Femtosecond and Attosecond Spectroscopy in the XUV Regime Arvinder S

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012 351 Femtosecond and Attosecond Spectroscopy in the XUV Regime Arvinder S. Sandhu and Xiao-Min Tong

(Invited Paper)

Abstract—Attosecond-duration, fully coherent, extreme- [7], [8]. Time-resolved experiments with these laser-generated ultraviolet (XUV) photon bursts obtained through laser XUV pulses provide new insights into the electronic processes high-harmonic generation have opened up new possibilities in the in atoms, molecules, and surfaces [1]Ð[6], [9]Ð[15]. study of atomic and molecular dynamics. We discuss experiments elucidating some of the interesting energy redistribution mecha- Strictly speaking, apart from attosecond XUV pulses, the im- nisms that follow the interaction of a high-energy photon with a plementation of ultrafast XUV spectroscopy also requires pre- molecule. The crucial role of synchronized, strong-field, near-IR cisely synchronized strong field IR laser pulses. In fact, many laser pulses in XUV pump–probe spectroscopy is highlighted. We new experimental possibilities have emerged from this marriage demonstrate that near-IR pulses can in fact be used to modify between conventional strong-field (IR) and weak-field (XUV) the atomic structure and control the electronic dynamics on attosecond timescales. Our measurements show that the Gouy spectroscopic techniques. We refer to this entire class of exper- phase slip in the interaction region plays a significant role in these iments as ultrafast XUV+IR spectroscopy. attosecond experiments. We perform precision measurement of In the framework of XUV+IR spectroscopy, we will focus interferences between strong field-induced Floquet channels to on the developments along two main directions. One is the extract the intensity and phase dependence of photoionization utilization of XUV pulses for initiation of ultrafast chemical dynamics. Applications of emerging table-top ultrafast XUV sources in the study of core electron dynamics are also discussed. dynamics through inner-valence/multielectron excitations. The resulting femtosecond electronic and nuclear processes in such Index Terms—Atomic physics, attosecond, femtosecond, experiments are probed using time-delayed IR pulses. The other extreme-ultraviolet (XUV) spectroscopy., high harmonics. direction represents the use of attosecond duration XUV pulse trains to study and control the transient, strong field induced modification of the electronic structure of atoms. In these ex- I. INTRODUCTION periments, the XUV and IR fields are simultaneously present LTRAFAST atomic and molecular science has undergone and their relative delay is precisely controlled on attosecond U quite a revolution in the last few years. One of the ma- timescale. jor changes has been brought about by the arrival of ultra- A brief outline of this paper is as follows. In section II, we fast table-top extreme-ultraviolet (XUV) sources in the form show that ultrashort XUV excitation is a precursor of novel of attosecond-duration, high-frequency, coherent light pulses. excited-state dynamics. The role of IR pulses in pumpÐprobe The birth of a new subfield, being termed as “attosecond sci- measurement of XUV excited electronic and nuclear wavepack- ence,” has been made possible by advances in laser technology, ets is investigated in Section III. Experimental methods are dis- detection methods, and theoretical calculations [1]. The excite- cussed in Section IV. Section V and VI focus on the attosecond ment in this field arises from the possibility of observation and measurements of XUV+IR ionization dynamics. The signifi- control at the level of electrons [2]Ð[6], which typically undergo cance of the Gouy phase slip and advantages of spatial imaging dynamics on the timescale of few-hundred attoseconds. of focal volume are demonstrated. We use the Floquet formal- The phenomenon underlying ultrashort XUV pulses is the ism to interpret the behavior of atomic structures in strong fields. extreme nonlinear interaction of intense near-IR laser pulses We show that ion-yield oscillations encode the IR field strength (>1014 W·cm−2 ) with atoms, which leads to the generation of dependence of transition matrix elements. Finally, we discuss laser high harmonics extending up to hundreds of electronvolts the new experimental possibilities in study of multielectron and core-electron dynamics.

Manuscript received December 27, 2010; revised March 8, 2011; accepted II. ULTRASHORT XUV PULSE-INITIATED DYNAMICS March 8, 2011. Date of publication May 19, 2011; date of current version January 31, 2012. This work was supported by the National Science Foundation Most physical and chemical phenomena occur through the under Grant PHY-0955274. photoexcitation and subsequent evolution of electronic and nu- A. S. Sandhu is with the Department of Physics and College of Optical clear wavepackets [16]. Ultrashort light pulses in the IR, visi- Sciences, University of Arizona, Tucson, AZ 85737 USA (e-mail: sandhu@ physics.arizona.edu). ble and UV have been extensively used to uncover the nature X.-M. Tong is with the Center for Computational Sciences, University of and dynamics of excited molecular states [17]. However, most Tsukuba, Ibaraki 305-8573, Japan (e-mail: [email protected]). time-resolved studies of wavepacket dynamics have been lim- Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. ited to low-lying excited states, only a few electronvolt above Digital Object Identiﬁer 10.1109/JSTQE.2011.2136332 the ground state. In contrast, many common processes in nature

Fig. 2. (a) Intense near-IR femtosecond laser pulse focused on rare gas atoms Fig. 1. Inner-shell photoionization and correlated two-electron shake-up pho- leads to XUV emission. (b) Spectral output is in the form of odd harmonics toionization (b) either case leads to formation of highly excited molecular ions extending to hundreds of electronvolts. (c) Generation mechanism is a three that undergo fast fragmentation along multiple pathways. step process involving tunneling, acceleration and recollision of electronic wavepacket with core (d) Laser driven recollision mechanism repeats every half-cycle leading to synchronized attosecond duration XUV bursts. (e.g., solar irradiation of atmospheric molecules) lead to formation of excited molecules high above the ground state (>20 eV). ciently generated in the photon-energy regime of 10Ð100 eV [see Fig. 1(a) illustrates the XUV photon initiated inner-shell ion- Fig. 2 (b)]. This is highly appropriate for probing excited state ization (solid line) and two-electron shake-up processes (dotted dynamics as most molecules exhibit peak oscillator strengths line) in a diatomic molecule generically labeled as A2 .Theterm in this photon-energy regime [19]. Third, the three step mecha- “shake-up” here broadly refers to the electronic processes where nism [20], [21] [see Fig. 2(c)] ensures the phase coherence and excitation accompanies the ionization. As seen from Fig. 1, the perfect synchronization between XUV attosecond pulse trains XUV interaction forms highly excited molecules in the multiple (APTs) (or single attosecond pulses) [22]Ð[26] and the driv- continua above the single or even double ionization threshold. ing IR pulses. This intrinsic subcycle synchronization allows The energy relaxation dynamics of these states often involves XUV+IR pumpÐprobe experiments that can time resolve what fragmentation along steep potential energy surfaces (PES) such happens in the attoseconds or first few femtoseconds of photonÐ as those depicted in Fig. 1(b). The evolution of such highly ex- molecule interaction. cited states presents an interesting realm that involves correlated As an opening example, we discuss the fragmentation dy- electronic and nuclear motion on ultrafast timescales. namicsofN2 molecule, which represents the first measurement However, the real-time dynamics of highly excited molecules of XUV pulse initiated femtosecond molecular dynamics [15]. have remained largely unexplored. Conventional synchrotrons In this experiment, XUV pulse is used to create a localized could not directly emphasize the “dynamics” due to the lack ionic wavepacket ∼40 eV above the ground state [see Figs. 1 of time resolution. Similarly, the multiphoton/strong-field ap- and 3(a)]. Using photofragment imaging technique discussed in proach with IR/visible pulses is inadequate, as it preferentially Section IV, we observed two main product channels. The inner- 2 2 2 3 targets the loosely bound electrons and cannot directly access valence (2σg 2σu ) ionized molecules fragment into N(2s 2p ) inner electrons. and N+ (2s2 2p2 ). More importantly, certain excited molecular +∗ + Fortunately, the table-top XUV pulses obtained through laser ions (N2 ) evolve into ground state N and an excited neutral high-harmonic generation (HHG) provide an excellent source atom that has loosely bound (n = 3) electron attached to it. The in terms of photon energy and time resolution required to probe second excitation and fragmentation path is shown as lower po- fast electronÐelectron and electronÐion dynamics. In Fig. 2, we tential energy curve in Fig. 3(a) and it represents an interesting have summarized the essential aspects of laser HHG. For a and unexplored relaxation channel. detailed discussion of this process the reader is referred to an Using a time-delayed IR pulse, we remove the weakly bound explanatory article by Kapteyn et al. [18]. Later, we focus on shake-up electron, leading to N+ N+ product channel shown the unique opportunities opened up by the application of HHG in Fig. 3(a). This channel was isolated by selecting coincident source. events pairs with zero center-of-mass momentum. The kinetic The advantages of a table-top, attosecond, XUV source are energy release (KER) of these events is shown in Fig. 3(b) as many fold. First, due to the short pulse duration [see Fig. 2(d), a function of time delay. The spread in KER data is a result of attosecond-few femtosecond], XUV excitation creates highly FrankÐCondon vibrational spread, delayed ionization of trapped localized wavepackets such as those shown in Fig. 1(b). Tempo- molecular ions and the finite bandwidth of our XUV pulse. rally and spatially localized wavepackets allow ultrafast time- The excellent agreement between calculation (black lines) and resolved study of excited-state chemical dynamics, naturally the peak KER region of the experimental data identifies the +∗ providing sub-Aû spatial sensitivity to the reaction coordinate. electronic excited state N2 in Fig. 3(a) as 4σu electron shake- Second, the high-harmonic-based XUV pulses are most effi- up accompanying the 3σg ionization. SANDHU AND TONG: FEMTOSECOND AND ATTOSECOND SPECTROSCOPY IN THE XUV REGIME 353

+ ∗ Fig. 3. (a) XUV photon forms excited state (N2 ) though electronic shake- 2+ up. Time-delayed IR probe pulse converts it to dication state N2 .(b)KERof coincident N+ /N+ channel as a function of XUV+IR delay (black lines are fit from theory). The KER variation elucidates the dynamics of loosely bound electron formed in the 4σu orbital during shake-up process. The wave function corresponding to 4σu electron is shown at three time delays i.e., internuclear distances (inset boxes in (a)). (Adapted from [15]). Fig. 4. XUV excitation of O2 . Dashed curve represents the dissociation limit + ∗ of autoionizing O2 . Solid curves are dication dissociation limits. Autoioniza- tion is allowed for internuclear distances greater than 30 Aû corresponding to ∼300 fs delay. Autoionization dynamics are time resolved using an IR probe. The sharp decrease in KER over the first 150 fs represents (b) Electron spectra as a function of time delay show the appearance of 2-eV a rapid change from an almost spherically symmetric initial peak corresponding to onset of autoionization at 300 fs. The reduction of 0.5-eV 2+ binding potential to a final two-center potential for the 4σ electron peak in 0-fs XUV+IR data is due to the direction formation of O2 u in the simultaneous presence of XUV and IR pulses. (Adapted from [14]). electron. The wave function corresponding to the antibonding 4σu orbital is shown in Fig. 3(a) below the potential energy curves. At R = 1.1 Aû there is almost no electron density between i.e., 1.5 eV + 0.5 eV ∼ 2 eV. The appearance of this 2-eV peak + the two N cores. However, at R > 3 Aû the electron density at ∼300 fs in Fig. 4(b) confirms the onset of autoionization. between two cores is substantial, and the two-center nature of It should be mentioned that Feifel et al. [27] had performed a the potential is apparent. coincident electron study in O2 ; however, these synchrotron ex- In another XUV+IR experiment, Sandhu et al. [14] per- periments did not have time resolution to uncover the dynamics. formed a time resolved study of autoionization dynamics of Our use of pumpÐprobe XUV+IR spectroscopy enabled direct highly excited O2 molecules. Autoionization after XUV pho- observation of the transformation of electronically bound states toionization of O2 is a complex multistep process. By interrupt- of the molecular ion into Feshbach resonances of the neutral ing this process with a short IR laser pulse, it was demonstrated oxygen atom. that autoionization cannot occur until the internuclear separa- tion of the fragments is greater than ∼ 30 A.û Fig. 4 (top left) shows the XUV excitation, molecular evolution and IR probing III. ROLE OF IR FIELDS IN XUV SPECTROSCOPY steps relevant to this photonÐmolecule reaction. The earlier examples clearly show that the IR pulse plays Potential energy curves in Fig. 4(a) show the FrankÐCondon an important role in time resolving the molecular dynamics of region near 1 Aû and the dissociation limits corresponding to XUV excited states. Obviously, the ultrashort duration (tens of various internal states of fragments. Energetically favored and femtosecond) of an IR pulse and its synchronization with XUV symmetry allowed autoionization happens through electronic make it an ideal probe pulse. However, the role of the IR pulse transition between the dashed line (O+ /O∗) and the lowest solid is more subtle than that. Actually, it is the high field strength curve representing ground state (O+ /O+ ) ion fragments, releas- associated with IR pulses that ensures the success of ultrafast ing ∼0.5-eV electron [27]. As shown in Fig. 4(a), the time- XUV spectroscopy. delayed 1.5-eV IR probe photon can be used to interrupt this Despite the high oscillator strengths at XUV wavelengths, process by forcing a transition to the excited ionic state (O+ typical reaction channels associated with highly excited states (4 S) + O+ (2 D)). This is followed by distinct electron ejection exhibit a low cross section. For example, if we ignore the valence at an energy equal to an IR photon plus the autoionization energy ionization, the net photoionization cross section [28] for N2 at 354 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012

TABLE I XUV EXCITATION PROBABILITY

50 eV is < 3 Mb. Hence, for typical parameters such as 1-mm supersonic gas jet with density ∼1011 molecules/cm3 , one needs 107 XUV photons for a single nonvalence event. Unfortunately, the efficiency of high-harmonic processes is fairly low (<10−6 ). Fig. 5. (a) Ti:Sa laser amplifier produces 30 fs IR pulses at 1-kHz repetition Hence, the number of XUV photons reaching the interaction ∼ 7 rate with pulse energy 2-mJ. XUV APT is obtained by HHG in a gas-filled region is typically of the order ∼10 per pulse. This implies waveguide. XUV and time-delayed IR pulses are focused on to gas target. (b) that for the N2 case discussed earlier, each XUV pulse will only In case of femtosecond molecular dynamics, photofragments are analyzed in a prepare ∼1 interesting nonvalence excited molecule in the focal momentum-imaging reaction microscope consisting of position sensitive delay line detectors. Particle hits (x,y,t) give the 3-D momentum vector of each particle. volume. To ensure that this excited molecule is indeed probed, (c) In attosecond strong field ionization dynamics, we use velocity mapping or the probe needs to have a high flux. spatial ion imaging. To get a rough idea of probe pulse requirements, let us assume the probe photoabsorption cross section is few megabit and the in the interaction region. A mirror with a hole recombines the focal volume of typical dimensions 100 μm × 100 μm × 1 mm. two beams collinearly. This suggests that in the visible/near-IR range >1013 photons/ The XUV+IR experimental setup is shown in the Fig. 5(a). pulse are required. In other words, peak intensity in the range High harmonics are generated in a gas-filled hollow waveguide of 1012Ð1013 W·cm−2 is required for the probe. (150-μm bore). Waveguide offers control over spectral and tem- Table I summarizes the estimated nonvalence photoexcita- poral properties of HHG [24], [29] and high conversion effi- tion probability in the focal volume for typical molecular beam ciency through phase matching [30]. XUV emission is focused geometries. The photoexcitation events per laser shot are deter- onto atomic or molecular targets using multilayer coated or mined by the number of photons/shot, the target number density, grazing incidence dielectric mirrors [31]. the interaction length, and the cross section, as follows: Two types of photofragment detection schemes were utilized here. Fig. 5(b) shows a reaction microscope designed for probing Nexcited = Nphotons × (nmolecules · L · σ). femtosecond molecular dynamics [32]. Velocity map imaging (VMI) [33] setup in Fig. 5(c) was used for attosecond resolved The earlier discussion makes it clear that in order to get studies of atomic ionization. reasonable statistics, a moderate-to-high strength probe field In the molecular experiments, due to simultaneous population is crucial for XUV spectroscopy. Hence, it is no surprise that of many excitation channels by the XUV and the complexity of most table-top XUV experiments utilize intense probe IR pulses, excited-state PES, the evolution of a specific reaction channel enabling what we call the XUV+IR spectroscopy. is extremely hard to deconvolve from the multitude of frag- If high-field IR pulses are required in XUV spectroscopy, ments that are typically observed in such experiments. In order this raises an interesting question, namely, what is the effect of to implement signal extraction and analysis in molecular experi- strong transient electric fields on the electronic structure? As we ments, a coincident photofragment imaging reaction microscope show in Section VI, the XUV+IR spectroscopy in fact provides was developed [31]. In this technique, photofragments gener- us an ideal tool to address this question. ated in each laser shot are collected using electric and magnetic fields [see Fig. 5(b)]. Using position and time sensitive detectors, 3-D momenta of fragments are then computed on a shot to IV. EXPERIMENTAL METHODS shot basis. Using electron-ion momentum correlations, it was Typical beam line geometry used in XUV+IR experiments possible to identify and study specific reaction dynamics [31]. involves splitting the intense IR pulse into two parts. One part To implement attosecond resolved measurements of atomic is used to generate high-harmonic XUV emission in the form of ionization dynamics with high count rates resulting from effu- attosecond pulses or pulse trains (Beam 1). The other part of the sive gas jet, we collected the electrons/ions produced in the focal IR pulse is time delayed (Beam 2) and is overlapped with XUV region using electrostatic fields and imaged to a microchannel SANDHU AND TONG: FEMTOSECOND AND ATTOSECOND SPECTROSCOPY IN THE XUV REGIME 355

Fig. 6. VMI of photoelectrons resulting from ionization of helium atom using XUV pulses generated in Ar-filled waveguide. Two cases are shown, XUV alone and XUV+IR. Presence of IR leads to formation of sidebands through dressing of electrons. plate (MCP)-phosphor assembly backed by a charge-coupled device camera [see Fig. 5(c)]. Two different imaging modes are used: 1) VMI for electrons and 2) one-to-one spatial mapping of ions from the point of origin in the focal volume to the point of their impact on the detector. The VMI allows high energy resolution, as all fragments with same initial velocity vector are imaged to the same point on the detector regardless of their point of origin in the focus [33]. The spatial imaging mode essentially Fig. 7. (a) Relative phase between XUV and IR fields is used a control parameter in attosecond experiments. (b) 2-D ion images of focal region for different maps the focal volume on to MCP detector, thus allowing us to time (phase) delays between the two IR pulses. The peak of the ion signal moves discriminate the low energy ions produced under different IR in the z-direction (propagation direction) when the delay is changed, indicating phase and intensity conditions. a phase slip along the focus. (c) Oscillations of Xe ion counts as a function of IR/IR delay for two different sections at z = −10 mm and z = 10 mm are almost The XUV spectrum was calibrated using the VMI of photo- π out of phase. (d) Calibration of Gouy phase shift as a function of distance electrons produced from helium. Fig. 6 shows the photoelectron along the laser focus. (Adapted from [48]). rings corresponding to the comb of odd harmonics (2ω spaced). The first ring corresponds to the 17th harmonic that is the first typically use methods that involve placing the target before or one above the ionization threshold of helium. In presence of the after the focus or limiting of the interaction to a fraction of the IR pulse, the continuum energy of the photoelectron is modified Rayleigh range [22]. through the IR field induced dressing. This leads to additional With increasing attention toward real-time measurement and rings in the form of sidebands that are spaced by the energy of control of electron dynamics, it becomes important to under- IR photons [22]. stand the role of Gouy phase slip in attosecond measurements. Here, we discuss a method [37], [38] for accurate characteriza- V. I NTERACTION REGION:PHASE AND INTENSITY EFFECTS tion of the phase slip in a typical two-beam focusing geometry In the XUV+IR experiments, attosecond resolution is ob- shown in Fig. 5. tained by controlling the relative phase between two fields [see In the XUV+IR experiments (see Fig. 5), the Gouy phase Fig. 7(a)]. Thus, for accurate data acquisition, it is of crucial im- shift of the XUV (beam 1) is unimportant as the wavelength portance that the relative XUV/IR phase remains constant over of XUV is very short and the Rayleigh parameter is very large the interaction region. in comparison to IR field. As a result, the relative phase slip is As the XUV interaction is a weak-field effect, it results in purely due to the Gouy shift of the IR pulse (beam 2). excitation of atoms over the entire path length through the gas We show that the phase slip of an IR pulse can be characterized jet. In contrast, the strong fields are relevant only in the high- through spatial imaging of Xe ionization [38]. The aluminum intensity region of the focal volume, which can be characterized filter in beam 1 is opened to allow IR output from the waveguide by the Rayleigh length. Hence, one needs to ensure that the to propagate and the XUV output is blocked by using a thin glass phase delay between two fields is constant over smaller of the plate. Of the two IR pulses (beam 1 and beam 2), the weakly Rayleigh length or the gas jet extent. focused beam 1 serves as a reference to measure the phase It is a well-known fact that an electromagnetic wave going slip of beam 2 as a function of longitudinal distance along the through the focus, experiences a phase change, called the Gouy propagation direction (i.e., z-axis). The intensities of each of the phase shift [34]. The Gouy phase shift for Gaussian beams is π IR pulses were chosen such that ionization happens only in the radians, but it can have arbitrary values for more complex pro- simultaneous presence of the two fields and the ionization yield files [35], [36]. As a result, there is a spatial phase slip between at a point in the focal region depends on the local electric field XUV and IR fields in the interaction region. This obviously leads resulting from two pulses. to signal averaging over a range of relative phases, adversely af- For a fixed time delay, as the two overlapping IR pulses prop- fecting the measurement accuracy in XUV+IR experiments. agate through the focus, any change in relative phase between To ameliorate the effects of the Gouy phase slip, researchers them due to the Gouy phase slip of beam 2 results in the spatial 356 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012 variation of the ion yield. In particular, peak ion yield will occur wherever the two IR fields are “in-phase.” Fig. 7(b) shows the spatially resolved ion images obtained for five different time (phase) delays between the two IR pulses. Ion images exhibit a peak, which shifts spatially (along z-direction) as the relative time delay is changed. This is a clear indication of the phase slip between the two IR pulses as they go through the focus [37], [38]. Fig. 7(c) shows ion yield versus time delay for two vertical sections of the ion image corresponding to z = −10 mm and z =+10 mm, i.e., before and after the focus. As expected, the ion counts from these two end sections show clear oscillations with a period equal to the laser cycle period of 2.6 fs. More importantly, due to the relative phase slip, the oscillations from each end of the interaction region are almost π out of phase! Repeating this measurement for many spatial sections along the propagation direction, one can build a map of Gouy phase slip Fig. 8. Excited states of He relative to the high harmonics 11th, 13th, 15th. The two-photon XUV+IR ionization leads to formation of He+ ions. Photoion- in the focal region, which is shown in Fig. 7(d). ization is affected by IR field induced modification of resonances and dynamic In the absence of knowledge about the exact profile of “annu- interferences between different ionization pathways. lar” beam 2, the measured phase shift can be fit to an expression, −1 φ = A · tan (z/zR ), where the multiplier A characterizes the net effect due to the Gouy phase shift of high-order modes [36] ligible direct ionization by the APT. The presence of a strong constituting the annular beam, and z is the Rayleigh range. femtosecond IR pulse dynamically modifies the electronic states R and tuning the phase and intensity of the IR field should provide A good fit is obtained for A = 1.5 and zR = 7 mm, which is in agreement with the expected Rayleigh range of beam 2. In a certain level of control over ionization pathways. summary, Fig. 7(d) represents in situ calibration of the unknown In a recent experiment [40], it was observed that the exact Gouy phase slip of a complex annular beam 2 as a function of harmonic spectrum and the strength of the IR field play an im- distance along the focus, providing us with a phase meter for pre- portant role in the efficiency of the ionization process. In a sep- cision attosecond experiments. The advantage of this imaging arate experiment [41], it was pointed out that the IR ionization approach is that it allows us to implement spatial selectivity to of electronic wavepackets excited by consecutive XUV pulses enhance the contrast of phase-dependent XUV+IR pumpÐprobe in an APT can lead to interference in the continuum, modulat- data, allowing us to uncover previously unobservable phase and ing the efficiency of this process as a function of relative phase intensity effects in XUV+IR ionization. We envision that addi- between the IR and APT. tional phase-dependent effects can be revealed by spatial gating Detailed analysis of transient ionization dynamics can be un- dertaken by the full solution of the time-dependent Schrodinger¬ of single-shot ion images, thus turning the deleterious phase slip ∼ into a useful tool. equation. However, the relatively long IR pulse duration ( 40 fs) and the periodic nature of the interaction provide a natural theoretical framework to model this problem. This formula- VI. ATOMS IN STRONG FIELDS tion [42] is based on the formation of Floquet states in a strong periodic IR field. An important application of attosecond XUV+IR spec- The dynamics of an atom in a periodic external field are gov- troscopy is in the study of atomic ionization dynamics. Mo- erned by the following time-dependent Schrodinger¬ equation tivation behind this line of investigation is to understand and (in atomic units): control a fundamental process, such as photoabsorption, on ultrafast timescale. It is known that strong IR fields can substan- ∂ψ(t) i =[H + V (t)]ψ(t). (1) tially alter the atomic structure and can even induce transparency ∂t 0 for X-rays [39]. H is the field free atomic potential and V(t) is a periodic poten- Here, we focus on the control of two-color XUV+IR ioniza- 0 tial. In the Floquet formalism [42], the solution can be written tion dynamics on few-femtosecond timescale in a simple system in the form such as helium atom. The schematic of this interaction is shown ∞ in Fig. 8. Helium has a fairly discrete excited state spectrum. n=+ −iεα t −inωt To access the He excited states, we use the APT corresponding ψα (t)=e e φα,n (2) −∞ to the 11th, 13th, and 15th harmonics obtained from Xe filled n= waveguide. These harmonics lie below the ionization threshold where εα is the complex quasi-energy, and its imaginary part is of helium (24.6 eV), and depending upon the energy overlap −Γ/2 with Γ the width (or ionization rate) of the Floquet states, between harmonics and excited states, the APT primarily popu- φα,n is the time-independent wavefunction for the nth Fourier lates the resonant “np” excited states. The above threshold 17th component of the α Floquet state, and ω is the frequency of harmonic has tiny presence in the XUV spectrum, implying neg- the external periodic field. Thus, in the presence of a laser field, SANDHU AND TONG: FEMTOSECOND AND ATTOSECOND SPECTROSCOPY IN THE XUV REGIME 357

Fig. 10. Energy structure of two Floquet states corresponding to 2p and 5p atomic states under the inﬂuence of a strong periodic ω IR ﬁeld. Relative positions of high harmonic 13th and 15th are also shown in the diagram.

near-threshold shifts can be approximated by the ponderomotive energy associated with the IR field. Fig. 9 clearly demonstrates that the photoabsorption cross section at a given frequency can be modified by many orders of magnitude through the application of IR fields. Importantly, this modification can be achieved on an ultrafast (femtosecond) timescale! In the following section, we demonstrate the use of XUV+IR spectroscopic methods to understand and control the Fig. 9. (a) Photoabsorption cross sections in helium as a function of the IR in- photoionization dynamics. tensity. The white line starting at ωp = 0.9 a.u. shows the variation of ionization threshold due to the ponderomotive shift. (b) Line outs of photoabsorption cross 12 -2 section at three intensities in terms of I0 = 10 W·cm . (Adapted from [43]). VII. XUV+IR IONIZATION DYNAMICS electronic structure can be conveniently described by Floquet A. Interfering Paths states, where each bound state is associated with many one- Fig. 8 shows that the 13th and 15th harmonics are the two photon-spaced sidebands. most relevant excitation frequencies in helium. Two IR dressed If the external field is strong enough to modify the excited and Floquet manifolds that can be excited by these frequencies are continuum states, but weak enough not to perturb the ground shown in Fig. 10. These Floquet manifolds correspond to the state, we can write the photoabsorption cross section for transi- 2p and 5p states. Each state has several Floquet components tion from ground state to a given Floquet state as separated by an IR laser frequency (ω). To begin the analysis of XUV+IR dynamics let us consider 4πω |ψ | d |φ | σ(ω )= p Im g α,n . (3) a single Floquet state that is dominant. The ionization proceeds p c (ε + nω) − (ε + ω ) − iη α,n α g p through coherent channels represented by the ω-spaced Floquet components of that state. These coherent paths interfere, and the Here ωp is the XUV frequency, d is the dipole operator, Ψg is resultant ionization probability depends on the XUVÐIR delay. ground state wavefunction, εg is the ground state energy, and η is Assuming that both the XUV and IR fields are linearly an infinitesimal parameter used to represent adiabatic switching polarized along z-direction, the external potential in (1) is of the interaction. V (t)=−z[EIR(t)+EXUV(t)]. If the XUV APT pulse arrives In principle, the time-dependent wave function Ψα (t) can at a time delay τ relative to IR pulse, we can write the XUV be obtained by solving the time-independent Floquet equa- field as tion. However, in practice it is a highly computation intensive task. Instead, we use a simpler method developed by Tong and −iωXUV(t−τ ) Toshima [43] to calculate the effects of IR field on the electronic EXUV(t)= f(ωXUV)e dωXUV (4) structure of helium atom. Fig. 9 summarizes the behavior of atomic resonances as a function of probing XUV photon energy and peak IR intensity. where f(ωXUV) represents the energy content of XUV pulse (i.e. Clearly, the discrete resonances evolve into a complicated struc- high-harmonic spectra) and also determines the attosecond time ture in intense laser fields. The low-lying 2p state (at 0.78 a.u.) structure. The transition amplitude from the ground state to a exhibits a small shift, whereas the higher excited-state man- Floquet state in IR field can be written as ifold is completely altered by strong fields and the width of ∞ excited states become comparable to, or even larger than the + Mg→α = ψα (t)| zEXUV(t) |ψg (t)dt. (5) spacing between unperturbed energy levels. As expected, the −∞ 358 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012

Substituting for Ψα (t) from (2); and EXUV(t) from (4) we are led to transition matrix element Mg→α = φα,n|z |φg f(ωXUV) n −∞

i(εα +nω−ω XUV−εg )t iωXUVτ × e e dωXUVdt. (6) Implementing the integration, we get matrix element propor- tional to the IR- and XUV-dependent terms as iωn τ Mg→α = φα,n| z |φg f(ωn )e (7) n where ωXUV = ωn = Re(εα )+nω −εg . Under our experimental conditions, we have two main harmonics (13ω and 15ω), which implies two Floquet components contribute to the transition to the Floquet state. Removing the common phase terms, the ionization probability, which is pro- portional to the transition probability, can be written as 2 −i(2ωτ) P (τ) ∝ M13f13 + M15f15e . (8)

The matrix elements between ground state and two Floquet Fig. 11. Helium ion yield as a function of XUVÐIR delay for sections z = components (M13 and M15) depend on the IR intensity. Equation 10 mm and z = 0 mm along with spatially integrated yield in focal volume. (8) shows that the interference between two Floquet components Period of oscillations is half-IR-cycle. End section and the center of the focal will modulate the ionization probability twice per IR cycle as a region are out of phase, leading to loss of contrast in the integrated data. (Adapted from [48]) function of time delay i.e., with 2ω frequency. Now, we compare the understanding gained from this Floquet formalism with our experimental observations. Fig. 11, bottom panel). The loss of the modulation contrast in Using the experimental setup described in Fig. 5, we perform integrated data is due to the averaging over different XUVÐIR attosecond-resolved imaging of two-color (XUV+IR) ioniza- relative phases (delays). This phase averaging in the focus neg- tion of He. This process has been the focus of many recent atively affects most attosecond pumpÐprobe experiments to a investigations [40], [41], [44]Ð[46]. However, here we obtain certain degree. In fact, in some cases this averaging can mask spatially resolved He+ ion yield in the focal volume as a func- the interesting phase-dependent effects. The imaging technique tion XUVÐIR delay to illustrate the importance of phase aver- described in Section V provides a snapshot of phase evolution in aging. Fig. 11 plots the ion yield for two vertical sections of the the entire focal region and allows us to implement spatial selec- ion image, as well as the entire focal region. These positions tivity to enhance signal contrast. Furthermore, the spatial gating of z = 10 and z = 0 mm sections can be understood from the of the phase slip allows us to uncover previously unobserved focal volume image shown in Fig. 7. In each section, we observe effects. 2ω or half-cycle oscillations as expected from two-component B. Phases and Amplitudes of XUV+IR Transitions Floquet interference. However, the important thing is that the oscillations in the The amplitude and phase of 2ω oscillations discussed earlier section after the focus (z = 10 mm) are almost completely out- encode information on the relative phases and amplitudes of of-phase with respect to the oscillations in the center section transition matrix elements. We aim to measure the dependence (z = 0). Thus, unlike the IR+IR case [see Fig. 7(c)], where the of transition matrix elements on the IR ﬁeld in a time resolved oscillations from two end sections were out-of-phase, the oscil- fashion. lations in XUV+IR case go out-of-phase over half the spatial The numerical calculations of XUV+IR ionization in the distance. The difference stems from the fact that due to the 2ω presence of the 13th and 15th harmonics along with strong IR oscillation of XUV+IR ionization signal, π/2 Gouy phase shift ﬁeld are discussed by Tong and Toshima in [47]. The results of the IR pulse (beam 2) relative to the attosecond XUV bursts clearly illustrate the dependence of the amplitude and phase of (beam1) results in a completely opposite physical situation. The the 2ω ion-yield oscillations on IR intensity. Fig. 12(a) shows Gouy phase shift curve for Beam 2 in Fig. 7(d) shows that z = that the 2ω oscillation contrast strongly depends on the peak IR 10 mm and z = 0 mm points differ in phase by ∼ π/2, which intensity. Oscillation amplitude exhibits maximum value for 5I0 explains the observed behavior. and is lower for I0 and 10I0 . Importantly, the phase of the I0 Furthermore, if we compare the ion-yield oscillation in a se- and 10I0 curve are the same; however, the 5I0 curve is shifted lected section of the focal region to the oscillation in the spatially in phase relative to the other two. integrated yield from the entire focal region, we observe that the The continuous variation of amplitude and phase with in- modulation contrast is much poor in the integrated yield (see tensity is depicted in Fig. 12(b). As intensity increases, the SANDHU AND TONG: FEMTOSECOND AND ATTOSECOND SPECTROSCOPY IN THE XUV REGIME 359

Furthermore, the π phase jump on the right-hand side of Fig. 12(b) is a manifestation of a change in relative phase between transition matrix elements. At low IR intensities, the 3p Floquet state is important and the transition matrix elements to this state, i.e., M13 and M15 in (8), have a phase difference of π (opposite sign). At high IR intensities, the 2p Floquet state is important and for transition to the 2p manifold the matrix elements for 13th and 15th harmonics have a phase difference of zero (same sign). Later, we show that IR intensity dependence of magnitudes and relative phases of transition matrix elements is clearly visible in the experiments.

C. XUV+IR+IR Experiments In principle, time-resolved XUV+IR measurements encode the information on intensity dependence of the electronic structure. However, due to experimental constraints such as ﬂuctua- tions and interferometric instabilities it is very hard to extract the relative phases and amplitudes of 2ω oscillations in a straight- forward manner. In order to extract these quantities in a time- resolved manner, we propose the use of XUV plus two-IR pulse technique [38], [40], [48] to convert the phase information to amplitudes of ion-yield oscillations. The 2IR pulse method was introduced in [40], and was used to demonstrate the enhanced modulation of ionization yield. Here, we employ this method to Fig. 12. (a) Normalized ionization probability as a function of XUVÐIR time 12 −2 delay for different IR intensities in terms of I0 = 10 W·cm . Pav is the provide a reference for the measurement of the phase of 2ω os- average of ionization probability over one optical cycle. Ionization oscillation cillations, thereby enabling precise measurement of ionization amplitude as a function of intensity (solid line). The time (phase) of oscillations dynamics. in units of optical cycles is shown (solids dots). (Adapted from [47]). In this technique [38], [48], we use the interference between two IR pulses to create a reference frequency ω, which allows oscillation amplitude increases to a maximum value at 6I0 and us to observe the phases and amplitude of the 2ω oscillations then decreases to minimum value at 10I0 . This behavior was in a robust manner. Experimentally, this is achieved by simply also observed in calculations reported in [41]. However, in that opening the aluminum ﬁlter to allow the HHG driving IR pulse work, only the amplitude of the 2ω oscillations was discussed. to copropagate with the high harmonics. Referring to Fig. 5, We show here that an equally important aspect of this interac- the probe IR pulse follows the usual beam 2 path, whereas the tion is encoded in the phase of the 2ω oscillations. We notice a second IR pulse copropagates with the XUV bursts in beam phase jump or time shift of 0.25 optical cycles between oscil- 1. Since the XUV APT is generated by the copropagating IR, lations at lower and higher intensities. In terms of 2ω ion-yield both are inherently phase locked. The copropagating IR pulse is oscillations, this shift corresponds to a π phase jump. weaker than the external probe IR, but strong enough to cause Fig. 12 encodes important Floquet dynamics. For the 13th modulation of signal at ω. and 15th harmonic energies used in this calculation, it emerges Another important aspect of our technique is Gouy phase gat- that 2p and 3p Floquet manifolds both play a role in the ioniza- ing, which removes any averaging due to phase slip and, hence, tion dynamics. At lower intensities, photoionization is mainly allows us to extract phases and amplitudes with an unprece- through the 3p Floquet state populated by the 15th harmonic dented resolution. Fig. 13 shows the ion yield as a function of with a small contribution from the 13th harmonic. As IR inten- delay between XUV+IR (Beam 1) and IR (Beam 2). As before, sity increases, due to ac Stark shift, the transition strength to the we plot the ion yields corresponding to two vertical sections (z = 3p state by the 15th harmonic increases. At the same time, the 10 and z = 0 mm) along with the spatially integrated ion yield transition strength to the sideband (2ω Floquet component) of 3p over the entire focus. We observe that the oscillations occur with increases even faster, since coupling to Floquet components is a periodicity of one IR cycle and a small dip in the middle of IR intensity dependent. Further, with increasing IR intensity, the each cycle is clearly visible, thus introducing half-cycle or 2ω ac Stark shift moves the 2p Floquet state even farther away from periodicity. The spatially discriminated sections show a distinct resonance, suppressing its contribution. These factors lead to an asymmetry between peaks on either side of this dip. This struc- increase in oscillation amplitude with increasing IR intensity. ture was predicted recently in [40], but has not been experimen- As we increase the intensity even further, due to Stark shifts, the tally observed earlier. Clearly, this detailed structure showing a transitions to both Floquet states become important. However, half-cycle asymmetry effect is washed out in the spatially inte- the two contributions are not in phase, therefore, cancellation grated data due to Gouy phase averaging. This problem, often between the two reduces the oscillation amplitude. understated in experiments, leads to substantial loss of signal 360 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012

Fig. 13. He ion yield with XUV and two IR pulses. Oscillations at 2ω are superposed on the ω oscillation. The relative phase between the two oscillations leads to the observed time-dependent asymmetric oscillations structure. Spatially discriminated data from the end and center sections show Gouy phase shift. The oscillations structure is washed out in the integrated data due to Gouy Fig. 14. XUV+2IR ionization in He as a function of probe IR intensity. Co- phase averaging. (Adapted from [48]) − propagating IR intensity is ∼5 × 1012 Wcm 2 . Notice the oscillation amplitude and phase changes with time delay on few-femtosecond time scale. The box 13 −2 in the top panel (Iprobe = 3.4 × 10 W·cm )at−7.5 optical-cycle at time contrast in attosecond experiments and can wash out signatures delay shows π phase jump similar to the prediction in Fig. 12. of interesting quantum processes. Next we measure the intensity dependence of ionization in strong laser fields. Our results show that it is possible to under- XUV+2IR experiments. Fig. 14 shows that ω and 2ω signals stand the interfering ionization pathways in terms amplitudes as function of time delay for multiple probe intensities. At low and phases of transition matrix elements. Moreover, this ap- intensities or at large negative time delays, the interference be- proach can allow control of ionization dynamics with suboptical tween different Fourier components of the Floquet state i.e., cycle resolution. 2ω oscillation is very small, hence the net ionization signal has one-cycle periodicity. As probe intensity increases, the 2ω inter- VIII. NEW DEVELOPMENTS AND APPLICATIONS ference between Floquet components becomes important. This can also be seen from the fact that oscillations develop half-cycle Advances in laser technology have enabled access to ever periodicity earlier at higher intensities. shorter attosecond pulses. Furthermore, the use of long wave- Importantly, we observe that relationship between ω and 2ω length drivers allows phase matching at very high photon ener- oscillations changes very fast during the interaction. If we focus gies approaching kiloelectronvolt [49]Ð[51], where even sub-10 on the transition region (rectangular box) on the top panel of attosecond pulses can be produced. Such pulses by the virtue Fig. 14, we see that oscillation structure is completely opposite of their high energy and short pulse duration can even enable before and after. Before −8 optical-cycle the structure shows access to core shell electrons. asymmetric high peak-low peak variation. After −6.0 optical- Another important direction for progress is the development cycle the asymmetry becomes low peakÐhigh peak. This implies of high repetition-rate lasers, which will help to improve the a π phase change of the 2ω interference signal. flux of table-top XUV sources. Apart from the table-top laser- These results confirm a phase jump similar to the one pre- based techniques, upcoming free electron laser (FEL) facilities dicted in the theoretical calculation shown in Fig. 12, represent- are also being used for time-resolved experiments. One of the ing a change in relative phase between matrix elements M13 and unique features of FEL sources is very high photon densities, M15 associated with Floquet components. Even more significant such that the strong-field response can be explored even in the is the fact that this change happens in about one optical cycle or X-ray regime. less, which is an extremely fast transfer of ionization pathway Assuming a 500 eV, 10-attosecond source, which is not too from one channel to another. far into the future, we can envision direct observation of core To summarize, XUV+IR photoionization study provides a electronic excitation and relaxation dynamics in molecules. One rich topic for investigation of attosecond electron dynamics in important example of correlated relaxation dynamics concerns SANDHU AND TONG: FEMTOSECOND AND ATTOSECOND SPECTROSCOPY IN THE XUV REGIME 361

sociation, electronÐelectron correlations in double ionization, electronic relaxation, and its dependence on dynamic structure. Such experimental investigations are crucial to understanding of nonequilibrium few-body interactions, and should provide pointers for manipulation of energy ﬂow at the level of chemical dynamics. The insight into attosecond resolved XUV+IR ionization gives us a handle on the dynamic evolution of electronic structure in strong ﬁelds. The knowledge gained from these studies, relating to the attosecond control of photoexcitation and photoionization dynamics, could also aid in the development of a new generation of ultrafast devices.

ACKNOWLEDGMENT The authors would like to thank H. Kapteyn, M. Murnane, E. Gagnon, V. Sharma, L. Cocke, R. Santra, P. Ranitovic, P. Ho, Fig. 15. Schematic for IR streaking of Auger, ICD, or autoionization electrons N. Toshima, and N. Shivaram for their substantial contributions in XUV excited molecules. For example, XUV ionized dimer system exhibits to the work reported here. time delayed electron decay. Kinetic energy of photoelectron and decay electron is shown on right. IR streaking field when timed correctly to instant of electron birth leads to observable modification of electron energy/momentum in the form REFERENCES of sidebands. [1] F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Modern Phys., vol. 81, pp. 163Ð234, 2009. the decay processes where an electron is spontaneously ejected [2] M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. into the continuum. These processes include autoionization, F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schroder, M. Lezius, Auger decay, interatomic Coulombic decay (ICD) [52], etc. K. L. Kompa, H. G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time obser- These mechanisms are strongly affected by and, in turn, influ- vation of electron tunnelling in atoms,” Nature, vol. 446, pp. 627Ð632, ence the internuclear dynamics. For example, the autoionization 2007. rate strongly depends on internuclear coordinates. Similarly, the [3] M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem., vol. 59, pp. 463Ð492, 2008. Auger process is heavily modified by the changes in valence [4] P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science, electron distribution that accompany a chemical reaction. The vol. 317, pp. 766Ð769, 2007. ICD process, which occurs efficiently in Van der Waals and [5] H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science, vol. 317, hydrogen-bonded systems, is intimately tied to nuclear degrees pp. 775Ð778, 2007. of freedom [53]. While the end result of these processes is often [6] T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of known, the crucial understanding of real-time dynamics is still nonlinear optics,” Rev. Modern Phys., vol. 72, pp. 545Ð591, 2000. [7] A. Lhuillier and P. Balcou, “High-order harmonic-generation in rare-gases lacking. The time-of-birth, energy, and angular momentum of with a 1-ps 1053-nm laser,” Phys. Rev. Lett., vol. 70, pp. 774Ð777, 1993. continuum electrons encode crucial information about the nature [8] Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. of the potential and time evolution of molecular wavepacket. To C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett., vol. 79, pp. 2967Ð2970, 1997. tag the “electron birth,” momentum impulse provided by the IR [9] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, probe (streaking) can be used to modify the electron energy at A. Scrinizi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and the time of its emergence in continuum (see Fig. 15). Monitor- F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature, vol. 419, pp. 803Ð807, 2002. ing the electron ejection and obtaining its energy and angular [10] J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, distribution, can allow us to understand electron dynamics and A. L’Huillier, and K. J. Schafer, “Coherent electron scattering captured by their dependence on internal (molecular) and external (laser) an attosecond quantum stroboscope,” Phys. Rev. Lett., vol. 100, p. 073003, 2008. potentials. Development along these directions could lead to [11] L. Nugent-Glandorf, M. Scheer, D. A. Samuels, A. M. Mulhisen, interesting time-domain analogs of successful molecular char- E. R. Grant, X. M. Yang, V. M. Bierbaum, and S. R. Leone, “Ultra- acterization methods such as electron spectroscopy for chemical fast time-resolved soft x-ray photoelectron spectroscopy of dissociating Br-2,” Phys. Rev. Lett., vol. 8719, p. 193002, 2001. analysis [54] . [12] T. Pfeifer, M. J. Abel, P. M. Nagel, A. Jullien, Z. H. Loh, M. J. Bell, D. M. Neumark, and S. R. Leone, “Time-resolved spectroscopy of attosecond IX. CONCLUSION quantum dynamics,” Chem. Phys. Lett., vol. 463, pp. 11Ð24, 2008. [13] L. Miaja-Avila, C. Lei, M. Aeschlimann, J. L. Gland, M. M. Murnane, In summary, ultrafast XUV+IR spectroscopy combines the H. C. Kapteyn, and G. Saathoff, “Laser-assisted photoelectric effect from surfaces,” Phys. Rev. Lett., vol. 97, p. 113604, 2006. strengths of conventional weak-field and strong-field spectro- [14] A. S. Sandhu, E. Gagnon, R. Santra, V. Sharma, W. Li, P. Ho, P. Ranitovic, scopies, thus offering a unique tool to understand and control C. L. Cocke, M. M. Murnane, and H. C. Kapteyn, “Observing the creation quantum dynamics in atoms, molecules, and materials on the of electronic feshbach resonances in soft X-ray-induced O-2 dissociation,” Science, vol. 322, pp. 1081Ð1085, 2008. natural timescales of electrons. [15] E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke, M. M. Murnane, H. C. Interesting processes that can be investigated through time- Kapteyn, and A. S. Sandhu, “Soft X-ray-driven femtosecond molecular resolved XUV spectroscopy include nonadiabatic effects in dis- dynamics,” Science, vol. 317, pp. 1374Ð1378, 2007. 362 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012

[16] A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical [40] P. Ranitovic, X. M. Tong, B. Gramkow, S. De, B. DePaola, K. P. Singh, W. bond,” J. Phys. Chem. A, vol. 104, pp. 5660Ð5694, 2000. Cao, M. Magrakvelidze, D. Ray, I. Bocharova, H. Mashiko, A. Sandhu, E. [17] A. Stolow, A. E. Bragg, and D. M. Neumark, “Femtosecond time-resolved Gagnon, M. M. Murnane, H. C. Kapteyn, I. Litvinyuk, and C. L. Cocke, photoelectron spectroscopy,” Chem. Rev., vol. 104, pp. 1719Ð1757, 2004. “IR-Assisted Ionization of Helium by Attosecond XUV Radiation,” New [18] H. C. Kapteyn, M. M. Murnane, and I. P. Christov, Phys. Today, vol. 58, J. Phys., vol. 12, p. 013008, 2010. p. 39, 2005. [41] P. Johnsson, J. Mauritsson, T. Remetter, A. L’Huillier, and K. J. Schafer, [19] Y. Hatano, “Interaction of vacuum ultraviolet photons with molecules. “Attosecond control of ionization by wave-packet interference,” Phys. Formation and dissociation dynamics of molecular superexcited states,” Rev. Lett., vol. 99, p. 233001, 2007. Phys. Reports-Rev. Section Phys. Lett., vol. 313, pp. 110Ð169, 1999. [42] S. I. Chu and D. A. Telnov, “Beyond the Floquet theorem: Generalized [20] P. B. Corkum, “Plasma perspective on strong-field multiphoton ioniza- Floquet formalisms and quasienergy methods for atomic and molecular tion,” Phys. Rev. Lett., vol. 71, pp. 1994Ð1997, 1993. multiphoton processes in intense laser fields,” Phys. Reports-Rev. Section [21] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. Lhuillier, and P. B. Corkum, Phys. Lett., vol. 390, p. 131, 2004. “Theory of high-harmonic generation by low-frequency laser fields,” [43] X. M. Tong and N. Toshima, “Controlling atomic structures and photoab- Phys. Rev. A, vol. 49, pp. 2117Ð2132, 1994. sorption processes by an infrared laser,” Phys.Rev.A, vol. 81, p. 063403, [22] P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. 2010. Muller, and P. Agostini, “Observation of a train of attosecond pulses from [44] P. Riviere, O. Uhden, U. Saalmann, and J. M. Rost, “Strong field dynamics high harmonic generation,” Science, vol. 292, pp. 1689Ð1692, 2001. with ultrashort electron wave packet replicas,” New J. Phys., vol. 11, [23] R. Kienberger, M. Hentschel, C. Spielmann, G. A. Reider, N. Milosevic, p. 053011, 2009. U. Heinzmann, M. Drescher, and F. Krausz, “Sub-femtosecond X-ray [45] X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms pulse generation and measurement,” Appl. Phys. B-Lasers Opt., vol. 74, of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. pp. S3ÐS9, 2002. Rev. A, vol. 81, p. 021404, 2010. [24] A. S. Sandhu, E. Gagnon, A. Paul, I. Thomann, A. Lytle, T. Keep, [46] M. Swoboda, T. Fordell, K. Klunder, J. M. Dahlstrom, M. Miranda, C. M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Generation of sub- Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, optical-cycle, carrier-envelope-phase—insensitive, extreme-uv pulses via “Phase measurement of resonant two-photon ionization in helium,” Phys. nonlinear stabilization in a waveguide,” Phys. Rev. A, vol. 74, p. 061803, Rev. Lett., vol. 104, p. 103003, 2010. 2006. [47] X. M. Tong and N. Toshima, “Infrared-laser-assisted photoionization of [25] G. Sansone, E. Benedetti, J. P. Caumes, S. Stagira, C. Vozzi, M. Nisoli, helium by coherent extreme ultraviolet light,” Phys. Rev. A, vol. 81, L. Poletto, P. Villoresi, V. Strelkov, I. Sola, L. B. Elouga, A. Zair, E. p. 043429, 2010. Mevel, and E. Constant, “Shaping of attosecond pulses by phase-stabilized [48] N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of polarization gating,” Phys. Rev. A, vol. 80, p. 063837, 2009. Gouy phase slip for high-detail attosecond pump-probe measurements,” [26] H. Mashiko, S. Gilbertson, M. Chini, X. M. Feng, C. X. Yun, H. Wang, S. Opt. Lett., vol. 35, pp. 3312Ð3314, 2010. D. Khan, S. Y. Chen, and Z. H. Chang, “Extreme ultraviolet supercontinua [49] M. C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, supporting pulse durations of less than one atomic unit of time,” Opt. Lett., D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, vol. 34, pp. 3337Ð3339, 2009. ultrafast soft X-Ray harmonics spanning the water window from a tabletop [27] R. Feifel, J. H. D. Eland, and D. Edvardsson, “Valencedouble ionization of light source,” Phys. Rev. Lett., vol. 105, p. 173901, 2010. O-2 at photon energies below and above the molecular double ionization [50] T. Popmintchev, M. C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. threshold,” J. Chem. Phys., vol. 122, p. 144308, 2005. Cohen, I. P.Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching [28] S. Krummacher, V. Schmidt, and F. Wuilleumier, “Inner-shell photoion- of high harmonic generation in the soft and hard X-ray regions of the ization in molecules—the nitrogen case,” J. Phys. B-At. Mol. Opt. Phys., spectrum,” Proc. Natl. Acad. Sci. USA, vol. 106, pp. 10516Ð10521, 2009. vol. 13, pp. 3993Ð4005, 1980. [51] G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. [29] I. Thomann, E. Gregonis, X. Liu, R. Trebino, A. S. Sandhu, M. M. DiMauro, “Attosecond synchronization of high-order harmonics from Murnane, and H. C. Kapteyn, “Temporal characterization of attosec- midinfrared drivers,” Phys. Rev. Lett., vol. 102, p. 093002, 2009. ond wave forms in the sub-optical-cycle regime,” Phys.Rev.A, vol. 78, [52] R. Santra, J. Zobeley, L. S. Cederbaum, and N. Moiseyev, “Interatomic p. 011806, 2008. Coulombic decay in van der Waals clusters and impact of nuclear motion,” [30] E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, Phys. Rev. Lett., vol. 85, pp. 4490Ð4493, 2000. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Extreme nonlinear [53] R. Santra, J. Zobeley, and L. S. Cederbaum, “Inner-valence ionization of optics: Attosecond photonics at short wavelengths,” IEEE J. Sel. Topics molecular anions and ultrafast relaxation by electron emission,” Chem. Quantum Electron., vol. 10, no. 6, pp. 1339Ð1350, Nov./Dec. 2004. Phys. Lett., vol. 324, pp. 416Ð422, 2000. [31] E. Gagnon, A. S. Sandhu, A. Paul, K. Hagen, A. Czasch, T. Jahnke, [54] K. Siegbahn, “Electron spectroscopy for chemical analysis (ESCA),” Phi- P. Ranitovic, C. L. Cocke, B. Walker, M. M. Murnane, and H. C. Kapteyn, los. Trans. R. Soc. London Series a-Math. Phys. Sci., vol. 268, p. 33, 1970. “Time-resolved momentum imaging system for molecular dynamics studies using a tabletop ultrafast extreme-ultraviolet light source,” Rev. Sci. Arvinder S. Sandhu received the Masters of Science degree from Indian In- Instrum., vol. 79, p. 063102, 2008. stitute of Technology, Kanpur, India, in 1998. He received the Ph.D. degree [32] J. Ullrich, R. Moshammer, A. Dorn, R. Dorner, L. P. H. Schmidt, and from the University of Mumbai, Mumbai, India, in 2005 for the research on H. Schniidt-Bocking, “Recoil-ion and electron momentum spectroscopy: high-intensity laser plasma interactions at the Tata Institute of Fundamental Reaction-microscopes,” Reports Prog. Phys., vol. 66, pp. 1463Ð1545, Research, Mumbai. 2003. He did postdoctoral research at JILA, University of Colorado on generation, [33] A. T. J. B. Eppink and D. H. Parker, “Velocity map imaging of ions control, and application of laser high-harmonics sources. In 2007, he joined the and electrons using electrostatic lenses: Application in photoelectron and University of Arizona, Tucson as an Assistant Professor in the Department of photofragment ion imaging of molecular oxygen,” Rev. Sci. Instrum., Physics and College of Optical Sciences. His research interests include the de- vol. 68, pp. 3477Ð3484, 1997. velopment of new attosecond and femtosecond spectroscopic techniques using [34] L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C.R. laser-based ultrashort XUV sources. He is currently pursuing precision mea- Acad. Sci. Paris, vol. 110, p. 1251, 1890. surement and control of ultrafast strong-field interactions in atoms, molecules, [35] R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light- and materials. beams,” J. Opt. Soc. Am., vol. 70, pp. 877Ð880, 1980. [36] S. M. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Xiao-Min Tong received the Ph.D. degree in theoretical AMO physics from Opt. Lett., vol. 26, pp. 485Ð487, 2001. Institute of Physics, Chinese Academy of Science, Beijing, China, in 1988. [37] A. Roberts, N. Shivaram, L. Xu, and A. Sandhu, “Optimization of few- From 1996 to 1999, he was engaged in research on interaction of intense cycle pulse generation: Spatial size, mode quality and focal volume ef- laser pulses with atoms and molecules at the University of Kansas, where he fects in filamentation based pulse compression,” Opt. Express, vol. 17, developed an effective method to solve the time-dependent Schrodinger¬ equation pp. 23894Ð23902, 2009. in the energy representation using the generalized pseudospectral method. From [38] N. Shivaram, H. Timmers, L. Xu, A. Roberts, and A. Sandhu, “Gouy phase 2001 to 2005, he was a Research Assistant Professor at Kansas State University. gating of two-color ionization to uncover attosecond structure,” in Proc. Since 2005, he has been with the University of Tsukuba, Ibaraki, Japan, as 17th Int. Conf. Ultrafast Phenomena, 2011, p. 30. an Associate Professor. His current research interests include the control of [39] C. Buth, R. Santra, and L. Young, “Electromagnetically induced trans- dynamical processes using ultrashort infrared laser combined with attosecond parency for X rays,” Phys. Rev. Lett., vol. 98, p. 253001, 2007. XUV pulses.