Attosecond tracing of correlated electron-emission in non-sequential double ionization

Abstract

Despite their broad implications for phenomena such as molecular bonding or chemical reactions, our knowledge of multi-electron dynamics is limited and their theoretical modelling remains a most difficult task. From the experimental side, it is highly desirable to study the dynamical evolution and interaction of the electrons over the relevant timescales, which extend into the attosecond regime. Here we use near-single-cycle laser pulses with well-defined electric field evolution to confine the double ionization of argon atoms to a single laser cycle. The measured two-electron momentum spectra, which substantially differ from spectra recorded in all previous experiments using longer pulses, allow us to trace the correlated emission of the two electrons on sub-femtosecond timescales. The experimental results, which are discussed in terms of a semiclassical model, provide strong constraints for the development of theories and lead us to revise common assumptions about the mechanism that governs double ionization.

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Received 26 Jan 2012 | Accepted 28 Mar 2012 | Published 8 May 2012 DOI: 10.1038/ncomms1807

Boris Bergues1,*, Matthias Kbel1,*, Nora G. Johnson1,2, Bettina Fischer3, Nicolas Camus3, Kelsie J. Betsch1,4, Oliver Herrwerth1, Arne Senftleben3, A. Max Sayler5,6, Tim Rathje5,6, Thomas Pfeifer3, Itzik BenItzhak2, Robert R. Jones4, Gerhard G. Paulus5,6, Ferenc Krausz1, Robert Moshammer3, Joachim Ullrich3,7 & Matthias F. Kling1,2

Despite their broad implications for phenomena such as molecular bonding or chemical reactions, our knowledge of multielectron dynamics is limited and their theoretical modelling remains a most difcult task. From the experimental side, it is highly desirable to study the dynamical evolution and interaction of the electrons over the relevant timescales, which extend into the attosecond regime. Here we use nearsinglecycle laser pulses with welldened electric eld evolution to conne the double ionization of argon atoms to a single laser cycle. The measured twoelectron momentum spectra, which substantially differ from spectra recorded in all previous experiments using longer pulses, allow us to trace the correlated emission of the two electrons on subfemtosecond timescales. The experimental results, which are discussed in terms of a semiclassical model, provide strong constraints for the development of theories and lead us to revise common assumptions about the mechanism that governs double ionization.

Attosecond tracing of correlated electronemission in nonsequential double ionization

1 Max-Planck-Institut fr Quantenoptik, D-85748 Garching, Germany. 2 J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA. 3 Max-Planck-Institut fr Kernphysik, D-69117 Heidelberg, Germany. 4 University of Virginia, Charlottesville, Virginia 22904, USA. 5 Institut fr Optik und Quantenelektronik, Friedrich-Schiller-Universitt, D-07743 Jena, Germany. 6 Helmholtz Institut Jena, D-07743 Jena, Germany.

7 Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany. *These authors contributed equally to this work. Correspondence and requests for materials should be addressed to B.B. (email: [email protected]) or to M.F.K. (email: [email protected]).

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Many fundamental processes in nature such as the formation and dissociation of molecules are governed by multi-electron dynamics (MED). Understanding MED is one

of the grand contemporary challenges of quantum physics. While the ground state properties of multi-electron systems are described with reasonable accuracy, the modelling of their dynamics is still in its infancy. Even for rather simple systems involving only a few interacting electrons such as low-Z atoms beyond helium (Z being the nuclear charge), the exact theoretical treatment of MED is hardly practicable. The identication of suitable approximations that capture the essential features of MED relies on the development of experiments aimed at resolving the electron dynamics on the characteristic attosecond timescale of their motion. An established technique for resolving one-electron dynamics on sub- femtosecond scales involves the use of a strong few-cycle infrared laser eld as a clock13. The well-known concept of attosecond streaking spectroscopy has permitted the observation of single-electron dynamics with attosecond time resolution4. Despite this progress, however, the ultrafast dynamics of multiple electrons has resisted direct observation, even though far-reaching conclusions were drawn from kinematically complete strong-eld double5,6 and multiple ionization7 experiments.

Among countless phenomena involving the motion of multiple electrons, non-sequential double ionization (NSDI) of atoms is a pure and, meanwhile, classic example for MED in the presence of strong elds. As reported for rare gases almost 30 years ago8, it manifests itself as an unexpected, orders-of-magnitude enhancement in the strong-eld double ionization yield. This nding cannot be explained within the framework of the single active electron approximation, where both electrons are assumed to be ionized sequentially and independently of each other. A mechanism correlating the emission of the two electrons must be included to adequately describe this eect and dierent models have been proposed5,9.

Since the pioneering works, NSDI has been the subject of numerous experimental and theoretical studies (for a recent review, see ref. 6 and references therein). Recording the momentum spectra of doubly10,11 and multiply7 charged ions provided clear evidence that the emission of the second electron is triggered by the laser-driven recollision of the rst electron with its parent ion. Even more insight into the process was gained in kinematically complete studies where the correlated two-electron momentum distributions were measured11 and investigated for dierent laser parameters1215. Measurements of the dynamics of NSDI in near-single cycle laser pulses have been restricted to recoil-ion spectra, which did not allow for the direct retrieval of the correlated electron-emission dynamics16,17. The sub-cycle dependence of electron correlation spectra has been explored by various theoretical studies, where the double-ionization dynamics were conned to a single cycle of a laser pulse12,18. A direct test of the validity of these theoretical models, however, has been impeded so far by the lack of kinematically complete experimental data obtained with ultrashort pulses and precise control or knowledge of the electric eld.

Here we present measurements of correlated two-electron momentum spectra for the strong-eld NSDI of argon atoms in the single-cycle limit. The measured spectrum exhibits a cross-shaped structure that qualitatively diers from spectra recorded in all previous experiments using many-cycle pulses. Conning the ionization dynamics to a single laser cycle by choosing an adequate carrier envelope phase (CEP) allows us to perform a clean experiment with only one single recollision event contributing to NSDI, thus excluding the contribution of multiple recollisions that hamper the interpretation of experimental results. From the CEP-resolved spectra the correlated emission of two electrons is traced on subfemtosecond timescales. In particular, we can determine at which time the second electron is released within the laser pulse.

ResultsExperimental set-up. A detailed sketch of our experimental set-up is given in the Methods. Briey, the experiments were performed using linearly polarized laser pulses with a central wavelength of 750 nm and a full-width at half-maximum (FWHM) of the temporal intensity envelope of 4 fs, which were generated at a repetition rate of 3 kHz19. The electric eld of the laser pulse can be approximated as E(t) = E0 cos2(t/) cos(t + ), where E0 is the eld amplitude,

is the carrier frequency, is the pulse duration, and is the CEP. Combining a reaction microscope (REMI)20 with a newly developed phase-tagging technique21, we obtained the CEP of the laser pulse for each and every ionization event22 recorded with the REMI. The laser was focussed to a maximum instantaneous intensity of I0 =

c0E02 = (3.0 0.6)1014 W cm 2 into a cold supersonic gas jet of neutral argon atoms located in the centre of the REMI. The momenta of electrons and ions created in the laser focus were measured in coincidence in the REMI. For the conditions of our experiment, the ratio of the measured Ar2 + to Ar + yields was about 0.1%.

Two-electron momentum distributions. Figure 1 shows experimental correlated two-electron momentum distributions, where the number of recorded double-ionization events is plotted as a function of the momenta p1 and p2 along the laser polarization axis of electron 1 and electron 2, respectively. The spectra are symmetric with respect to the p2 = p1 diagonal because the two electrons, the recolliding electron and the one liberated as a result of this recollision, cannot be distinguished in the experiment. The CEP-averaged correlation spectrum is shown in Fig. 1a. The cross-shaped structure indicates that the momentum of one electron is always close to zero whereas the momentum of the other electron varies between 1.5 to 1.5 atomic units. Similar structures were found in a recent theoretical study on NSDI of argon employing S-matrix theory18. So far, however, such a cross-shaped two-electron momentum distribution has not been observed experimentally. This strongly suggests that the physical mechanisms that govern NSDI in the near single- cycle regime dier from the many-cycle regime, where previous experiments were performed. The CEP-resolved correlation spectra presented in Fig. 1be exhibit a strong CEP dependence. For CEP values of 155 (Fig. 1c) and 335 (Fig. 1e), the signal is predominantly (with more than 80% of the counts) located below and above the red diagonal line (p2 = p1), respectively. For intermediate CEP values of 65 (Fig. 1b) and 245 (Fig. 1d), the signal is distributed on both sides of the red diagonal.

The semiclassical model. To interpret the experimental results, we investigate the recollision-induced ionization dynamics using a semiclassical model (for details, see Methods). In the present intensity regime, essentially two mechanisms may contribute: the rst is the (e, 2e)-mechanism, in which the recolliding electron directly promotes a second electron into the continuum via electron impact ionization23. The second is recollision-induced excitation with subsequent ionization (RESI)24,25, where the recolliding electron excites the parent ion, which is subsequently ionized by the laser eld as depicted in Fig. 2a. A key property of the RESI process is the delayed emission of the second electron with respect to the recollision event, the latter occurring near the zero crossing of the electric eld of the laser. As shown below, our experimental results identify RESI as the dominant process, and, more importantly, enable the determination of the emission delay.

In our semiclassical model, the probability to liberate the rst electron at any moment in time is calculated using the instantaneous AmmosovDeloneKrainov (ADK) tunnelling rate including a correction factor to account for over-the-barrier ionization26. The propagation of the electron aer the ionization in the electric eld of the laser pulse is treated classically, neglecting the Coulomb interaction with the ionic core and with the other electron. For the RESI

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a

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Figure 2 | Comparison of experimental and theoretical results. (a) Illustration of the RESI mechanism dominating NSDI at the experimental parameters: the laser electric eld as a function of time is drawn alongwith schematics of the electronic conguration of the outer shell of Ar at three key time steps of the process. First, an electron e1 is liberated from Ar, leaving a hole (small circle) in the outer shell of Ar + (light blue). Second,an excited Ar + ion (pink colour) is produced upon recollision of electron e1

near the zerocrossing of the electric eld. Finally, a second electron e2 is liberated from the excited Ar + ion forming Ar2 + (purple). (b) Calculated twoelectron momentum spectrum averaged over CEP for the experimental parameters using the semiclassical RESI model, described in the text. (c) Experimental recoilion momentum spectra (for momenta p|| parallelto the polarization axis) for single (Ar + ions, blue open dots) and double ionization (Ar2 + ions, black crosses), respectively, averaged over CEP.

The experimental data are compared with the model results for single ionization (blue line), and double ionization ((e, 2e)mechanism (dashed red line) and RESImechanism (black line)). Scattering angles = 0 and = 20 are used to simulate the (e, 2e) and RESI processes, respectively. (d) Comparison of the experimental and calculated asymmetry A as a function of the CEP for Ar + and Ar2 + (using the same symbols and colour coding as in (c)). All the theoretical results shown in (b,c,d) were obtained from the same simulation with the parameters given in the text.

1

0

d

e

1 0 1 1 0 1

p1 (a.u.)

Figure 1 | Correlated two-electron momentum spectra. Experimental twoelectron momentum distributions for the double ionization of argon with nearsingle cycle, 4 fs laser pulses at a maximum instantaneous intensity of I0 = 3.01014 Wcm2. Here p1 and p2 are the momentum componentsof the rst and the second electron along the laser polarization direction, respectively. The cartoons in (a) illustrate the emission direction of the two electrons (green spheres) and the ion (orange spheres). The arrows represent the sign of the longitudinal momentum of the fragments. An event in the rst or third quadrant corresponds to the emission of two electrons into the same direction; electrons emitted in opposing directions appear in the second or fourth quadrant. A crossshaped structure is seen in the phaseintegrated plot (a), reecting the correlated nature of the NSDI process. In images (be), spectra are shown for different values of the CEP, namely (b) 65, (c) 155, (d) 245 and (e) 335. The spectraare averaged over a /6 CEP range and are symmetrized with respectto the p2 = p1 diagonal. Images (c,e) correspond to CEPs with maximum asymmetry in the Ar2 + emission and (b,d) to CEP with zero asymmetry in the Ar2 + emission. The same colour scale is used for all (ae).

process, the calculation is performed as follows: if the rst electron recollides with the parent ion with sufficient kinetic energy, the lowest excited state of Ar + is populated and the second electron is liberated by subsequent eld ionization. For the (e, 2e) process, we consider only recolliding electrons having sufficient energy to overcome the second ionization potential of argon. In this case, the second electron is assumed to be liberated with zero-initial momentum via electron impact ionization. In both the RESI and (e, 2e) processes, the magnitude of the rst electron momentum, just aer the recollision, is determined by energy conservation. The direction of this momentum vector, described by the scattering angle (where is the angle between the momentum vectors just before and just aer the recollision), is undetermined in our model and constitutes the only free parameter. The dependence of the simulated correlation spectra on the scattering angle is discussed in the Methods.

Comparison of measured and calculated spectra. The results of our calculations are displayed in Fig. 2bd, for the instantaneous peak intensity of I0 = 2.91014 Wcm2 (the cycle-averaged peak intensity equals I0/2) and a pulse duration of 3.8 fs (FWHM in intensity). In Fig. 2c, the measured CEP-averaged momentum distributions of Ar + and Ar2 + are compared with their simulated counterparts for the (e, 2e) and RESI mechanisms. The calculated width of the Ar + spectrum is in good agreement with the measurement. The double hump structure of the Ar2 + spectrum is also correctly reproduced by the simulation for the RESI mechanism, where the best agreement was reached with = 20. We note that small contributions of higher excited Ar + states or the (e, 2e) mechanism would lead to a slightly broader momentum distribution of the Ar2+ ions in the calculations. The prediction for the (e, 2e) mechanism alone (red line in Fig. 2c), however, does not reproduce the experimental Ar2 + spectrum even if we use = 0, where the best agreement was reached for this mechanism. Interestingly, the double hump structure, which was previously believed to originate from an (e, 2e) mechanism27 can be reproduced considering the RESI mechanism only. Figure 2b shows the calculated CEP- averaged correlation spectrum for the RESI process, which exhibits the characteristic cross-shaped structure observed in the experiment.

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The corresponding two-electron momentum distribution for the (e, 2e) process is shown for comparison in the Methods.

Comparison of measured and calculated asymmetries. In earlier work, the (e, 2e) mechanism was invoked to explain the CEP-dependent Ar2 + recoil-ion spectra at about twice the intensity16,28. Our results clearly indicate that, under the conditions of the present experiment, electron impact excitation to the lowest excited Ar + state and subsequent eld ionization (RESI) constitutes the main contribution to NSDI of argon. To discuss the CEP dependence of NSDI, it is instructive to introduce the asymmetry parameter A = (N + N )/(N + + N ), where N + and N denote the number of ions with positive and negative momentum along the polarization axis, respectively. In Fig. 2d, the measured asymmetries of the Ar + and Ar2 + yields as a function of CEP are compared with the results of our calculations (using the parameters given above). The experimental CEP is only determined up to a constant oset (see Methods). We use the theoretical Ar + asymmetry as a reference to set the value of the oset such that the maximum of the measured Ar + asymmetry curve coincides with the maximum of the calculated one. Remarkably, both the amplitude and the shape of the simulated Ar + asymmetry curve exactly match the measurement. Whereas the amplitudes of the calculated and measured Ar2 + asymmetry curves are in good agreement, the calculated phase shis between the Ar + and the Ar2 + asymmetry curves (154 for RESI and 177 for (e, 2e)) do not match the measured phase shi of 114. We would like to emphasize that such asymmetry data obtained simultaneously for single and double ionization is only accessible in the few and near single-cycle regime and was not available before. The measured phase shi represents a useful observable to test the validity of theoretical models. In spite of the small discrepancies between the experimental data and the simulation results, the overall agreement is impressive, considering the simplicity of the theoretical model.

Discussion

In light of the good agreement between simulation and experiment, the electron dynamics can now be analysed in more detail. In Fig. 3, experimental (Fig. 3a,b) and simulated (Fig. 3c,d) correlation spectra are compared for CEP values that correspond to maximum (Fig. 3a,c) and zero (Fig. 3b,d) Ar2 + asymmetry, respectively.

Figures 3e and 3f show the calculated ionization rates of the rst (green area) and second (red area) electron together with the temporal prole of the laser electric eld for these two CEP values. Due to depletion of the excited Ar + population, the second electron is emitted before the maximum of the laser electric eld. Our analysis thus reveals that under our experimental conditions, it is the momentum of the rst electron that is close to zero while the momentum of the second electron is non-zero and varies as a function of the CEP. Averaged over the CEP, this results in the cross-shaped structures seen in Figs 1a and 2b. This nding is in contrast to the common assumption that the second electron in the RESI mechanism is released at the peak of the electric eld and acquires a small momentum distributed around zero7.

Multiple recollision events, which occur in the several-to-multi-cycle regime, severely hamper the interpretation of measured correlation spectra. Figure 3 illustrates how the short pulses used in our study allow for a clean experiment by conning NSDI to essentially one single recollision event for an appropriate choice of the CEP yielding the maximum Ar2 + asymmetry. For a CEP corresponding to a zero Ar2 + asymmetry (Figs 3b and d), precisely two recollision events from consecutive half-cycles contribute to NSDI. Here the second electron, liberated as a result of the rst recollision, acquires a higher momentum with positive sign whereas the second recollision results in a lower momentum with negative sign. Even in this case, the change in sign of the slope of the electric eld allows for distinguishing the contributions from the two consecutive recollision events.

With the analysis presented in Fig. 3, we can also unambiguously determine whether excitation of the singly charged ion occurs without recollision, that is, via laser excitation alone. Recollision-induced excitation takes place about three quarters of a cycle aer the emission of the rst electron. In contrast, a laser-excited ion would be efficiently ionized in the half-cycle following ionization of the rst electron, leading to a signal on either side of the red diagonal in Fig. 3a, which is not observed. Disentangling laser excitation from recollisional excitation is possible only because the double ionization process has been conned to a single cycle.

Using the infrared eld as an inherent clock and neglecting the eect of the Coulomb potential as commonly assumed in the attosecond streaking scenario1,29, we can retrieve the electrons most likely emission time, which is directly mapped onto its dri momentum. Specically, t = arccos(p0/pmax)/, where p0 and pmax

are the most probable and the maximum momentum of electron 2, respectively. From the experimental data, we nd the maximum emission probability of the second electron at 210 40 attoseconds before the peak of the half-cycle following the recollisional excitation. This is in good agreement with our simulations predicting the emission leading the maximum of the eld by 230 attoseconds.

In conclusion, using a near-single-cycle laser pulse with appropriate CEP, the double ionization dynamics of argon could be conned to an isolated recollision event, allowing us to investigate the elementary process responsible for NSDI. The measured correlated two-electron momentum spectrum has a cross-shaped structure, which has not been observed in previous experiments, all of them using longer laser pulses. This suggests that the transition from the multi-cycle to the near-single-cycle regime substantially modies the dynamics of NSDI. Resolving the CEP-dependence of the correlated two-electron spectra has provided new insights into the double ionization dynamics. In particular, we have shown that, owing to depletion of the excited Ar + ions, the second electron is emitted before the maximum of the laser electric eld. The mean delay between the zero crossing of the electric eld and the emission of the second electron could be determined unambiguously. More generally, the highly dierential data obtained in our experiment provide strong constraints to multi-electron theories and may greatly stimulate their development. Whereas our semiclassical model captures the essential features of

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Figure 3 | Timing of the rst and second ionization. Comparison of measured (a,b) and calculated (c,d) twoelectron momentum distributions for CEPs corresponding to a maximum (a,c) and zero value (b,d) ofthe Ar2 + asymmetry. The predicted ionization rates of the rst (greenshaded area) and second (redshaded area) electron contributing to NSDI are displayed in (e) and (f) together with the electric eld of the laser pulse (black line) for maximum and zero Ar2 + asymmetry parameters, respectively. Each black arrow points to the time of recollision for electrons liberated near the tail of the arrow. In (a,c,e) only a single recollision leads to NSDI, while in (b,d,f) two recollision events in successive halfcycles contribute.

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the data, electron correlations enter the model only indirectly via the ionic excitation and the scattering angle. More sophisticated models accounting for Coulomb and exchange interaction are certainly needed to fully resolve the correlated electron motion and predict the correct value for the phase shi observed between the Ar + and Ar2 + asymmetry curves. Extension of our approach to the study of molecular dynamics may give a more detailed insight into the breaking of chemical bonds.

Methods

Experimental technique. The experiment was performed at the AS-1 attosecond beamline at the Max Planck Institute of Quantum Optics19. Linearly polarized laser pulses with a central wavelength of 750 nm, an energy of 400 J and a FWHM of the temporal intensity envelope of 4 fs are generated at a repetition rate of 3 kHz in an amplied laser system. Active stabilization of the CEP is difficult to conciliate with the long data-acquisition times (32 h for the present experiment) imposed by coincident particle-detection schemes. As a signicant advance over previous eorts to measure the sub-femtosecond dynamics of the NSDI of argon, we recorded the CEP of each laser pulse by sending a fraction of the laser beam (25 J) into a single-shot stereographic above-threshold ionization (Stereo-ATI) phase-meter21 (see Fig. 4).

A detailed description of the CEP measurement technique using ATI and the Stereo-ATI phase meter can be found in refs 17,21,22,30,31. Briey, the time-ofight spectra of electrons emitted along both directions of the laser polarization axis are recorded on either side of the apparatus (le and right detector in Fig. 4). For each laser shot, the CEP is inferred from the asymmetry between the le and the right TOF spectra. The CEP is measured up to a constant oset in the phase meter.

A fraction (11 J) of the remaining part of the laser beam is focussed with a spherical mirror (f = 25 cm) into a well-localized (1 mm width) and cold supersonic gas jet of neutral argon atoms in the centre of a REMI20. Ions and electrons created in the laser focus (~40 m diameter) are extracted by a weak electric eld towards microchannel plate (MCP) detectors equipped with delay line anodes for position readout at the le and right side of the instrument, respectively. A pair of Helmholtz coils generates a homogenous magnetic eld to guide the electrons towards their detector reaching a 4 acceptance angle for all electrons of interest (Fig. 4). The 3D momentum vectors of ions and electrons are reconstructed from their measured ight times and impact positions on the corresponding detectors. The low density of the jet allows for detection of on average less than one ionization event per laser shot, an important constraint to mini-

mize the number of false coincidences, when measuring ions and electrons in coincidence. In the present experiment, 0.25 ions per laser shot were detected on average.

Data processing and false coincidences. To generate the correlated two-electron momentum distributions shown in Fig. 1, we select laser shots where at least one electron and one Ar2 + ion are detected. As most of the time only one of the two electrons generated together with Ar2 + is detected (because of the single-particle detection efficiency of ~50%), the momentum of the missing second electron is calculated using momentum conservation. Electrons emerging from single ionization of argon introduce a false coincidence background in the electron correlation spectra of less than 15%.

The contribution of false Ar2 + events ( < 0.5% of the total Ar2 + signal) is negligible.

Laser intensity and CEP offset measurement. The analysis of the Ar + spectra, recorded in the same measurement, provides important information allowingfor in situ determination of the peak intensity of the laser pulse in the interaction region, as shown in Fig. 5. Furthermore, the comparison of the measured and calculated Ar + asymmetry curves allows for the determination of the absolute CEP of the laser pulses in the interaction region in the REMI.

Simulation procedure. The yield Y(t) of electrons emitted in a time interval [t, t + dt] is calculated using the instantaneous ADK tunnelling rate wADK (refs 32,33) summed over all occupied degenerate states of the outer shell. This rate is further multiplied with the correction factor from (ref. 26) to account for above the barrier ionization:

w t w t Z E t

I I

( ) ( ) exp ( )

( ) .

/

2

=

ADK

a

(1)(1)

(2)(2)

p p

2

3 2

Here Ip is the ionization potential and is a numerical factor adjusted such that the rate, w(t), ts the result obtained by solving the Schrdinger equation numerically.

The value of parameter is 9 for Ar and 8 for Ar + (ref. 26).The ionization yield is calculated as

Y t N t w t t w t t

i ti

t( ) ( )exp ( ) ( ) ,

=

Helmholtz coils

Ion detector

PD

d d

where N(ti) is the initial population of the electronic state under consideration. Aer ionization, at time t0, the electron enters the continuum with zero momentum at a distance xt of the parent ion, where xt is the exit of the tunnel. The electron is propagated classically in the electric eld of the laser pulse, neglecting the interaction with the parent ion. The electron may return at a later time t1, to the position at x0, with sufficient energy to either excite the parent ion in the case of

RESI or to directly ionize the parent ion in the case of the (e, 2e)-mechanism.

For the RESI process, the calculation is performed as follows: if the kinetic energy, Ekin(t1) of the returning electron is higher than the excitation energy, Eexc = 13.5 eV, needed to reach the lowest excited state of Ar + , this state, (3s 3p6) 2S1/2, is populated with the probability Y(t0) and the propagation of the re-scattered electron is continued with an initial kinetic energy Ekin(t1) = Ekin(t1) Eexc. For the ionization of the second electron from the excited ion, we proceed in the same way as for the ionization of the rst electron, using the parameters of the excited state for the ionization rate.

Left Right

Gas supply

e-detector

Catcher

BS

1

Figure 4 | Experimental set-up. Schematic of the setup consistingof a singleshot StereoATI phase meter (left chamber) and a REMI spectrometer (right chamber). A beamsplitter (BS) directs the laser pulses into both chambers. Each arm is equipped with a pair of fusedsilica wedges for compensating residual chirp. The phase meter contains a layer of metal to shield from external magnetic elds. The inner gas cell is lled with xenon gas at a pressure of about 510 3 mbar. In the StereoATI, xenon atoms are ionized near the focus of the horizontally polarized laser beam, and the electrons produced enter the highvacuum drift tubes through slits. Electrons resulting from the ionization by a singlelaser shot are detected by MCP detectors to the left and to the right, enabling the determination of the CEP for each REMI event, as described in the text. Simultaneously, ions and electrons created in the overlap of the laser focus and a skimmed supersonic jet of the REMI are extracted from the interaction region by a weak electric eld (3 V cm 1)

and detected by MCP and delay line detectors on the left and right sideof the instrument, respectively. Helmholtz coils are used to facilitate the detection of electrons over a solid angle of 4. The jet is efciently pumped by the catcher. The master trigger for the electronics is provided by a fast photodiode (PD). The ion and electron optics are symmetric in reality, and a few electrodes have been removed for visualization of the laser path.

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Figure 5 | Determination of the peak intensity. The peak intensity in the laser focus is inferred from the momentum spectra of Ar + ions (parallel to the polarization axis) by comparison with simulations. The measured Ar + spectrum (open circles) is plotted together with simulated spectra calculated for three different intensities: 3.01014 W cm 2 (red line),

2.41014 W cm 2 and 3.61014 W cm 1 (narrow and wide black spectra respectively). The gray area inbetween the two black curves represents the error bars of 20% in the determination of the peak intensity.

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1

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Figure 6 | Simulation results for electron impact ionization. Predicted twoelectron momentum distribution for the (e, 2e) mechanism and = 0.

The discrepancies between the (e, 2e) calculations and the measured data become even larger for other values of .

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Signal (arb.units)

Figure 7 | Sensitivity with respect to the scattering angle. Simulated twoelectron momentum distribution assuming the RESI process for three different scattering angles .

To simulate the (e, 2e) process, a recolliding electron with sufficient energy to overcome the second ionization potential of argon is assumed to produce a second electron with zero-initial momentum. The magnitude of the rst electron momentum just aer the recollision is determined by energy conservation. As indicated in the main text, the experimental data cannot be described by our model assuming the (e, 2e) process. In addition to the predicted recoil-ion momentum spectrum and asymmetry curve presented in Fig. 2, the two-electron correlation spectrum calculated assuming the (e, 2e) mechanism is shown in Fig. 6.

For both the (e, 2e) and RESI processes, the nal dri momentum of the rst electron depends on the scattering angle (the angle between the momentum vectors just before and just aer the recollision). The sensitivity of the simulation on the scattering angle is shown in Fig. 7 for the RESI process. We nd that the cross-shaped structure is signicantly altered if is varied by 10 degrees. Focal volume averaging is taken into account by assuming a Gaussian intensity prole, neglecting the intensity variation across the argon gas jet of 1 mm diameter.

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Acknowledgements

We acknowledge fruitful discussions with M. Lezius and H. Schrder and experimental support by C.-D. Schrter and N. Kurz. We are grateful for support by the Max Planck Society, the Chemical sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy under DE-FG02-86ER13491 and DE-FG02-00ER15053, the National Science Foundation under CHE-0822646 and the DFG via the Emmy-Noether program, the International Collaboration in Chemistry program and the Cluster of Excellence: Munich Center for Advanced Photonics (MAP). We acknowledge support by the EU via the ITN ATTOFEL and LaserLab Europe.

Author contributions

B.B. and M.K. performed the measurements and calculations, analysed and interpreted the data; N.G.J., K.J.B., O.H., R.M., R.R.J., and M.F.K. provided experimental support during the measurements; M.F.K. planned the experiment and supervised the work; part of the REMI and support in its operation was provided by A.S., R.M. and J.U.; the phase-meter and support in its operation was provided by A.M.S., T.R. and G.G.P.; B.F., N.C., T.P., I.B., and F.K. contributed to the discussion of the results; the manuscript was prepared by B.B., M.K., N.G.J., K.J.B. and M.F.K and was discussed among all authors.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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How to cite this article: Bergues, B. et al. Attosecond tracing of correlated electron-emission in non-sequential double ionization. Nat. Commun. 3:813 doi: 10.1038/ncomms1807 (2012).

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