Attosecond Spectroscopy Comes of Age

Tracking Light Oscillations: Attosecond Spectroscopy Comes of Age

Ferenc Krausz

Can time-resolved spectroscopy be extended into the attosecond domain to capture the motion of electrons in atoms? This article reviews recent research providing the basic tools for the emerging field of attosecond atomic spectroscopy and addresses what remains to be done to make the technique applicable to a broad range of processes and atomic systems.

n 1887, Hertz observed that ultraviolet their concern might have been the ultra- have appeared impossible until recently, light that originates from an electrical high speed with which the strength of the the basic concepts underlying its recent discharge could be used to affect (or light field varies: half of a femtosecond implementation emerged before the end I 1 -15 influence) another discharge. This famous (1 fs = 10 s) or less elapses while the elec- of the nineteenth century. As early as 1866, experiment provided the first conclusive tric or magnetic field of visible light Töpler was able to capture the periodic evidence that light is an electromagnetic changes in strength from zero to its maxi- variation of atmospheric pressure in wave. But can the oscillations of a visible mum value or vice versa. Hence, to capture acoustic waves.2 To this end, he used a light wave be tracked and rendered directly the temporal evolution of light fields re- spark to induce a sound wave. This spark perceivable? If Hertz and his contempo- quires an attosecond sampling technique was also used to trigger the ignition of a raries had thought to ask this question, (1 as = 10-18 s). second spark through a delay line. The they might have been skeptical about a Although the development of an at- time-delayed spark emitted a flash of light positive answer. The most likely reason for tosecond sampling technique might well that recorded the instantaneous refractive-

62 Optics & Photonics News May 2002 1047-6938/02/05/0062/7-$0015.00 © Optical Society of America ATTOSECOND SPECTROSCOPY

Figure 1. All-optical sampling system. The ultra- short light pulse delivered by a collimated laser beam is split in two by a partially transmitting mir- ror. One of the two replicas serves as a pump Electrons, pulse to induce a transient change in the micro- Probe Pump Photons scopic structure of the investigated sample; the other delayed pulse probes the process triggered Beam Detector splitter by the pump pulse. The delay is most simply ac- complished by translating a mirror: an increase in Interaction the optical path length by 0.3 mm adds a 1000-fs medium delay.Changes in the microscopic structure are of- Delay ten probed more directly at frequencies (or wave- line lengths) that differ from those of the pump pulse. To this end, the carrier fre- quency (i.e., photon energy) of the pump and/or probe light can be shifted by frequency conversion techniques, ex- ploiting the nonlinear polariza- tion response of matter to in- tense radiation.The ultrashort duration of light pulses from mode-locked lasers benefits this generic scheme in several ways. First, it improves the temporal resolution of the sampling system. Second, the confinement of finite light en- ergy in a short time interval implies high peak intensities. This is crucial for efficient nonlinear frequency conver- sion of the pump or probe light and significantly enhances the versatility of the optical sampling system.

index change of air induced by an acoustic ration of the pump and probe pulses (con- Figure 2. Motorcyclist in motion. The image is wave, from which the instantaneous den- sisting of the first and second spark, re- blurred because the object noticeably changes po- sity or pressure could be deduced. Snap- spectively) and a sufficiently high timing sition during exposure. From position change x shots were taken at different delays be- accuracy between each. Because the oscil- (which can be assessed from the blurring) and speed of the motorcyclist, the camera exposure tween the first spark that triggered the lation cycle of sound waves is of the order time can be readily determined: exp = x/ (if the sound wave and the second that emitted a of a millisecond or somewhat less, a flash camera is assumed to be stationary for the sake of light flash. The temporal evolution of the of microsecond duration with microsec- simplicity).This same concept forms the basis for density oscillations in the acoustic wave ond timing accuracy allowed Töpler to evaluation of the subfemtosecond x-ray pulse du- could be reconstructed from the series of take freeze-frame shots of the waves at ration from the x-ray photoelectron spectra freeze-frame shots. precise instants to reconstruct their oscil- shown in Fig. 6. The success of Töpler’s pioneering ex- lations. In principle, the same technique periment relied on a sufficiently short du- might ultimately prove suitable for prob-

May 2002 Optics & Photonics News 63 ATTOSECOND SPECTROSCOPY

1400 3.0 ing the electromagnetic field of a light More than a hundred years later, im-

1200 =/2 wave provided that a sampling apparatus, plementation of Töpler’s concepts in con- 2.5 1000 =0 with a level of resolution measured in at- junction with ultrashort laser pulses paved 2.0 800 toseconds, or in other words, a trillion the way for much higher time resolutions 1.5 times higher than that of the device used 600 and opened the door for the study of a by Töpler, were available. More than a wide range of microscopic dynamics. Ul- 400 1.0 century after Töpler’s experiment, as can trashort light pulses of sufficient energy, 200 0.5 be seen in the “After Image” photo that ap- delivered by mode-locked lasers,4 can be 0 0.0 Temporal Intensity (arb. u.) Temporal -4 -3 -2 -1 0 1 2 3 4 5 pears on p. 80 of this issue of OPN, such a used to induce measurable (either tran- On-axis Electric Field (arb. u.) Time (fs) sampling apparatus does indeed exist. The sient or permanent) changes in the elec- photograph shows how x-ray photoelec- tronic or nuclear structure of matter. Mea- EL(t)=A(t) cos ( Lt+ ) tron spectra produced in the presence of a suring the characteristics of photons or strong light field exhibit modulations that electrons that exit the sample after irradia- Figure 3. Calculated far-field, near-axis temporal trace the electric field oscillations in a visi- tion by a delayed replica of the same pulse, intensity profile of a soft-x-ray pulse (solid curves) ble light wave. The attosecond sampling one can record snapshots of the evolving that emerges from few-cycles-driven high-harmon- system used to take this measurement of- ic generation.The x-ray photons are selected with- microscopic structure of the investigated in a 5-eV spectral range near 90 eV and are pro- fers an unparalleled level of temporal reso- sample. From the snapshots taken at dif- duced in a 3-mm-long 200-mbar neon-gas source lution for studies of the fundamental dy- ferent arrival times of the probe pulse, one 3 by a 7-fs (full width at half-maximum), 750-nm namics of matter. Snapshots taken with can retrieve the temporal evolution of the Gaussian laser pulse with an on-axis peak intensity attosecond exposure allow us to capture microscopic dynamics. The concept can of 9 x 1014 W/cm2. For the electric field of the driv- the motion of electrons in atoms, for the be implemented with an all-optical sam- 2 2 ing laser pulse, E L(t) exp(-t / L ) cos( 0 t+ ) was first time to my knowledge, by means of pling system, as illustrated in Fig. 1. assumed at the input of the gas source, where , L attosecond spectroscopy. What can we sample with an all-optical , and represent the pulse duration, angular 0 sampling system? The answer depends on carrier frequency, and absolute phase of the few- cycles pump pulse. The dashed curves show the Time-resolved spectroscopy the response time of the light-induced ex- on-axis electric field of the laser pulse that exits In his pioneering experiment, Töpler in- citations, relaxations, or displacements of the interaction region for an initial absolute phase troduced several new concepts of far- electrons and/or nuclei in the illuminated of = 0 (cosine pulse, red curve)and = /2 (sine reaching importance that form the basis of sample. The response time can be fast or pulse, blue curve), and the solid red and blue modern time-resolved spectroscopy (also slow depending on the duration of the curves that depict the calculated x-ray intensities, known as pump–probe spectroscopy). pump and the probe light. An important in a frame that moves at the phase velocity of the First, to ensure synchronization, he used specific example for the fast response lim- laser pulse. Efficient generation of isolated subfem- it is light-field-induced electron displace- tosecond x-ray pulses under the above experi- the same event to trigger the process under ment in a transparent (insulating) crystal. mental conditions is predicted for ≈ 0 only, indi- investigation and to produce the flash that cating the importance of stabilization and control probed it. Second, he introduced a variable The induced dipole moment and macro- of the absolute phase. delay between the triggering event (pump scopic polarization associated with this displacement tend to be a slightly nonlin- ear function of the instantaneous light field, resulting in the emission of photons at the second harmonic of the incident light waves. Measuring the second-har- X-ray pulse monic photon flux as a function of delay Electrons, between two identical replicas of the inci- Photons dent light pulse yields a nonlinear auto- correlation function that provides insight Beam Detector splitter into the temporal structure of the light Visible light wave Interaction bursts. Autocorrelation techniques based medium on this concept provide the only means of measuring the duration of light pulses in Delay line the femtosecond regime. We can, therefore, conclude that, with- in the limit of instantaneous material re- sponse, the optical sampling system de- Figure 4. Two-color (x-ray–visible-light) optical pulse) and the probing flash (probe pulse). picted in Fig. 1 can be used to sample the sampling system. With a subfemtosecond x-ray By means of the probe pulse, he finally light pulses themselves rather than the burst and a strong visible light wave, this scheme recorded an instantaneous change in the processes in the illuminated material. So could offer attosecond resolution if an interaction physical properties of the matter under that the optical sampling system can be steered by the x-ray intensity and by the light field study. From the snapshots taken at differ- used to sample the dynamic material re- could be found. ent instants, he reconstructed the tempo- sponse, i.e., the microscopic processes trig- ral evolution of the entire process. gered by the incident light, the probe event

64 Optics & Photonics News May 2002 ATTOSECOND SPECTROSCOPY must be shorter than the time scale of the duced only at substantially shorter, ex- px induced processes. Otherwise the optical treme-ultraviolet (XUV) or x-ray wave- lengths. To date, only one demonstrated sampling system would fail to resolve the n(W) dynamics, just as in Fig. 2 the camera XUV generation technique offers this po- failed to take a freeze-frame shot. In addi- tential. Atoms exposed to a strong fem- tion to an excessive exposure time, there tosecond laser radiate coherent XUV light pz W px(t 1) are several other effects that can impair the at high-order harmonics of the driving temporal resolution of the optical sam- laser.7,8 At the highest photon energies, this W p source was predicted9 and recently x pling system. These include uncertainty in px(t 2)=0 the time that elapses between the begin- demonstrated10 to emit a series of attosec- n(W) ning of the process and the exposure; this ond XUV (or soft-x-ray) bursts separated uncertainty can be caused by finite by half of the laser oscillation period. The- p pump–pulse duration or timing jitter be- ory also predicts that time-dependent po- z larization of the laser pulse11 or its con- tween the pump and the probe pulses. W0 W Owing to steady progress in the devel- finement to several wave cycles12 (hence- opment of mode-locked laser technology forth: few-cycle pulse) could filter out a px n(W) and nonlinear frequency-conversion tech- single burst from the ultrahigh-repetition- px(t 3) niques over the past thirty-some years, rate train. Such filtering is important for p light pulses with durations of the order of spectroscopic applications. Figure 3 shows z 10 fs can now be produced over a substan- the result of a numerical simulation per- tial fraction of the visible and near-in- formed by Nenad Milosevic and Thomas W frared wavelength ranges.5 These pulse du- Brabec in Vienna, which indicates the rations are comparable to or shorter than emergence of an isolated 0.5-fs pulse emit- the oscillation period of molecular vibra- ted at an ~14-nm wavelength from a Figure 5. Free electrons born in a strong light tions, which defines the minimum time it neon-gas source driven by 0.5-mJ, 7-fs, field. The absorption of an x-ray photon can give 750-nm laser pulses. Although laser pulses takes for a molecule to undergo structural rise to the detachment of electrons either directly with these parameters are readily avail- (photoelectron) or indirectly by the Auger process distortion and possibly evolve toward a able13 and have been used for high har- (Auger electron). Suppose that the momentum new chemical state because of broken monic generation14 for some five years, the distribution of the freed electrons is isotropic, as and/or newly formed chemical bonds. As a lack of an attosecond-resolution sampling depicted by the arrows in the center illustration. consequence, femtosecond light pulses are technique frustrated the temporal charac- Shining a strong light field into the interaction short enough to track the motion of atoms terization of these soft-x-ray pulses and medium could modify this distribution depending on the phase of the electric light field (polarized in molecules and to take snapshots of their use for attosecond spectroscopy until transition stages of chemical processes along the x direction). Birth instants t1, t2 = t1 + recently. T /4 and t = t + T /2 were chosen such that the with the optical sampling system (pump– Why can’t we simply adapt to the soft 0 3 1 0 light field crosses zero at t1 (as well as t3), and the probe apparatus) shown in Fig. 1. The x-ray pulses a tested sampling system that light-induced momentum change px deformed ability to view the dynamics of chemical has been tried in the visible and near-spec- the electron momentum distribution as shown. reactions in real time has led to the emer- tral ranges (see Fig. 1)? We, of course, can, The diagrams on the right-hand side show the en- 6 gence of femtochemistry, currently one of especially for the wavelength range around ergy distribution of electrons collected within the the most important applications of time- 13 nm where efficient multilayer reflectors depicted cone. Different colors represent elec- resolved spectroscopy. In contrast with and beam splitters exist (which is why this trons of different final kinetic energy with an in- nuclei, electrons can follow oscillations of wavelength range was chosen for the crease in energy from the red to the blue.The mo- mentum transfer and hence the change in the en- the light field as discussed above, i.e., to above simulations), allowing for the con- change their position inside atoms to ergy spectrum is largest if the electric field of the struction of an x-ray sampling system light pulse crosses zero at the moment of birth of within an attosecond time frame. Can based on the scheme shown in Fig. 1. the electron (top and bottom figures). For these time-resolved spectroscopy be extended However, for this apparatus to sample instants of birth, the final energy distribution of the into the attosecond domain to enable us to something (either material response or x- electrons collected within the indicated cone is capture the motion of electrons in atoms, ray-pulse structure), one of the x-ray puls- broadened. For a birth instant that coincides with just as femtosecond spectroscopy captures es must be capable of exciting a sufficient- the peak of the light electric field (center figure), the motion of atoms in molecules? ly large number of atoms so that the other the final energy spectrum is unaffected by the light pulse can produce a detectable number of field. The variation of the energy spectrum on a time scale of T /4 (≈ 0.6 fs for 750-nm light) offers Subfemtosecond pulse photons or electrons to monitor the num- 0 generation attosecond resolution for the sampling scheme ber of excitations created by the first pulse. shown in Fig. 4. The first step toward attosecond spec- The probability of such a two-photon-me- troscopy must be the generation and diated process scales with the sixth power measurement of individual subfemtosec- of the wavelength, i.e., is at x-ray wave- ond pulses. Because the wave cycle of visi- lengths more than a billion times lower ble light lasts longer than 1 fs, bursts sub- than in the visible spectral range The stantially shorter than 1 fs can be pro- physical origin of this unfavorable scaling

May 2002 Optics & Photonics News 65 ATTOSECOND SPECTROSCOPY

12 Before attosecond spectroscopy can be attempted, 8

W (eV) 4 one must verify whether the x-ray pulse 0 meets the necessary conditions of duration 85 and timing accuracy. 80

75 is the rapid decrease in polarizability of and energy that might be somewhat 70 matter with increased frequencies in the changed with respect to its initial values. 65 XUV–x-ray-spectral range. The initial photoelectron energies are This low transition probability, togeth- spread over a range of several electron 60

Photoelectron Energy (eV) Photoelectron er with the moderate energy (< 1 nJ) of volts, resulting from Heisenberg’s uncer- -15 -10 -5 0 5 10 15 the x-ray pulses from high-harmonic gen- tainty and the assumed subfemtosecond eration, prevents attosecond autocorrela- time structure of the x-ray excitation. For Delay, td (fs) tion as well as x-ray pump–x-ray probe the light-induced changes to be reliably spectroscopic measurements from being measurable, the light field must be strong Figure 6. Correlation of a subfemtosecond x-ray pulse with a few-cycles light wave (based on the realized. The problem of the low transi- enough to modify the kinetic energy of the scheme in Fig. 5). Lower panel, contour plots of the tion probability of a process mediated by electron by several electron volts or more. 15 photoelectron spectra (vertical axis) as a function two x-ray photons can be circumvented A simple semiclassical formalism in- of delay t d of the soft x-ray pulse with respect to only by a scheme in which the role of one dicates that the momentum transferred the light pulse (horizontal axis).3 The spectra unaf- of the x-ray photons is taken over by one from a light wave to an electron depends fected by the light field (i.e., those recorded at or more laser photon(s). If the field of the not only on the amplitude and the fre- large delays) are centered at ~ 75 eV (equal to the visible laser pulse is strong and consists of quency but also, most importantly, on the x-ray photon energy minus the binding energy of only a few oscillation cycles, this two-color phase of the light field at the moment the ~ 14 eV of the electron). The modulation of the scheme depicted in Fig. 4 paves the way for electron is born. Figure 5 shows how this spectral width with a period of T /2 (as predicted 0 attosecond sampling. by Fig. 5) is clearly visible. Upper panel, width W momentum transfer modifies the initially isotropic momentum distribution of the of the energy spectrum versus delay td. If the x-ray Ionization mediated by x rays photoelectron at three different instants pulse were much shorter than T0/2, at certain de- lays the electrons could be set free exactly at the in a strong light field: a route to during half of an oscillation cycle of the peak of the laser field, which would leave their en- attosecond sampling light field. The final kinetic energy spec- ergy spectra unaffected. Under this condition, the The duration of even the shortest possible trum of electrons collected within a cone local minima of the W(t ) correlation function d light pulse appears to prevent achievement aligned orthogonally to the laser polariza- shown in the upper panel would have to be equal tion (see Fig. 5) broadens twice within ≈ of attosecond resolution. Can the limita- to the value of W0 5 eV at large delays.The ob- tion set by the femtosecond duration of each laser oscillation period as the mo- served minima of W(td) are larger than W0, which indicates that the light field is not perfectly the laser pulse be overcome? Yes, provided ment of birth is scanned through the laser frozen during the birth of the photoelectrons, that the process mediated in the interac- pulse by variation of the delay of the x-ray leading to some broadening of the photoelectron tion medium by the combined action of burst (Fig. 4). spectrum, just as the finite exposure time in Fig. 2 the visible and x-ray pulses is guided by It is this modulation of the final (and resulted in a blurring of the image of the motorcy- the instantaneous electric field of the light hence measurable) electron spectrum, clist. Knowing the light oscillation cycle, this broad- pulse rather than by its cycle-averaged in- with a period of T0/2 (i.e., of the order of ening allows for determination of the x-ray pulse, tensity. In this case, in fact, the ~ 0.6-fs in- 1 fs), that offers the potential of attosec- just as knowledge of the speed of the motorcyclist terval required by the field of a 750-nm ond sampling. Should the x-ray pulse have permits the evaluation of the camera exposure a duration or timing jitter comparable to time from the blurring of the image (see the Fig. 2 light wave to change its strength from zero or longer than T /2, the modulation caption). to its maximum provides a sufficiently 0 short sampling interval for attosecond res- would be blurred, just as the photo of the olution. motorcyclist is blurred in Fig. 2. Exploita- Consider an ensemble of atoms ex- tion of the attosecond potential of this vis- posed, in the presence of a strong light ible-light–x-ray sampling scheme relies on wave, to a very short x-ray pulse: x << an x-ray pulse that is synchronized to the T0/2, where T0 is the oscillation period of light wave with attosecond accuracy and the visible light wave. The electron ejected with an attosecond pulse duration. If these from the atom after absorption of an x-ray conditions are fulfilled, the two-color photon starts to quiver along the electric- sampling apparatus that uses the interac- field vector of a strong, linearly polarized tion described in Fig. 5 can be used to femtosecond light wave and, after the light measure the duration of x-ray pulses or pulse has passed through the interaction the speed of fundamental electronic medium, is left behind with a momentum processes with attosecond resolution.

66 Optics & Photonics News May 2002 ATTOSECOND SPECTROSCOPY

Sampling x rays and visible light wave, implying an x-ray pulse duration V (PHz) with attosecond resolution and timing jitter of less than 1 fs. This at- inst inst (nm) tosecond sampling system does not only Before attosecond spectroscopy can be at- 0.55 550 tempted, one must verify whether the x- provide access to the duration of the x-ray ray pulse meets the necessary conditions burst, it also makes field oscillations in a 0.50 600 visible light wave directly perceivable. 650 of duration and timing accuracy. If the 0.45 sampling system is to measure the correla- Figure 7 shows the variation of the in- 700 tion function of the incident pulses for de- stantaneous carrier frequency of our few- 0.40 750 cycles light pulse that was evaluated with 800 termination of their temporal structure, as -6 -4 -2 0 2 4 6 discussed above, the response time of the the data in Fig. 6 (dots) together with the Delay, td (fs) interaction medium on the relevant time theoretically predicted carrier frequency scale must be instantaneous. The photo- sweep created by ionization in the x-ray- electrons set free by the x-ray pulse with generation process. The less than 2-fs dy- Figure 7. Instantaneous carrier frequency of the light field (dots) evaluated from W(t ) shown in namic frequency shift indicates that opti- d an initial kinetic energy of W0 = h x - Wb Fig. 6. For comparison, the curve shows the fre- cal-field ionization is confined to less than (h x is the x-ray photon energy and Wb quency sweep in the calculated few-cycles laser represents the atomic binding energy of a one-wave cycle in our 7-fs pulse, in pulse that exits the neon harmonic source the electron) are expected to respond to agreement with theoretical prediction. (dashed curve in Fig. 3). the x-ray excitation virtually instanta- This could be regarded as the first time-re- neously, even on an attosecond time scale. solved measurement of strong-field ion- Hence, detecting the photoelectron energy ization. The extremely fast rise time of the spectrum in the geometry described above blueshift, rise < 1 fs, also provides—in (Fig. 5), at the output of the two-color agreement with other observations—con- sampling system sketched in Fig. 4, per- clusive evidence that the x-ray emission is mits measurement of the correlation func- substantially confined to a <1-fs time tion (convolution) of the electric field of frame. In the absence of a carrier frequen- the visible light wave and the intensity en- cy sweep of the probe laser pulse, the qua- velope of the x-ray pulse. si-periodic modulation in the photoelec- In collaboration with Markus Dresch- tron spectral width in Fig. 6 could also be er, Ulf Kleineberg, and Ullrich Heinzmann reconciled with a subfemtosecond pulse of the University of Bielefeld, a two-color accompanied by several equidistant satel- sampling system for the measurement of lites spaced by T0/2. However, the strong this correlation function was construct- transient blueshift and its subfemtosecond 15 ed. X-ray pulses at ~90-eV photon ener- rise rule out the possibility that these satel- gy (~ 14 nm), with a bandwidth of ~ 5eV lites carry a substantial fraction of the were produced by few-cycle-driven high- spectrally filtered 90-eV radiation. Hence harmonic generation under experimental the isolated subfemtosecond-x-ray pulse conditions that correspond to those simu- predicted earlier by others12 as well as by lations shown in Fig. 3. (Note that absolute the numerical simulations in Fig. 3 could phase was random in our laser pulses. As now be verified experimentally.3 a consequence, only a fraction of the laser Is it possible to determine the duration pulses, those with ≈ 0, produced an en- of the x-ray pulse more precisely? Yes. Just ergetic x-ray pulse as shown in Fig. 3, with as the exposure time for the blurred image the others providing only a minor contri- bution to signals accumulated over many in Fig. 2 can be determined if one knows laser shots; see, e.g., the data in the speed at which the motorcyclist travels, Fig. 6.) The x-ray pulse was fed, together analysis of the speed and wavelength of with the 7-fs, 750-nm light pulse used for light in Fig. 6 allows us to determine the its generation, into our two-color sam- x-ray pulse duration, which was found to pling system as depicted schematically in be x = 650 ± 150 as, in reasonable agree- Fig. 4 and described in detail in Refs. 3 and ment with theoretical prediction (Fig. 3). 15. Figure 6 shows the false-color repre- The x-ray pulse duration is limited by the sentation (lower trace) of the x-ray photo- bandwidth (~5 eV) of the bandpass electron spectra measured as a function of (Mo–Si multilayer mirror) that filters photons near 90 eV.According to numeri- delay td between the x-ray pulse and the few-cycles light pulse.15 Modulation of the cal simulations, the few-cycle-driven har- photoelectron spectrum is clearly resolved monic source might be capable of produc- even near zero delay, where the modula- ing 90-eV x-ray pulses shorter than 200 as. tion period decreases to less than 1 fs ow- At somewhat higher photon energies, even ing to a dynamic blueshift of the light less than 100-as pulses appear feasible.

May 2002 Optics & Photonics News 67 ATTOSECOND SPECTROSCOPY

Electron pulse serves as an attosecond probe. In E (t) energy Attosecond spectroscopy: L Photoelectron spectrum time-resolved atomic physics strong contrast with conventional versus td pump–probe spectroscopy, however, the X-ray pulse duration With the subfemtosecond-x-ray pulse syn- t pump pulse is much weaker than the d chronized to a few-cycles light wave, a probe pulse. The pump pulse can be weak Auger electron spectrum powerful tool is now at our disposal for versus t because the electrons are excited into d use in attosecond spectroscopy. Surpris- EX (t) states (free states with high kinetic energy) Inner-shell relaxation times ingly, the attosecond sampling system used for the measurement of x-ray pulse that are not populated before excitation. duration might be able to provide insight The absence of a disturbing background into atomic electron dynamics without arising from electrons detached by multi- Spread of electron kinetic energy any major modification. For x-ray metrol- ple absorption of laser photons and a high Photoelectrons Auger electrons ogy, we chose to observe the dynamics of strength of the probe laser field are crucial ≤T /20 ≤ prerequisites for the reliable implementa- 0 0 innershell T0/20 photoelectrons, because their production =T0/5 =T /5 0 tion of this new spectroscopy. These re- =T /2 0 =T0/2 is temporally confined to the duration of =2T0 =2T quirements can best be reconciled by use 0 the x-ray pulse used for excitation (Fig. 8, upper panel). From the measured tempo- of the shortest possible light pulse as a ral structure of the photoelectron wave probe, otherwise the (relatively long) strong light pulse tends to produce an ex- W0 packet, we can determine the x-ray pulse duration. For this measurement, we used cessive number of free (background) elec- T /2 Delay trons by means of multiphoton ionization. 0 the photoelectron that originates from the most weakly bound state (characterized by Furthermore, the attosecond sampling Figure 8.Time-resolved atomic spectroscopy.Up- technique allows for the evaluation of x- per panel, a subfemtosecond x-ray pulse detaches the smallest binding energy, Wb). The same x-ray pulse, however, de- ray pulse duration or inner-shell relax- electrons from outer as well as inner shells (pho- pending on its photon energy, could also ation time for any values of x , inner-shell toelectrons) in the presence of a strong visible ≥ light field. Inner-shell relaxation processes could kick off electrons that reside in strongly T0/20 including the range of values com- result in secondary electron emission (Auger elec- bound states. The vacancies that emerge in parable to or slightly longer than the half- trons).The kinetic energy distribution of the freed this manner in inner shells of atoms are oscillation period (see note at the end of electrons can be measured as a function of the de- extremely short-lived: they are refilled by Fig. 8 caption), only if the laser pulse du- lay between the x-ray pulse and the strong few-cy- an electron from an outer shell within a ration is comparable to the carrier-wave cles light wave in the geometry depicted in Fig. 5. time frame that typically ranges from a cycle. As a consequence, few-cycles light is Just as study of the photoelectrons measures the few femtoseconds to hundreds of attosec- beneficial to attosecond sampling both by x-ray pulse duration with attosecond resolution, allowing the generation of isolated sub- investigation of the Auger electrons provides ac- onds, depending on the binding energy of femtosecond x-ray pulses and by allowing cess to inner-shell relaxation processes within the the liberated electron. The energy released same time frame. Lower panel, qualitative depend- in this electronic transition can liberate a implementation of sampling at low-x-ray ence of width of the photoelectron or Auger elec- second, so-called Auger electron (Fig. 8). fluence levels available from present-day tron spectrum on the delay between the x-ray Auger electrons are ejected until the inner- sources. pump and the visible probe pulse for different val- shell vacancies are completely refilled. Of The research presented here appears to ues of the x-ray pulse duration and of the inner- course, this applies only if the duration of provide the basic tools and concepts for shell relaxation time, respectively.The actual value attosecond spectroscopy. Nevertheless the x-ray pulse is substantially shorter of x or inner-shell can be inferred from the depth of much research is still needed to make this quasi-periodic modulation or from broadening of than the inner-shell relaxation time(s) to be measured. If this condition is fulfilled, emerging technique routinely applicable the x-ray-pump–visible-probe correlation function for a broad range of processes and atomic for , < T /2 and , > T /2, re- all we have to do is repeat the measure- x inner-shell 0 x inner-shell 0 systems. Major emphasis must be placed spectively. The maximum modulation depth is ment with our attosecond sampling sys- ≤ on the precise control of electric-field evo- achieved for x , inner-shell T0 /20, indicating the tem by measuring the variation of the ki- lution of intense few-cycles light (by stabi- resolution limit of the sampling system. Using laser netic energy spectrum of Auger electrons pulses at = 750 nm (T = 2.5 fs) yields a tempo- lization of the absolute phase16; see Fig. 3) 0 rather than photoelectrons as a function ral resolution close to 100 as. So that the x-ray for reproducible isolated attosecond x-ray of delay between the subfemtosecond pulse duration or inner-shell relaxation time can pulse generation and by extension of the x-ray and the few-cycles light pulse. Mea- be reliably determined for x or inner-shell slightly wavelength range to the kilo-electron-volt suring the emission duration of Auger longer than T0 /2 from a broadening of the overall regime to gain access to inner shells in correlation trace, the laser pulse duration must electron wave packets with the attosecond larger atoms. It will take several years be- not be much longer than wave cycle T . 0 sampling system provides direct informa- fore time-resolved atomic spectroscopy is tion about inner-shell relaxation times, well established, but we can confidently just as measuring the photoelectron emis- state that the new experimental field is on sion time (Fig. 6) yielded the x-ray pulse the horizon. duration (Fig. 8, lower panel).

In this concept, the subfemtosecond x- Ferenc Krausz is a professor at the Photonics Institute ray burst serves as the pump pulse, and the of the Vienna University of Technology. His e-mail ad- oscillating electric field of a visible light dress is [email protected].

68 Optics & Photonics News May 2002