Main

The emergence of attosecond science (1 as = 10−18 s) in the new millennium opened an exciting area of physics bringing the dynamics of electron wave functions into focus. The important goal of real-time visualization of the interplay between electrons and their role in molecular bonding now seems to be in reach. After a decade where attosecond light sources4,5 were characterized and their potential demonstrated, the next phase will include the exploration of correlated electron dynamics in complex systems. A series of ground-breaking studies on single ionization (SI) in atoms using attosecond light pulses sheds light on the escaping electron and its interaction with the residual ion6,8, and the resulting coherent superposition of neutral bound states9,10.

Double ionization (DI) by absorption of a single photon is an inherently more challenging phenomenon, both experimentally and theoretically1,2,3. The two-electron ejection can be understood only through interactions between electrons, and is usually discussed in terms of different mechanisms11. In the knockout mechanism, the electron excited by interaction with the light field (the photoelectron) collides with another electron on its way out, resulting in two emitted electrons. In the shake-off mechanism, orbital relaxation following the creation of a hole ionizes a second electron. Electron correlations may also lead to indirect DI processes via highly excited states of the singly-charged ion12. One-photon experimental investigations with the pair of electrons detected in coincidence can provide a fairly complete DI description without, however, following the dynamics of the electron correlation in real time. Multiphoton experimental investigations have been performed both on the femtosecond and attosecond timescales13,14, but DI in strong laser fields does not require electron correlation.

In this work, we study DI of xenon in the near-threshold region using attosecond extreme ultraviolet (XUV) pulses for excitation and multi-electron coincidence techniques to disentangle SI and DI events. Using an interferometric technique with a weak infrared laser field, we demonstrate the existence of different ionization mechanisms and get new insight into the quantum dynamics of one-photon DI with evidence for inter-shell correlation effects.

In our experiment (Fig. 1 and Supplementary Methods) a train of attosecond pulses corresponding to a coherent comb of odd harmonics was generated by the interaction of an intense femtosecond laser with Ar gas and focused on a jet of Xe atoms. Electrons were detected in coincidence in a magnetic bottle spectrometer and their energies retrieved from their flight times. The weak dressing infrared field was collinear with the ionizing XUV field and could be delayed with attosecond precision. Interference patterns resulting from multiple infrared-induced quantum paths were studied as a function of the delay (τ) between the XUV and infrared fields.

Figure 1: Principle of the experiment.
figure 1

A xenon atom is ionized by an XUV attosecond pulse train in the presence of a weak infrared field, with photon energy 1.54 eV and intensity of 5 × 1011 W cm−2. The electron energies are measured in a magnetic bottle electron spectrometer. The pressure and the XUV flux are chosen to detect an average of 0.07 electrons per laser shot. The experimental result is shown as a 2D coincidence spectrum. The colour indicates the probability of the electron pair as a function of the total and lowest kinetic energy of the pair, the latter denoted ‘slow electron energy’. Such maps are recorded for different delays (τ) between the attosecond and infrared pulses. The energy diagram corresponding to our interferometric scheme is shown to the right for a final-state energy near 4.6 eV.

Full size image

First we consider the interaction of Xe with XUV pulses only. Fig. 2a illustrates the relevant electronic structure in the vicinity of the double-ionization threshold together with measured and simulated two-electron coincidence spectra (Fig. 2b). The spectra contain horizontal stripes arising from different final states and harmonic orders. In agreement with previous work7, we find that 3P2 and 1D2 are the dominant Xe2+ final states. In each stripe the electron pair exhibits both a continuous energy distribution characteristic of direct DI and discrete peaks due to indirect processes. The simulation uses spectroscopic data7,15,16 and takes into account our experimental parameters (see Supplementary Methods). The excellent agreement between experimental and simulated spectra allows us to unambiguously identify the majority of the observed features.

Figure 2: Double ionization of Xe by attosecond pulse trains.
figure 2

a, Schematic energy level diagram in the vicinity of the double ionization threshold showing the XUV excitation and decay processes to the Xe2+ final states. The Xe2+ configuration has several multiplets spanning 4.5 eV due to strong spin–orbit splitting. Indirect single-photon DI occurs through autoionization of Xe+∗ Rydberg states converging to the 1S0 and1D2 states of Xe2+. b, Measured two-electron coincidence spectra compared with simulated data (see Supplementary Methods). The electron pair spectrum contains stripes with constant total kinetic energy arising from different Xe2+ final states and harmonics 23, 25 and 27, as labelled on the projection on the total energy axis (rightmost panel). The projection on the slow-electron energy axis (top panel) shows peaks due to autoionization of Xe+ 5p4 (1D)nd and (1S)nd to Xe2+ 3P2. The thickness of the orange lines indicates the Poisson standard deviation of the data, while black lines represent the simulated spectra. Because we are using an attosecond pulse train (a frequency comb), the energy resolution is given by the harmonic bandwidth (~0.2 eV) for the total energy. For the slow energy, our resolution is given by the spectrometer (~50 meV).

Full size image

The infrared field required for our interferometric measurement opens new processes for two-electron ejection17,18,19,20,21. Ionization takes place in a ‘non-sequential’ process with the absorption of two photons from the atomic ground state or via a ‘sequential’ process, where the XUV photon is absorbed by the neutral atom, and the infrared photon by the ion in an excited state. The experimental two-electron coincidence spectra obtained with both XUV and infrared radiation (Fig. 1 and Supplementary Fig. 1) exhibit features already present in Fig. 2b, albeit with modified intensity. In addition, new peaks appear throughout the spectrum and extend to higher total kinetic energy.

To understand the effect of the infrared field, we examine the difference between one-dimensional (1D) projections of spectra with and without infrared. In Fig. 3a we see a clear modulation of the projection on the total kinetic energy axis. DI peaks due to absorption of single harmonic photons (harmonic, H) are reduced whereas those due to two-colour DI (sidebands, SB) are enhanced. In Fig. 3b an enhancement of low-energy electrons induced by the infrared field is visible. The simulation including both sequential and non-sequential two-photon processes reproduces the projected experimental spectra very well. The non-sequential contribution accounts for the majority of the features seen in the projection on the total kinetic energy axis (Fig. 3a). The sequential contribution produces the low-energy peaks in the projection on the slow-electron energy axis (Fig. 3b) due to ionization from Xe+∗ states lying within one infrared photon energy below the DI threshold. There is no experimental evidence for sequential processes via higher lying (autoionizing) Rydberg states.

Figure 3: Sequential and non-sequential double ionization.
figure 3

a,b, Difference of spectra obtained with and without the infrared field. Projections on the total kinetic energy (a) and the slow electron energy axes (b). The signal unit is the same as for the projections in Fig. 2. The experimental data (orange) are well reproduced by the full simulation (black). The contributions to the simulation can be broken into sequential (dashed grey) and non-sequential (solid blue) processes, which allows us to determine their respective contributions. The non-sequential absorption is responsible for the formation of sidebands in a, whereas sequential absorption due to one infrared-photon absorption from Xe+∗ states leads to additional low-energy peaks in b. The peak at 1.3 eV in b is due to absorption from 5p4 (1D)7d and the 0.4 eV-peak is attributed to (1S)6d and (3P)7d.

Full size image

Summarizing our interpretation of the spectra, we find that xenon atoms in the presence of two (weak) XUV and infrared fields can be doubly ionized both through sequential and non-sequential processes. In contrast to previous studies using femtosecond light pulses22, both of these contributions can be clearly identified in the two-electron coincidence spectrum (Fig. 1). The sequential process affects only the region below 1.5 eV for the slow electron whereas the non-sequential process dominates when the energies of the two electrons are similar. Final states can then be populated by two quantum paths: absorption of a harmonic and an infrared photon or absorption of the next harmonic and stimulated emission of an infrared photon, as shown in Fig. 1 (right). These two paths can interfere, indicating that the two-electron wave packet remains coherent during the measurement. The interference signal, which varies with the delay between the XUV and infrared pulses, carries the signature of the two-electron emission dynamics.

We concentrate our temporal study on non-sequential DI at a fixed total absorbed energy of 40.1 eV, corresponding to sideband 26. We choose this sideband to have a clear interferometric interpretation, because sideband 26 can be reached from below by harmonic 25 and from above by harmonic 27. Fig. 4a shows the corresponding coincidence spectrum, with total kinetic energies 4.6 and 6.8 eV for ionization to the 1D2 and 3P2 states and in Fig. 4b presents the spectral regions where the signal oscillates as a function of the delay between the XUV and infrared fields. The colour-coded DI time delays are obtained by fitting the experimental data, as in Fig. 4e. The reference ‘clock’ is given by the Xe+5p−1 single ionization signal recorded in the same experimental scan. In Fig. 4e, the DI delay relative to SI is τDIexp − τSIexp = 55 ± 61 as. The uncertainty is much smaller than our measurable delay range, which is ± 670 as (half of the laser period).

Figure 4: Temporal study of double ionization.
figure 4

a, Electron pair spectrum corresponding to non-sequential DI. The colour scale is the same as in Fig. 2b. b, Experimental delays (τDIexp − τSIexp). Coloured areas indicate spectral regions where the signal oscillates in the experiment. c,d, Calculated delays (τDItheo − τSItheo) for the shake-off (c) and knockout (d) mechanisms with τSItheo = −50 as. The red labels on the right indicate the final ionic states corresponding to sideband 26 (above the dashed line) and sideband 24 (below the dashed line). e, SI and DI signals as a function of infrared delay. The DI signal is due to direct ionization to the 1D2 state (dashed box in a). In the case of DI, the vertical error bar is statistical, corresponding to one-standard deviation for a Poissonian distribution, whereas for SI, it arises from fitting a sideband intensity profile to the photoelectron spectrum. Horizontal error bars show the standard deviation of raw data points between different scans. See Supplementary Methods for further details.

Full size image

A quantum mechanical description of SI time delays involved in attosecond interferometric experiments6 (or similarly in streaking8,23) shows that the measured delay is the sum of two different contributions: the group delay of the electronic wave packet created by one-photon absorption (τSI1ph), which contains information on the atomic potential, and the delay added by the interaction with the infrared field24,25,26 (τcc). In general τSI1ph = ∂ arg M/∂ E, where M is the (complex) photoionization matrix element and E is the (total) kinetic energy (atomic units are used throughout). In the case of single ionization and a dominant non-interacting channel with a certain angular momentum, τSI1ph = dη/dE is the so-called Wigner delay, equal to the derivative of the scattering phase η. It describes the dispersion of the electronic wave packet in the potential well, analogous to the group delay dispersion of a light pulse in a medium. The interaction with the infrared field results in a negative delay (τcc < 0), which can be calculated analytically using asymptotic expressions for the continuum wave functions26.

The theoretical description of double ionization is still an open problem, especially for complex systems such as xenon27 and, to date, there is no formalism regarding the delay for the escape of the two electrons. In the present work, we establish using lowest-order many-body perturbation-theory (see Supplementary Methods) that the measured delay is equal to τDI1ph + τcc, with

τDI1ph is expressed as the average of the one-electron emission delays, E1 and E2 being the kinetic energies of the two emitted electrons, plus a correction term τee describing the interaction between the two electrons. We calculate τDI1ph using the random phase approximation with exchange28 for the two fundamental direct DI mechanisms (shake-off and knockout, see Supplementary Methods). These time delays are positive, typically a few hundreds of attoseconds, and compensate those due to the interaction with the infrared field (τcc).

The results of our calculations are presented in Fig. 4c,d. The near synchronization between SI and DI observed in the experiment is supported in the calculations. For the particular case shown in Fig. 4e, we have τDItheo − τSItheo = +80 as for shake-off and τDItheo − τSItheo = +5 as for knockout. Our experimental result lies closer to the calculated value for the shake-off mechanism. In helium, shake-off can be described by taking the overlap between the neutral and ionic one-electron wavefunctions11 (sudden approximation), but in xenon 5s and 5p inter-shell correlation effects must be included. Our analysis emphasizes the need for first-principles calculations to obtain a quantitative evaluation of the relative strength between shake-off and knockout and to include the influence of other mechanisms, for example DI via an indirect process23.

In conclusion, we demonstrate that interferometric methods with attosecond pulses give us new insight into several aspects of DI (sequential/non-sequential, direct/indirect and shake-off/knockout). With further refinement of both attosecond sources at higher repetition rate and coincidence schemes, including for example angular resolution, our approach could be extended to the dynamics of more complex systems with potential applications in materials science29 and biology30.