

(a)

(b)

Figure 2.2: (a) HHG pattern usually used to calibrate the TOF spectrometer, by linking the peaks of photoelectrons (green points in (b)) with the correspondent XUV harmonic order. (b) Calibration fit functions. The green points represent the peaks of photoelectrons in the time-of-flight axes. Orange line: parabolic fit of low-tof (high energy) peaks; blue line: parabolic fit of all photoelectron peaks; red line: fit function from Eq. 2.2.

Attosecond electron dynamics in complex molecular systems

Politecnico di Milano