A high-repetition rate attosecond light source for time-resolved coincidencespectroscopy
Sara Mikaelsson, Jan Vogelsang, Chen Guo, Ivan Sytcevich, Anne-Lise Viotti, Fabian Langer, Yu-Chen Cheng, Saikat Nandi, Wenjie Jin, Anna Olofsson, Robin Weissenbilder, Johan Mauritsson, Anne L'Huillier, Mathieu Gisselbrecht, Cord L. Arnold
AA high-repetition rate attosecond light source for time-resolved coincidencespectroscopy
Sara Mikaelsson, Jan Vogelsang, Chen Guo, Ivan Sytcevich, Anne-Lise Viotti, FabianLanger, Yu-Chen Cheng, Saikat Nandi, Wenjie Jin, Anna Olofsson, Robin Weissenbilder, Johan Mauritsson, Anne L’Huillier, Mathieu Gisselbrecht, and Cord L. Arnold Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden ASML Veldhoven, De Run 6501, 5504 DR, Veldhoven, The Netherlands
Attosecond pulses, produced through high-order harmonic generation in gases, have been suc-cessfully used for observing ultrafast, sub-femtosecond electron dynamics in atoms, molecules andsolid state systems. Today’s typical attosecond sources, however, are often impaired by their lowrepetition rate and the resulting insufficient statistics, especially when the number of detectableevents per shot is limited. This is the case for experiments where several reaction products must bedetected in coincidence, and for surface science applications where space-charge effects compromisespectral and spatial resolution.In this work, we present an attosecond light source operating at 200 kHz, which opens up theexploration of phenomena previously inaccessible to attosecond interferometric and spectroscopictechniques. Key to our approach is the combination of a high repetition rate, few-cycle laser source, aspecially designed gas target for efficient high harmonic generation, a passively and actively stabilizedpump-probe interferometer and an advanced 3D photoelectron/ion momentum detector. Whilemost experiments in the field of attosecond science so far have been performed with either singleattosecond pulses or long trains of pulses, we explore the hitherto mostly overlooked intermediateregime with short trains consisting of only a few attosecond pulses. We also present the firstcoincidence measurement of single-photon double ionization of helium with full angular resolution,using an attosecond source. This opens up for future studies of the dynamic evolution of stronglycorrelated electrons.
I. INTRODUCTION
The advent of attosecond pulses in the beginning ofthe millennium [1, 2] enabled the study of fundamentallight-matter interactions with unprecedented time reso-lution [3], revealing sub-femtosecond electron dynamicsin atoms, molecules and solids, such as ionization timedelays [4–7], the change of dielectric polarizability [8],and the timescale of electron correlations [9, 10].Attosecond pulses are generated through high-orderharmonic generation (HHG), when intense femtosecondpulses are focused into a generation gas [11]. Close tothe peak of each half-cycle, an electron wave packet isborn through tunnel ionization. It is subsequently accel-erated by the electric field of the driving laser pulse andfinally may return to its parent ion and recombine, uponwhich its excess energy is emitted as an attosecond pulsein the extreme ultraviolet (XUV) to soft-X-ray spectralrange [12, 13]. The process repeats itself for every half-cycle of the driving field, resulting in an attosecond pulsetrain (APT) in the time domain and a comb of odd-orderharmonics in the frequency domain. If the emission orig-inates from only one half-cycle, a single attosecond pulse(SAP) is emitted with a continuous frequency spectrum.Two well-established pump-probe techniques, based oncross-correlating the attosecond pulses with a low fre-quency field (usually a replica of the generating pulse)while the photoelectron spectrum originating from a de-tection gas is recorded, give access to dynamics on theattosecond time scale. The RABBIT (Reconstruction ofAttosecond harmonic Beating By Interference of Two- photon transitions) is well suited for the characteriza-tion and use of APTs, while the streaking technique ismostly applied to SAPs [1, 2]. The requirements to per-form such experiments are challenging in terms of lasersources, HHG and pump-probe interferometric optical se-tups, as well as photoelectron detectors. Traditionally,mostly chirped pulse amplification, Titanium:Sapphire-based lasers with repetition rates in the low kHz rangehave been used, rendering experiments that have high de-mands on statistics or signal-to-noise ratio (SNR) timeconsuming [9].Here, we present a high-repetition rate, flexible at-tosecond light source, particularly designed for the studyof gas phase correlated electron dynamics as well as time-resolved nano-scale imaging. This article both summa-rizes and extends previous work [14, 15]. The laser sys-tem, located at the Lund High-Power Facility of the LundLaser Centre, is based on optical parametric chirpedpulse amplification (OPCPA), providing sub-6 fs longpulses with stabilized carrier-to-envelope phase (CEP)in the near-infrared with up to 15 µ J pulse energy ata repetition rate of 200 kHz [14]. The 200-fold increasein repetition rate, compared to standard 1 kHz systems,promotes experiments with high demands on statistics.A 3D momentum spectrometer [16], capable of measur-ing several correlated photoelectrons/ions in coincidence,fully resolved in momentum and emission direction, hasbeen installed as a permanent experimental end station.The combination of CEP control, where the phase of theelectric field is locked to the pulse envelope, and theshort pulses, comprising only two cycles of the carrier a r X i v : . [ phy s i c s . a t o m - ph ] A ug wavelength, provides control of the characteristics of thegenerated APTs. For example, we can choose the num-ber of pulses in the train to be equal to two or threepulses, which allows exploring the transition between thetraditional streaking and RABBIT regimes. As a proofof concept for a statistically very demanding experiment,we present measurements on single-photon double ioniza-tion of helium, which is an archetype system of stronglycorrelated pairs of photoelectrons [17–19].Figure 1 shows a schematic of the experimental setup.The laser pulses enter the first vacuum chamber (A),green, which contains a pump-probe interferometer, asmall gas jet for HHG and an XUV spectrometer fordiagnostics. The XUV pump and infrared (IR) probeare then focused by a toroidal mirror (B), yellow, intothe sensitive region of the 3D momentum spectrometer(C), red. A refocusing chamber (D), purple, contains asecond toroidal mirror for re-imaging to the second inter-action region, (E), where different end stations for sur-face science, usually a photoemission electron microscope(PEEM), can be installed [20–22]. The beamline is de-signed for simultaneous operation of both end stations.FIG. 1: Beamline footprint . (A) HHG generationand characterization and XUV-IR interferometer. (B)Focusing chamber. (C) First interaction region, 3Dmomentum spectrometer. (D) Refocusing chamber. (E)Second interaction region, flexible endstation.The paper is structured as follows: The first section in-troduces the optical setup by briefly discussing the lasersource and the XUV-IR pump-probe interferometer, be-fore examining the gas target design for HHG and thecontrol of the emitted attosecond pulse trains and finally,introducing the 3D photoelectron/ion spectrometer. Thefollowing section discuss the utilization of our light sourcefor attosecond time-resolved spectroscopy. We close bypresenting measurements of the fully differential cross-section for double ionization of helium, an experimentthat to our best knowledge has not been performed withattosecond pulses before.
II. XUV LIGHT SOURCE AND PUMP-PROBESETUPA. Laser Source Characterization
The OPCPA laser that the beamline is operated with isseeded by a Titanium:Sapphire ultrafast oscillator. Theseed pulses are amplified in two non-collinear opticalparametric amplification stages, pumped by a frequency-doubled, optically synchronized Ytterbium-fiber chirpedpulse amplifier (CPA). The details of the laser are de-scribed elsewhere [14]. Figure 2 shows temporal charac-terization of the output pulses performed with the dis-persion scan (d-scan) technique [23], revealing a pulseduration of 5 . >
200 kHz. Figure 2E shows measurementresults demonstrating a short term CEP stability with aRoot Mean Square (RMS) of approximately 160 mrad.Single-shot CEP detection is an essential tool to ensurethat our light source is stable. Furthermore, the CEPdata can be tagged to additionally reduce the noise inphotoelectron/ion data. An additional f:2f interferome-ter is used to actively compensate for long term drift.
B. XUV-IR Interferometer
The XUV-IR pump-probe interferometer is designedfor high temporal stability. Suppressing instabilities fromvibrations and drifts as much as possible is essential forrecording data with high SNR [25] over several hours oreven days. To promote passive mechanical stability, alloptical components of the interferometer are mounted ona single mechanically stable breadboard inside the mainvacuum chamber. The breadboard is stiffly mounted toan optical table, but vibrationally decoupled from thevacuum chamber in order to isolate from vibrations origi-nating from turbo and roughing pumps. Figure 3A showsthe interferometer layout and beam path.After entering the vacuum chamber, the laser pulsesare split into pump- and probe arms of the interferome-ter by a thin beamsplitter optimized for ultrashort laserpulses (Thorlabs UFBS2080), reserving 80% of the powerfor HHG in the so-called pump arm and 20% for theprobe arm. In view of the short pulse duration and broadspectrum of the few-cycle pulses, dispersion managementbetween the two interferometer arms is imperative. Itis achieved by a 1 mm thick AR-coated glass plate inthe probe arm (compensating the beam-splitter) and apair of fused silica wedges at Brewster angle in the pumparm (for other dispersive elements). A spurious reflexFIG. 2:
Laser output characterization. (A)Measured and (B) retrieved d-scan traces; a d-scantrace is a two-dimensional representation of the secondharmonic signal (intensity in colors) as a function ofwavelength and glass insertion; (C) Retrieved spectrum(black) and spectral phase (red), (D) Retrievedtemporal pulse intensity profile (black) and phase (red),(E) Single-shot CEP measurement, showing themeasured CEP as a function of time; The root meansquare is indicated in red (see statistics on the right).from the glass plate in the probe arm is used to feed abeam pointing stabilization system (TEM-Messtechnik)outside the vacuum chamber.The delay between the interferometer arms is con-trolled by a retro reflector in the pump arm, mountedon a linear piezo stage (Piezo Jena Systems) with 80 µ mtravel. The pump arm is then focused by a 90 ° , off-axisparabola into the generation gas target for HHG, shownin an insert in Figure 3A and described in more detailin the next section. In the probe arm, a lens is used tomimic the focusing in the pump arm, ensuring that afterrecombination pump- and probe pulses will focus at thesame position. In the pump arm, the generated XUVattosecond pulses are separated from the driving near-infrared pulses by different thin (usually 200 nm) metallicfilters, transparent to the XUV but opaque to the driv-ing pulses. In order to reduce the thermal load on thefilter, an aperture cutting most of the driving pulses isplaced before the filter, utilizing the smaller divergenceof the attosecond pulses. A holey mirror at 45 ° is usedfor recombining the probe- and pump arms of the inter-ferometer (see recombination mirror inset in Figure 3A).The XUV attosecond pulses pass through a 1 . ° angle of incidence with a clear aperture of125 ×
25 mm and 350 mm focal length, and thus maximizethe pulse energy that is refocused.In order to stabilize the delay for slow thermal drift, wecouple a Helium-Neon (He-Ne) laser beam into the inter-ferometer, shown in green in Figure 3A. This is achievedby illuminating the beamsplitter from the so far unusedside. The metallic filter after HHG is suspended on atransparent substrate to transmit the part of the HeNe-laser beam with large divergence, which is then reflectedby the back-side-polished recombination mirror (see re-combination mirror inset of Figure 3A). Light from theother arm of the interferometer is transmitted throughanother hole in the recombination mirror. A spatial in-terference pattern is observed with a camera and used torecord the phase drift in order to feed back to the delaystage. Figure 3B shows the short term stability of theinterferometer, determined by using a fast CCD detector(10 kHz read-out). This fast detection enables us to getinformation on high acoustic frequencies that might con-tribute to instabilities (Figure 3C). The sharp peaks inFigure 3C can be attributed to the different turbo pumps.A short-term stability of 26 as is achieved.
C. Gas Target
As a consequence of the high repetition rate of the few-cycle laser system, the energy of the individual pulses israther low, compared to the kHz repetition rate Tita-nium:Sapphire lasers often used for generating high-orderharmonics. This has important implications for HHG:First, tight focusing is required to achieve sufficientlyhigh intensity and second, phase-matching and scalingconsiderations imply a localized, high density generationgas target [26, 27]. The off-axis parabola used to focusthe driving pulses into the gas target has a focal lengthof f = µ m andintensities in excess of several 10 W / cm can easily beachieved. Numerical simulations, based on solving thetime dependent Schr¨odinger equation for the nonlinearresponse and the wave equation for propagation [28, 29],suggest a gas density corresponding to 5 bar pressure anda medium length of 40 µ m. The gas density should falloff as rapidly as possible outside the interaction region inorder to avoid re-absorption of the generated XUV radi-ation. Such a gas target imposes substantial engineeringchallenges.The gas target consists of a nozzle with an exit hole of42 µ m, operated for the case of argon at 12 bars of backingFIG. 3: XUV-IR interferometer. (A) Interferometer beam-path and components. The near-IR beam path isshown in red, the XUV in blue, and a HeNe-laser which can be used for active delay stabilization is shown in green.(B) Stability measurement, showing the measured delay as a function of time; The root mean square is indicated inwhite (see statistics on the right). (C) Single sided amplitude spectrum of interferometer stability measurement.pressure. The small nozzle exit diameter ensures longi-tudinal (i.e. along the laser propagation direction) andtransverse confinement of the interaction region. How-ever, the high mass flow rate, around 4 × − g/s, ofsuch a nozzle, if used to inject gas directly into the vac-uum, would challenge the capacity of the turbo pumpsand contaminate the vacuum inside the chamber, result-ing in severe re-absorption. Therefore, we use a catcherwith a hole of 1 mm diameter mounted less than 200 µ mfrom the injection nozzle and connected to a separateroughing pump. The goal is to catch the majority of theinjected gas directly before it expands into the vacuum.The nozzle-catcher configuration is attached to a man-ual three dimensional translation stage, for adjusting theposition of the gas target with respect to the laser focuswithout changing the positions of nozzle and catcher withrespect to each other. Comparing the pressure inside thevacuum chamber with and without the catcher indicatesthat the catcher takes away >
90% of the injected gas.In order to further reduce possible contamination ofthe surrounding vacuum, the gas target is placed in anadditional small chamber, pumped by an extra turbopump (see gas target inset in Figure 3A). The laser entersand exits the cube-shaped chamber through differentialpumping holes, placed as closely to the interaction re-gion as possible. As a result, the beam only traversesa distance of approximately 3 mm inside this compara-bly high pressure environment. During regular opera- tion, when generating in argon (12 bar backing pressure),the pressure inside the cube is around 3 × − mbar,while the pressure in the surrounding chamber remainsat 2 . × − mbar. Following the beam path towardsthe first experimental chamber, the pressure further re-duces via differential pumping to 1 × − mbar in theXUV spectrometer compartment, to 2 × − mbar inthe chamber housing the toroidal mirror and finally to2 × − mbar at the 3D photoelectron spectrometer. Apressure below 5 × − mbar in the second end stationis easily reached.Simulations of the gas density in the interaction regionwere performed using the STARCCM+ compressible flowsolver. The results are summarized in Figure 4. The lineout along the direction of the gas flow (Figure 4B) indi-cates that the density drops rapidly away from the nozzle.Figure 4C shows a line out transversely to the gas flowat a distance of 10 µ m from the nozzle exit (marked witha dashed blue line), which corresponds to the approxi-mate distance at which the laser traverses the gas targetduring operation. According to the simulations, the gastarget has an approximately super-Gaussian shape witha width of 36 µ m (FWHM) at this distance to the noz-zle with a peak density of 8 . / m , corresponding to4.7 times the density of argon at standard pressure andtemperature condition (1.7 kg/m ). The obtained den-sity and gas medium length are in excellent agreementwith the calculated best phase matching conditions (5FIG. 4: HHG gas target simulations. (A) Simulatedgas density in the interaction region with a 42 µ m nozzlecentered around z = 0. (B) Density at z = 0 (black). (C)Line out of the gas density at a distance of 10 µ m fromthe nozzle. In A and B the dashed blue line indicatesthe position of the line-out in C. In A the dashed greyline indicates the position of the line-out in B.bar, 40 µ m). Experimentally, we used the fringe patternresulting from the interference of the stabilization He-Nelaser pump and probe beams (see Fig. 3A) in order toget information on the actual gas density. We measureda phase shift of the fringes, between the cases of activeand inactive gas target, equal to 0 .
65 rad. Using refrac-tive index data for argon [30], a phase shift of 0 .
625 radcan be calculated from the simulation data in 4C, indi-cating that the simulation results are in close match tothe actual conditions in our gas target.
D. High-Order Harmonic Generation
The process of HHG significantly changes from thecase of multi-cycle, long driving pulses, where the at-tosecond pulses emitted from subsequent half-cycles arenearly identical except for a π -phase shift between them,to the case of few-cycle driving pulses, where attosec-ond pulses emitted from consecutive half-cycles can bevery different from each other. In this case, attosecondpulses are only emitted by the most intense half-cycleswith an amplitude that is nonlinearly related to the fieldstrength during the half-cycle, the delay between themis not strictly the time between two half-cycles and theirphase difference is not exactly π [31]. These properties are also reflected in the spectrum, with spectral peakswhich are not necessarily located at the expected posi-tions for odd-order harmonics.The electric field of the few-cycle pulse, and con-sequently the characteristics of the HHG pulse trainstrongly depend on the CEP of the driving pulses, im-plying that a stable laser CEP is required for generat-ing a reproducible HHG spectrum and attosecond pulsetrain [32]. For the two-cycle, sub-6 fs pulses provided byour OPCPA laser, the APTs consist of either two or threestrong attosecond pulses, when the CEP of the drivingpulse is π / HHG Dispersion Scan.
Spectrogramshowing the XUV spectrum (horizontal scale) as afunction of BK7 glass insertion for HHG in neon. Thespectrum is filtered by a 200 nm thick zirconium thinfilm.To demonstrate the pulse train control achieved in ourexperiments, we present in Figure 5 the XUV spectrumobtained using Ne gas for the generation, as a functionof glass insertion. A zirconium filter, cutting all emissionbelow 65 eV, was used to record the spectrum. For largeglass insertion (i.e. > < -2.5 mm), the pulseis stretched in time to the extent that the peak intensitybecomes too low for HHG, while for small amounts of dis-persion, the effect is primarily a change of the CEP. Asthe CEP varies, the position of the harmonics shift ap-proximately linearly over the whole dispersion and energyrange in Figure 5, reflecting a CEP-dependent change ofthe relative phase between consecutive attosecond pulses.This originates from the CEP-dependent variation of thestrength of the field oscillations used for the attosecondpulse generation [31]. The highest photon energies withup to 100 eV are obtained at zero glass insertion, i.e. forthe shortest pulses and the highest intensity. The pho-ton flux was characterized in an earlier stage of the lightsource development (see [14] for details). We estimatethe current fluxes to be higher than 15 × photons/sin argon and 0 . × photons/s in neon, respectively. E. 3D photoelectron/ion spectrometer
A schematic overview of the 3D photoelectron/ionspectrometer used to study attosecond dynamics inatoms or molecules in gas phase is shown in Figure 6.This spectrometer is based on a revised CIEL (Coinci-dences entre ions et electrons localis´es) design [16], whichis conceptually similar to REMI (reaction microscope) orCOLTRIMS (Cold Target Recoil Ion Momentum Spec-troscopy) [33, 34]. Momentum imaging instruments ofthis type have been widely used for the study of pho-toionization dynamics [35, 36] and can with the helpof electric and magnetic fields, collect high-energy elec-trons over the full solid angle (i.e. 4 π collection). Thecharged particles produced through ionization are accel-erated with a weak electric extraction field. In order forthe lighter electrons not to escape the spectrometer be-fore they reach the detector, a magnetic field is appliedover the whole spectrometer, which confines the electronsto a periodic cyclotron motion with a radius determinedby their momentum and direction. By using a positionsensitive detector (PSD), which can measure both arrivaltime and transverse position of the charged particles, andassuming uniform magnetic and electric fields, the fullthree dimensional momentum information can be calcu-lated from simple classical equations [16].If the electrons hit the PSD at an integer multiple ofthe cyclotron period, the transverse position of these elec-trons is independent of their initial transverse momen-tum. The corresponding points in the time of flight (ToF)spectrum are called magnetic nodes. At these nodes themomentum information is no longer unambiguous, lead-ing to loss of data [33, 34]. In the CIEL design, thetime-of-flight of all electrons falls between two adjacentmagnetic nodes, allowing for 4 π -angle resolved measure-ments without data loss.The spectrometer was designed to be compact. Thedimensions of the extraction region on both the electronand and ion detector sides as well as the length of thedrift tube are shown in Figure 6A. The extraction fieldsare on the order of 5-15 V / cm, and the detected rangeof electron kinetic energies is defined by adjusting theexternal magnetic field. Figure 6B introduces the spher-ical coordinate system used for analysis of measurementdata: the elevation θ defines the angle with respect tothe light (linear) polarization direction, and the azimu-tal angle ϕ determines the position of the projection ontothe plane defined by the laser propagation direction (x)and the spectrometer axis (y). FIG. 6: Reaction microscope. (A) Working principleof a reaction microscope. (B) Coordinate system usedfor measurements, along with a 3D representation of theelectron momentum distribution, indicating theazimutal angle ( ϕ ) and elevation angle ( θ ) with respectto the plane of the laser polarization (along the z axis).The gas sample is delivered via a long needle with alength-diameter ratio of approximately 1000, resulting ina directional and confined effusive jet [37]. The needle ismounted on a manual three dimensional translation stagewhich allows for precise positioning of the gas target withrespect to the XUV and IR focus, and can be biased tomatch the potential of the extraction field.The detection system of the spectrometer consists oftwo commercially available PSDs (RoentDek HandelsGmbH) based on multi-channel plates and delay line de-tectors, installed on both sides of the spectrometer, i.e.one to detect ions and the other electrons. The ion anodehas a standard design [38], while the electron detectorprovides unambiguous time and position information formultiple hits [39]. This gives us the possibility to detectone ion in coincidence with several correlated electrons. III. XUV-IR INTERFEROMETRY IN THE FEWATTOSECOND PULSE REGIME
The combination of the CEP-controlled, few-cycle lasersource, high repetition rate, efficient HHG and a highly-stable XUV-IR pump-probe interferometer together witha 3D photoelectron/ion spectrometer that can record sev-eral correlated charged particles in coincidence estab-lish excellent experimental conditions for exploring thephysics of the interaction of few pulse APTs with atomicand molecular systems.Recently, we studied single photoionization of he-lium by a few attosecond pulses (two or three pulses)in combination with a weak infrared (dressing) laserfield [15]. Instead of using the XUV-IR interferometerdescribed above, the IR laser pulses used for the gener-ation were not eliminated by a metallic filter, but prop-agated collinearly with the APTs, after attenuation byan aperture, to the interaction region of the 3D spec-trometer. Both the IR intensity and the XUV-IR delaywere therefore fixed. The recorded photoelectron spectrawere found to differ considerably depending on whethertwo or three attosecond pulses were used for the ioniza-tion. In the case of two pulses, the spectra were similarto those obtained with XUV-only radiation, except for ashift of the photoelectron peaks induced by the dressingIR field, towards high or low energy depending on theelectron emission direction (up or down, relative to thelaser polarization direction). In the case of three pulses,additional peaks, so-called sidebands, appeared exactlyin between the peaks due to XUV-only absorption. Theycan be attributed to a two-photon process, where a har-monic photon is absorbed and an additional IR photonis either absorbed or emitted [1]. The reader is referredto our earlier work [15] for details on the experiment andthe simulations and for an intuitive interpretation of theresults in terms of attosecond time-slit interferences.In the present work, we use the XUV-IR pump-probeinterferometer to record photoelectron spectra in heliumas a function of XUV-IR delay in the two- and threeattosecond pulse cases. Figure 7 (A,B) present exper-imental photoelectron spectra at zero delay after inte-gration over the azimutal angle ϕ as a function of theelevation angle θ , while Figure 7 (C,D) and (E,F) showspectra integrated over 2 π solid angle in the down direc-tion as a function of delay for the two- and three pulsescases, respectively. (C,D) are experimental results while(E,F) are simulations using the Strong-Field Approxima-tion [15, 40, 41], with an IR intensity of 6 × W / cm .The simulations agree well with the experimental mea-surements and illustrate the main features of the results,without experimental noise and/or irregularities.Figure 7 (A,B) reproduce and confirm our previousresults [15], with energy-shifted photoelectron spectra inthe two pulse case and the apparition of sidebands in thethree-pulse case in the down direction. The energy shiftcan intuitively be understood by a classical picture, as instreaking [42]. An electron emitted due to ionization byan attosecond pulse with a momentum p gains or loosesmomentum from the IR field: p → p − e A ( t i )/ c , where A ( t i ) is the vector potential at the time of ionization t i , e the electron charge and c the speed of light. The 3Dmomentum distribution becomes therefore asymmetric inthe up- and down emission directions (Figure 7A). Inthe three pulse case, the interpretation is more subtle.Here, in the down direction, sidebands appear betweenthe peaks observed in the case of XUV-only radiation.Depending on the delay between the XUV and IR fields,sidebands are observed in only one direction (here thedown direction).In Figure 7 (C,E), the photoelectron peaks are shiftedtowards lower or higher energies depending on the de-lay between the APTs and the IR pulses, similarly toattosecond streaking [42, 43]. Unlike a usual streakingtrace, where a continuous photoelectron spectrum cor-responding to ionization by a single attosecond pulse isperiodically shifted in kinetic energy, here, the spectrumis in addition modulated by interference of the two elec-tron wave packets created by the two attosecond pulses. FIG. 7: Two-color photoionization of helium. (A,B) Angular-resolved spectograms. Red dashed linesmark the position of absorption peaks corresponding toodd harmonics in the XUV only case. (C,D)Experimental and (E,F) simulated XUV-IR delaytraces, by integrating in the down direction. A, C, andE show the two pulse-case (CEP π /2), and B, D, and Fthe three pulse-case (CEP 0).The interference structure of the photoelectron spectrumprovides spectral resolution, which is missing in ordinarystreaking traces by a single attosecond pulse and mayonly be obtained by iterative retrieval procedures.Figure 7 (D,F) shows simulated and experimental pho-toelectron spectra vs. delay for the three pulse case. Theresults are quite different from those obtained with twoattosecond pulses. Instead of modulations of the kineticenergy, sidebands appear at certain delays, similarly toRABBIT spectrograms [44], but with a major difference:The sidebands observed in the present case oscillate witha periodicity equal to the laser period, and not twice thelaser period as in RABBIT. Oscillating sidebands are alsoobserved in the up direction, but with a phase shift of π compared to the down direction. The asymmetry in theup- and down directions can be attributed to a paritymixing effect and is only observed in the few attosecondpulse case [15].The photoionization experiments presented here com-bining few attosecond pulses and a weak infrared fieldhave similarities with streaking (for the two pulse case)and RABBIT (for the three pulse case) experiments,but are also distinctly different, presenting both chal-lenges and new possibilities, especially concerning spec-tral resolution. In addition, the high repetition rate en-ables increased statistics, which is essential for full three-dimensional momentum detection. Advanced detectionmodes like coincidence become possible. Such a case isdiscussed in the next section. IV. SINGLE-PHOTON DOUBLE IONIZATION
Single-photon double-ionization in atoms andmolecules is one of the most fundamental processeswhich leads to the emission of correlated photoelectronpairs [17–19]. In the simplest two-electron system, he-lium, previous works carried out primarily at synchrotronfacilities have measured the absolute Triply DifferentialCross Section (TDCS) for a range of excess energiesand angular configurations [45, 46]. The availability ofattosecond techniques to probe single-photon doubleionization [9] opens up new prospects for measuring theevolution of electron correlation in time.In order to demonstrate the unique capabilities pro-vided by our high repetition-rate setup, we report thefirst ever results on single-photon double ionization ofhelium with full 3D momentum detection using an at-tosecond light source. Taking benefit of the full imagingcapabilities of the CIEL spectrometer, our measurementsshow that processes hitherto unexplored by attosecondscience are now within reach.Measuring double-ionization in helium presents, how-ever, a few challenges for traditional attosecond lightsources. Firstly, the threshold for this process at 79 eV isbeyond the energies easily achieved with standard HHGin argon using near-IR pulses. This can be circumventedby a change of generation gas, and as shown in section2.4, we can reach sufficiently high energies by using neon.Secondly, to perform a kinematically complete experi-ment we need to detect several charged particles in co-incidence. We are thus limited in the final acquisitionrate to one tenth of the repetition rate, to ensure thatthe event rate is below one event per shot, i.e. to min-imize the likelihood of false coincidences. To reduce thenumber of single ionization events by absorption of low-order harmonics, leading to photoelectrons with similarenergies as those due to double ionization by high-orderharmonics, we use a zirconium filter which only transmitsphoton energies at ≈
65 eV and above.Figure 8A shows a typical XUV spectrum generatedwith neon after this filter (black), along with the crosssections of both the single (red curve) and double (dashedred line) ionization process. In the photon energy regionof 79-100 eV, the average ratio of the double versus sin-gle ionization cross section is ∼ ∼
15% fortriple coincidence (two electrons and the doubly chargedion), the maximal acquisition rate for a 200 kHz systemreduces further to 30 Hz, which is comparable to acquisi-tion rates achievable at synchrotron facilities.To compensate for the relatively low XUV photonflux in this energy range, e.g. compared to the singlephotoionization experiments presented in Section 3, thebacking pressure of the effusive jet for gas delivery in ourspectrometer is increased and the jet is moved very closeto the focus. We achieved a final detection rate of ∼
15 Hz,slightly lower than the nominal 30 Hz, in order to oper-ate the light source with good long-term stability over 40hours. Clearly, without a high laser repetition rate, thisexperiment would be challenging.Figure 8B-D shows the measured TDCS for equal en-ergy sharing of the two electrons (E =E =5 ± θ = ° , 60 ° , and30 ° with respect to the polarization axis, and with a totalkinetic energy E + E = ± . P o symmetry, the differential cross-section forequal energy sharing can be written as [45, 50, 51]: d σdE d Ω d Ω = a g ( E , E , θ ) ( cos θ + cos θ ) , (1)where θ and θ are the emission angles of the two elec-trons with respect to the polarization axis (in accordancewith the coordinate system defined Figure 6B). The term ( cos θ + cos θ ) , arises from the geometry of the light-matter interaction. A quantum-mechanical descriptionof double photo-ionization with an electron-pair in thecontinuum must obey the Pauli principle and symmetriesdepending on the total orbital angular momentum, L ,the total spin, S , and the parity of the final two-electronstate. This leads to a selection rule prohibiting the back-to-back emission, that is observed as a node in the TDCS(see Figure 8B-D). The complex amplitude, a g , describesthe correlation dynamics of the electron-pair and only de-pends on the excess energy and the mutual angle θ . AGaussian ansatz provides an excellent parametrization ofthis amplitude [45, 46]: a g ( E , E , θ ) = a exp (− [( θ − o )/ γ ] ) , (2)where a is a scaling factor depending on the cross sec-tion, and γ is the full-width at half maximum correlationfactor, which depends on the excess energy. This term af-fects the opening angle between the two ”lobes” seen forexample in Figure 8B. A theoretical calculation [52, 53]predicts that the opening angle γ should be around 93 ° .FIG. 8: Single-photon double ionization ofhelium. (A) XUV spectrum (black) and cross sectionfor single-photon single (solid red) and double (dashedred) ionization of helium [47, 48]. (B-D) TDCS forsecond electron (black dots) with equal energy sharingand co-planar emission, with emission angle of the firstelectron being 90 ° , 60 ° , and 30 ° (red arrow), comparedto Eq. 1 (red curve). (E) Distribution of kineticenergies of second electron, integrated over all azimutalangles, when the first electron is emitted at θ = ° forco-planar and equal energy sharing emission.We find experimentally a value of γ = ° ± ° , in bet-ter agreement than previous reported values of approxi-mately 85 ° at this excess energy [46, 54].The results in Figure 8B-D were achieved by integrat-ing over only a small total energy interval for comparisonwith previous works. However, since the ionizing XUVradiation has a very broad spectrum, this filtering doesnot give an complete representation of the two-electronwave-packet (EWP) dynamics. To visualize this EWP,we show in Figure 8E the result obtained over the wholeenergy range, integrating over the azimutal angle and fora 90 ° emission angle of the first electron, as in Figure 8B.Interestingly the variation in emission direction and en-ergy of the second electron exhibits the nodal properties (selection rule) that are usually observed in the fully dif-ferential cross section. Using the pump-probe capabilitiesof our setup in a future experiment, the time evolution ofthe EWP can be studied by observing the change of thefinal state of the two-electron EWP in the continuum. V. CONCLUSION
In this work, we present a compact, high-repetition-rate, attosecond light source and demonstrate its capa-bility to perform time-resolved measurements and coin-cidence experiments. The high repetition-rate, enabledby the partially fiber-based laser architecture, opens upfor applying the extraordinary time-resolution promisedby attosecond science to new processes and phenomena.We study single photoionization of He atoms usingAPTs consisting of only a few pulses in combination witha weak, delayed, IR field. This new regime opens up newexciting possibilities for control of photoemission througha tailored sequence of pulses. The case of two attosec-ond pulses, in particular, is promising, as the results canintuitively be understood as in streaking experiments.Compared to streaking with a single attosecond pulse, itadds spectral resolution due to the interference structureinduced by the two attosecond pulses, similar to Ram-sey spectroscopy, and lower intensity can be used for thedressing field because of the gained spectral resolution,thus less perturbing the system under study. Generally,the potential of the few pulse attosecond train regimeseems to have been widely overlooked by the attosecondscience community that traditionally has either workedwith single attosecond pulses (streaking) or long attosec-ond pulse trains (RABBIT).Our setup includes the possibility to add a second end-station in order to perform time-resolved surface scienceexperiments (Fig. 1). As in coincidence spectroscopy,these experiments strongly benefit from high repetitionrate in order to avoid space charge related blurring ef-fects in spectroscopy and imaging applications [21]. Asthe setup is designed for the two end-stations to be usedsimultaneously, the gas phase experiments can serve asa benchmark for simultaneous time-resolved studies onnanostructured surfaces. Our ultimate goal is to in-vestigate and control charge carrier dynamics on thenanoscale with attosecond temporal resolution.Finally, as a proof of principle, we successfully measuresingle-photon double ionization in helium by our broad-band attosecond XUV source over a complete 4 π solidangle. The next experiment will be to add a weak IRlaser field in order to study the time evolution of the two-electron wave packet. More generally, our high-repetitionrate setup is well adapted for the study of highly corre-lated many-body processes in the temporal domain.0 ACKNOWLEDGMENTS
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