SUPPLEMENTARY INFORMATION · PDF fileThe synthesis of these sub-femtosecond pulses is achieved by high-harmonic generation in a 2 mm gas cell a hole diwith ameter

In the format provided by the authors and unedited.

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

#Theseauthorscontributedequallytothiswork.*Correspondingauthors:[email protected],[email protected]

SUPPLEMENTARY INFORMATION

State-resolved attosecond reversible and irreversible dynamics in

strong optical fields Mazyar Sabbar1#*, Henry Timmers1#, Yi-Jen Chen2,3#, Allison K. Pymer4, Zhi-Heng Loh5, Scott

G. Sayres6,7, Stefan Pabst8,9, Robin Santra2,3, Stephen R. Leone1,10,11*

1Department of Chemistry, University of California, Berkeley, CA 94720, USA 2Center for Free-Electron Laser Science, DESY, D-22607 Hamburg, Germany 3Department of Physics, University of Hamburg, D-20355 Hamburg, Germany 4Eastman Chemical Company, Kingsport, TN 37660, USA 5Division of Chemistry and Biological Chemistry, and Division of Physics and Applied Physics, School of Physical

and Mathematical Sciences, and Centre for Optical Fibre Technology, The Photonics Institute, Nanyang

Technological University, Singapore 639798, Singapore 6School of Molecular Sciences, Arizona State University, Tempe, AZ 85287, USA 7Biodesign Center for Applied Structural Discovery, Arizona State University, Tempe, AZ 85287, USA 8ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA 9Physics Department, Harvard University, Cambridge, MA 02138, USA 10Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 11Department of Physics, University of California, Berkeley, CA 94720, USA

Sec. 1 Experiment

Sec. 1.1 Details on the experimental technique

Intense few-cycle pulses with a 5.2 fs duration were generated by compressing the output of a

commercial carrier-envelope-phase (CEP) stabilized amplifier system (Femtopower Pro,

Femtolasers GmbH), which delivers near-infrared (NIR) pulses (centered at 790 nm) of 26 fs

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS4027

NATURE PHYSICS | www.nature.com/naturephysics 1

http://dx.doi.org/10.1038/nphys4027

http://www.nature.com/naturephysics


2

Figure S1 Illustration of the apparatus used to conduct ATAS measurements and temporal characterization

of the NIR and XUV pulses. A few-cycle NIR pulse first hits a beamsplitter with a ratio of 50:50 thereby creating

two equally strong laser pulses. The reflected part is used to generate an attosecond pulse via HHG. A hole mirror is

then used to recombine the attosecond beam with the delay-adjustable NIR pulse originating from the transmission

on the beamspltter. The two spatially and temporally overlapped pulses are subsequently focused into either of two

different types of targets to perform absorption or electron spectroscopy with attosecond time resolution. To avoid

overly confusing beampaths, the delay stabilization scheme has been excluded in this schematic. More details can be

found in the supplementary text.

duration and 2 mJ pulse energy at a repetition rate of 1 kHz. The compression into the few-cycle

limit is achieved in a homebuilt hollow-core fiber filled with neon at a pressure of around 2 bar in

combination with a broadband chirped mirrors compressor (Ultrafast Innovations GmbH). The

overall transmission through the compression stage typically corresponds to about 40%,

effectively providing few-cycle pulses with ~ 0.8 mJ energy available for experiments. Figure S1

illustrates the setup used following the compression: The NIR pulses are coupled into an

attosecond interferometer through a broadband beamsplitter with a 50:50 ratio. The one arm






3

following the reflection of the beam contains the NIR strong-field pump pulses that can be

precisely delayed with respect to the other arm in which the attosecond probe pulses are

generated. The synthesis of these sub-femtosecond pulses is achieved by high-harmonic

generation in a 2 mm gas cell with a hole diameter of 300 µm backed with about 30 Torr of

argon. To ensure the isolation of single attosecond pulses, a combination of an amplitude gate1,2

and a weak polarization gate is used. Details about this technique, which is referred to as

Polarization ASSisted Amplitude GatE (PASSAGE), can be found elsewhere3. An aluminum

filter of 200 nm thickness is used as a high-pass filter that blocks out the residual NIR driving

field and transmits most of the attosecond XUV radiation. The interferometer is subsequently

finalized by recombining both arms with the help of a silver mirror with a central hole. To control

the delay between both pulses, a Piezo-driven retro reflector stage has been set up in the beam

path of the NIR beam. This delay stage is actively stabilized by monitoring the spatial

interference fringes of a co-propagating CW laser4,5. The scheme typically allows for a long-term

stability of about 25 as rms. However, the use of the automated shutter in one arm of the

interferometer operated at a frequency of around 0.5 Hz leads to a periodic loss of interference

fringes and hence the information about the delay position (phase). In this configuration, which

has been applied in this study, we achieve a stability of about 80 as rms. It is worth noting that

while this approach allows for a well-defined delay increment, the choice of a time zero still

remains arbitrary.

The two spatially and temporally overlapping pulses are focused with a toroidal mirror

into an absorption cell of 4 mm thickness filled with Xe. The Xe pressure was varied to achieve

highest optical densities without exceeding the critical density at which significant reabsorption

occurs. To finally record the absorption features imprinted onto the attosecond pulse, we first






4

Figure S2 Attosecond pulse characterization. The attosecond pulses used to conduct the ATAS measurement have

been characterized by applying the FROG-CRAB method. The measured trace is shown in a. It has been fed into the

algorithm and run for 10,000 iteration steps. The resulting reconstructed trace depicted in b nicely resembles the

characteristics of the experimental data. From the quantities involved in the reconstruction the corresponding spectral

(c) and temporal characteristics (d) of the attosecond pulse can be accurately determined.

block the strong NIR field using a 200 nm aluminum filter. The spectrum of the residual XUV

radiation is then measured with a homebuilt spectrometer consisting of a concave diffraction

grating and an XUV sensitive CCD camera. Absorption spectra are recorded as a function of time

delay between the isolated attosecond pulse and the NIR by measuring instantaneous delta optical

densities given by ΔOD= -ln(Ion/Ioff). Here Ion and Ioff correspond to the XUV spectra taken with

and without the NIR pulse, respectively using a shutter in the NIR arm. These high fidelity ΔOD

Temporal domainSpectral domain

ReconstructionMeasurement6055504540353025

Elec

tron

ener

gy (e

V)

-4 0 4 Delay (fs)

1.0

0.8

0.6

0.4

0.2

0.0

Norm. intensity

Delay (fs)

6055504540353025

Elec

tron

ener

gy (e

V)

-4 0 4

1.0

0.8

0.6

0.4

0.2

0.0

Norm. intensity

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mali

zed

spec

tral in

tens

ity

806040200 Electron energy (eV)

-2

-1

0

1

2

Spectral phase (rad)163 as

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mali

zed

tem

pora

l inte

nsity

-1000 -500 0 500 1000 Time (as)

-4

-2

0

2

4

Temporal phase (rad)

a b

c d






5

spectra have been achieved by averaging over 50 subsequently repeated measurements at each

delay step, where the exposure time of the CCD camera for each spectrum (Ion and Ioff) was set to

0.5 s.

To characterize the temporal properties of the high harmonic radiation we have

implemented an electron time-of-flight spectrometer and an effusive gas jet, which are used to

conduct attosecond streaking spectroscopy1,2,6. This technique in conjunction with an iterative

algorithm known as FROG-CRAB7 (Frequency-Resolved Optical Gating for Complete

Reconstruction of Attosecond Bursts) allows for the reconstruction of the temporal properties of

the XUV pulse. Before each set of absorption measurements, we first record streaking spectra in

neon to ensure that a single, isolated attosecond pulse is produced. Figure S2 presents the

corresponding measured (Fig. S2a) and reconstructed (Fig. S2b) spectrograms. The FROG-

CRAB reconstruction based on the LSGPA8 (Least-Square Generalized Projection Algorithm)

reveals a clean attosecond pulse with a duration of 163 as. From the modulation of the electron

spectra, which essentially follows the vector potential of the NIR laser pulse, the waveform of the

NIR pulse is also extracted. The FWHM pulse duration of the NIR field is 5.2 fs.

Sec. 1.2 Experimental results

For this study, ATAS measurements have been performed for two intensities at 2.0x1014 and

3.5x1014 W/cm2. The corresponding recorded raw traces are shown in Fig. S3a and b. For the

surface plot representation of the data recorded with 3.5x1014 W/cm2 (Fig. 1b of the main

manuscript) a weak Fourier-filter has been applied to remove fast energetic structures in each

transient absorption spectrum. Figure S3c depicts the details of the filtering exemplarily for the

spectrum at the last delay position at Δt=7.6 fs. For the sake of convenience, the Fourier-

transform is not represented as a function of the corresponding time in the Fourier domain.






6

Figure S3 Raw and Fourier-filtered ATAS spectrograms. Panels a and b depict the raw traces recorded for this

study with NIR intensities of 2.0x1014 W/cm2 and 3.5x1014 W/cm2 . For the surface plot representation of the

transient absorption trace with an intensity of 3.5x1014 W/cm2 a Fourier filter on each spectrum has been applied. A

super-Gaussian function in the Fourier domain removes oscillatory features with periods faster than about 0.17 eV

(c), here shown for the last delay position at Δt=7.6 fs. Panel d shows the resulting Fourier-filtered trace.

Instead the time axis t has been converted to energy (E=h/t) to allow for a convenient comparison

to the resolution of the spectrometer. As is indicated in Fig. S3c, in each recorded spectrum only

components below 0.17 eV are removed. Given the instrument’s resolution of about 0.2 eV, it is

reasonable to attribute the filtered portion to instrumental noise.

While the weak Fourier-filter has been applied to produce Fig. 1b of the main paper, the

actual extraction of the populations (presented in Fig. 2) has been performed on the measured raw

data, thus avoiding any sort of data-processing-induced artifacts that could lead to systematic

errors in the population dynamics extraction. Finally Fig S3d depicts the Fourier-filtered scan for

the intensity of 3.5x1014 W/cm2. A qualitative comparison to Fig. S3b illustrates that the filtering






7

process does not change the observed lineshape but allows for the removal of high frequency

structures that cannot be resolved with the instrumental resolution.

Sec. 1.3 Extracting time traces via fitting model

We use the fitting model proposed by S. Pabst et al.9 to extract the effective SFI dynamics from

the ATAS data with overlapping pump and probe pulses. The corresponding expression is given

by

𝜎𝜎"#$(𝜔𝜔, 𝜏𝜏) = 4𝜋𝜋𝜔𝜔𝑐𝑐 𝑧𝑧0(𝜏𝜏)

Γ0/2 cos𝜙𝜙0(𝜏𝜏)+ 𝜔𝜔 − 𝜔𝜔0 sin𝜙𝜙0(𝜏𝜏)𝜔𝜔 − 𝜔𝜔0 < + Γ0</40

,

where σdip denotes the absorption cross section, T is the specific spectral line under consideration,

ω and ωT are the photon frequency and transition frequency, respectively, ΓT is the lifetime of the

excited state, and zT and φT denote the transition strength and the dipole phase, respectively.

This model has been successfully applied to the analysis of an experiment conducted by

A. Wirth et al.10. For each spectral line T, there are two delay-dependent fitting parameters in the

model, zT(τ) and φT(τ). The parameter φT(τ) is designed to capture the lineout deformation, whose

physical origin has been explained in Ref. 9. Here, we focus on the other fitting parameter zT(τ),

which is proportional to the effective valence-hole population zT(τ)= |dT|2𝜌𝜌>?@@(𝜏𝜏). In this equation,

dT is the dipole transition matrix element between the specific 5p hole and 4d hole along the

polarization axis. Strictly speaking, the above interpretation is correct under the condition that

there is no quantum coherence between (5p1/2)-1 and (5p3/2)-1 in the ion sub-system. An analytical

theory for the ATAS with non-overlapping pump and probe pulses11 clearly shows that this

coherent superposition of the ionic states can make an additional contribution to the spectral line

corresponding to the transition (5p1/2)-1→ (4d3/2)-1 while probing the dynamics after the SFI

process (Note that this multichannel coherence can also affect the spectral line corresponding to






8

the transition (5p3/2)-1→ (4d3/2)-1, whose ionization dynamics are beyond the scope of the current

study due to the low signal-to-noise ratio in the experimental and stimulated ATAS

spectrograms). As will be shown in the next section, such multichannel coherence has a

negligible impact on zT(τ) while probing the dynamics during the SFI process. Hence, the

effective dipole strength zT(τ) represents the effective hole population 𝜌𝜌>?@@ 𝜏𝜏 for both (5p1/2)-1

and (5p3/2)-1 when the pump and probe pulses overlap.

While the above expression was directly used for fits to the TDCIS datasets, for the

experimental data, the finite spectral resolution of the apparatus has to be taken into account. This

is accomplished via a convolution of the above fitting expression with a Gaussian function that

resembles the spectrometer resolution of about 200 meV.

Sec. 1.5 Error bars on experimental raw data

The error bars shown in Fig 2 of the main manuscript represent the error given by the uncertainty

of the fitting procedure described in Sec. 1.3. (95% confidence interval). Besides the fitting error,

there is also the error bars given by the uncertainty of the measurement of the ΔOD itself.

Unfortunately, this value was not assessed during the experimental acquisition. However, the

performance of the instrument has proven to be robust, and we thus measured the error bars of a

typical Xe ATAS scan in a post-measurement.

The result can be seen in Fig. S4. Across the Xe+ absorption range, the error bars exhibit a value

of ~ 0.01 ΔOD under similar experimental acquisition times – a result that is consistent with the

observed accuracy of the measured structures.






9

Figure S4 Error bars from a typical Xe ATAS lineout with 50 subsequently measured ΔOD runs. The error

bars represent a standard deviation of ~ 0.01 ΔOD throughout the scan.

Sec. 2 Theory

Sec. 2.1 Effects of multichannel coherence on the retrieved effective (5p1/2)-1 hole dynamics

As mentioned in the above section, in order to associate the effective transition strength zT(τ) of

the spectral line (5p1/2)-1→ (4d3/2)-1 to the effective (5p1/2)-1 population, the multichannel

coherence between (5p1/2)-1 and (5p3/2)-1, which is described by the off-diagonal element of a

reduced ion density matrix (IDM)9,12, must have a negligible impact on the retrieved zT(τ)9,11.

For the spectral line (5p3/2)-1→ (4d5/2)-1, the multichannel coherence does not affect zT(τ), so the

effective transition strength directly represents the effective (5p3/2)-1 population9,11.






10

Numerically, we can easily switch off the effects of multichannel coherence by

performing a single-channel calculation in the TDCIS model12. In this simplified calculation, the

few-cycle NIR is only allowed to generate a (5p1/2)-1 hole and is forbidden to form a (5p3/2)-1 hole,

so the off-diagonal IDM matrix element 𝜌𝜌ABC/D,ABE/D is automatically zero.

Figure S5 Comparison between the calculated transition strength zT(τ) in the simplified single-channel model

and in the multi-channel model for the 5p1/2 channel. The NIR intensity is 1.5x1014 W/cm2.

Figure S5 shows the comparison between the effective transition strength in the simplified

single-channel calculation and that in the multichannel calculation. The ATAS spectra are

calculated at a NIR peak intensity of 1.5x1014 W/cm2, and the effective transition strengths for the

(5p1/2)-1 channel are obtained by fitting the spectra using the aforementioned fitting model9. The

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

-2 -1 0 1 2 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

z T(τ

) in

sing

le-c

hann

el c

alc.

(arb

.u.) zT (τ) in m

ultichannel calc. (arb.u.)

Time delay (fs)

Effective transition strength zT(τ) for 5p-10.5 → 4d-1

1.5

E(t)2Single-channel calculationMultichannel calculation






11

effective transition strengths predicted by the two models clearly exhibit the same dynamics (up

to a scaling constant). Particularly, the overshoots occur at the same time delays. The only

difference between the two is the absolute magnitude of zT(τ). The zT(τ) in the single-channel

calculation has a larger magnitude, because the 5p1/2 channel in this case does not need to

compete with the 5p3/2 channel to depopulate the Xe neutral ground state. Fig. S5 provides

evidence that all the temporal structures of zT(τ) seen in the multichannel calculations and in the

experiment can be attributed to the dynamics of the effective hole populations 𝜌𝜌>?@@(𝜏𝜏) ; the

multichannel coherence does not bring any interference effect on the sub-cycle dynamics of zT(τ)

when the pump and probe pulses temporally overlap.

Sec. 2.2 Effects of many-electron correlations on valence-hole dynamics during SFI

processes

Our TDCIS theory includes essential electron correlation effects beyond the description of the

mean-field model12,13. Hence, by turning on and off the residual electron-electron interactions in

our simulations, we are able to assess the importance of many-electron effects during the SFI

process13.

Figure S6 shows the instantaneous valence-hole dynamics calculated with and without the

many-electron correlations within TDCIS. The instantaneous dynamics are computed in the sole

presence of the few-cycle NIR pump pulse (without the XUV probe) at an intensity of 2.8x1014

W/cm2. Since the instantaneous hole dynamics closely resemble the effective hole dynamics

extracted from ATAS (see Figure 3 in the main article), we will discuss how various properties of

the N-electron Hamiltonian influence the instantaneous dynamics in this and the next sections.

The hole dynamics with and without the residual electron-electron interactions almost lie on top

of each other. This demonstrates that the many-electron effects only play a minor role in the sub-






12

Figure S6 Instantaneous valence-hole dynamics with and without the many-electron effects during the few-

cycle SFI process. The NIR intensity is 2.8x1014 W/cm2 in the calculation.

cycle SFI process, and that the photoelectron’s dynamics can be viewed as a movement in an

effective potential generated by the ion.

Sec. 2.3 Effects of the long-range Coulomb potential on valence-hole dynamics during SFI

processes

The above analysis shows that we can adopt the notion of an effective potential to picture the

interaction between the photoelectron and the ionic core during the SFI process. An important

question immediately follows: how important is the long-range Coulomb tail of the ionic

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-2 -1 0 1 2

Inst

anta

neou

s ho

le p

opul

atio

ns

Time delay (fs)

E(t)2

5p-11.5: with correlations

5p-11.5: without correlations

5p-10.5: with correlations

5p-10.5: without correlations






13

Figure S7 Instantaneous valence-hole dynamics with and without the long-range Coulomb effects during the

few-cycle SFI process. The NIR intensity is 2.8x1014 W/cm2 in the calculation.

potential for the sub-cycle SFI dynamics, which is commonly ignored in SFI models such as the

standard SFA14-18?

In the afore-shown valence-hole dynamics without electronic correlations, the

photoelectron feels an ionic potential with -1/r dependence at large electron-ion distances. Here,

we perform another calculation, where the ion-electron interaction is discarded and the excited

electron simply senses the short-range Hartree-Fock potential of the neutral xenon atom13.

Figure S7 shows the calculated SFI valence-hole dynamics with and without the effects of

the long-range ionic potential. Evidently, the Coulomb tail has a dramatic impact on the few-

cycle SFI dynamics. Without the Coulomb interaction, the ionization rates for both the 5p3/2 and

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-2 -1 0 1 2Time delay (fs)

E(t)2

5p-11.5: with Coulomb

5p-11.5: without Coulomb

5p-10.5: with Coulomb

5p-10.5: without Coulomb

Inst

anta

neou

s ho

le p

opul

atio

ns






14

5p1/2 channels are much lower. Also, the absolute time delays between the overshoots in the hole

dynamics and the local maxima of E2(τ) as well as the relative time delays between the

overshoots of (5p1/2)-1 and (5p3/2)-1, which can be measured in the experiment, are notably

reduced. The importance of Coulomb interaction on the sub-cycle SFI processes has also been

discussed in the theoretical study of O. Smirnova et al19.

The Coulomb effects enhance the irreversible tunneling hole generation mechanism as

well as the reversible polarization hole generation mechanism. A long-range potential has a lower

and thinner potential barrier when it is tilted by the laser field, and thereby gives a higher tunnel

ionization rate and ion yield (see the increments of the ionization steps and the final ion yields in

Fig.7). Because a long-range potential accommodates more bound states than a short-range

potential, it predicts a higher polarizability (see the amplitudes of the oscillatory features in the

hole dynamics at τ < -2 fs in Fig. S7).

Sec. 2.4 Calculations of wave-packet densities within TDCIS

Here we explain the detailed numerical procedure to obtain the snapshots of the wave-packet

densities shown in Fig. 5. For simplicity, we neglect spin-orbit splitting here so that the angular

part of the hole orbital is just a single spherical harmonics (With spin-orbit splitting, the hole

orbital is a spinor whose two components are characterized by two different spherical

harmonics8). Without loss of generality, we choose 5p0 as the active hole orbital (or ionization

channel)12,13. As the Hamiltonian has cylindrical symmetry about the polarization axis z, we plot

the dynamics of the field-induced 1-particle charge density of the N-body wave function in the x-

z plane. We assume a half-cycle NIR pulse with a cosine envelope.

To derive the expression for the induced 1-particle charge density of the N-body wave

function, first we introduce the wave function ansatz within TDCIS12,13:






15

|𝜓𝜓 𝑡𝑡 = 𝛼𝛼J(𝑡𝑡)|ΦJ + 𝛼𝛼LMM,L

(𝑡𝑡)|ΦLM ,

where |ΦJ is the mean-field Hartree-Fock ground state, and |ΦLM is a singly excited

configuration (with a hole in active occupied orbital i and an electron in virtual orbital a). Time

dependence of the wave function is encapsulated in the time-dependent expansion coefficients

𝛼𝛼J(𝑡𝑡) and 𝛼𝛼LM(𝑡𝑡). The 1-particle charge density20 of the N-electron wave function at a time t

reads:

𝑛𝑛 𝒙𝒙, 𝑡𝑡 = − 𝜓𝜓 𝑡𝑡 ΨQ 𝒙𝒙 Ψ 𝒙𝒙 𝜓𝜓 𝑡𝑡 1

= 𝑛𝑛J 𝒙𝒙 + 𝑛𝑛STSU 𝒙𝒙, 𝑡𝑡 + 𝑛𝑛VWTS 𝒙𝒙, 𝑡𝑡 + 𝑛𝑛STSUXVWTS 𝒙𝒙, 𝑡𝑡 .

Here,

𝑛𝑛J 𝒙𝒙 = − 𝜑𝜑[Q 𝒙𝒙 𝜑𝜑[ 𝒙𝒙

[

,

𝑛𝑛STSU 𝒙𝒙, 𝑡𝑡 = − 𝛼𝛼LM∗ 𝑡𝑡 𝛼𝛼L] 𝑡𝑡 𝜑𝜑M

Q 𝒙𝒙 𝜑𝜑] 𝒙𝒙M,],L

,

𝑛𝑛VWTS 𝒙𝒙, 𝑡𝑡 = + 𝛼𝛼LM∗ 𝑡𝑡 𝛼𝛼^M 𝑡𝑡 𝜑𝜑L

Q 𝒙𝒙 𝜑𝜑^ 𝒙𝒙 ,M,L,^

and

𝑛𝑛STSUXVWTS 𝒙𝒙, 𝑡𝑡 = −2ℛℯ 𝛼𝛼LM∗ 𝑡𝑡 𝛼𝛼J 𝑡𝑡 𝜑𝜑M

Q 𝒙𝒙 𝜑𝜑L 𝒙𝒙M,L

.

In Eq.(1), Ψ 𝒙𝒙 is the field operator14. 𝑛𝑛J 𝒙𝒙 represents the ground-state charge density, which is

a summation over the densities of all the occupied spin orbitals φb 𝒙𝒙 in the ground state. As

𝑛𝑛J 𝒙𝒙 is a constant and involves no dynamics, we do not plot this “back-ground” density in Fig.

5. 𝑛𝑛STSU 𝒙𝒙, 𝑡𝑡 represents the electron charge density, with φc 𝒙𝒙 and φd 𝒙𝒙 being virtual

orbitals. 𝑛𝑛VWTS 𝒙𝒙, 𝑡𝑡 is the hole charge density, with φ# 𝒙𝒙 and φe 𝒙𝒙 being active occupied

orbitals. Finally, 𝑛𝑛STSUXVWTS 𝒙𝒙, 𝑡𝑡 stands for the charge density due to the interference between the






16

electron and the hole. This interference term can govern 𝑛𝑛 𝒙𝒙, 𝑡𝑡 only if the excited electron stays

close to the hole. This is exactly what happens in the reversible hole creation mechanism: the

transiently displaced electron cloud created through ground-state polarization always stays

nearby the ion, hence producing an induced charge density with compact and intricate

interference patterns (see Fig. 5a). In the irreversible hole creation mechanism, the excited

electron is quickly stripped away from the ion after tunnel ionization. Hence, the wave-packet

density shows almost no interference pattern and is dominated by the individual electron charged

density 𝑛𝑛STSU 𝒙𝒙, 𝑡𝑡 and the hole charge density 𝑛𝑛VWTS 𝒙𝒙, 𝑡𝑡 (see the snapshots at t > -T/8 in Fig.

5b).

References1 Kienberger,R.etal.Atomictransientrecorder.Nature427,817-821(2004).2 Goulielmakis,E.etal.Single-CycleNonlinearOptics.Science320,1614-1617(2008).3 Timmers,H.etal.Polarization-assistedamplitudegatingasaroutetotunable,high-

contrastattosecondpulses.Optica3,707-710(2016).4 Chini,M.etal.Delaycontrolinattosecondpump-probeexperiemts.OpticsExpress

17(2009).5 Sabbar,M.etal.CombiningattosecondXUVpulseswithcoincidencespectroscopy.

ReviewofScientificInstruments85,103113(2014).6 Drescher,M.etal.X-raypulsesapproachingtheattosecondfrontier.Science291,

1923-1927(2001).7 Mairesse,Y.&Quéré,F.Frequency-resolvedopticalgatingforcomplete

reconstructionofattosecondbursts.Phys.Rev.A71,011401(2005).8 Gagnon,J.,Goulielmakis,E.&Yakovlev,V.S.TheaccurateFROGcharacterizationof

attosecondpulsesfromstreakingmeasurements.Appl.Phys.B92,25–32(2008).9 Pabst,S.etal.Theoryofattosecondtransient-absorptionspectroscopyofkryptonfor

overlappingpumpandprobepulses.Phys.Rev.A86,063411(2012).10 Wirth,A.etal.Synthesizedlighttransients.Science334,195-200(2011).11 Santra,R.,Yakovlev,V.S.,Pfeifer,T.&Loh,Z.-H.Theoryofattosecondtransient

absorptionspectroscopyofstrong-field-generatedions.Phys.Rev.A83,033405(2011).

12 Greenman,L.etal.Implementationofthetime-dependentconfiguration-interactionsinglesmethodforatomicstrong-fieldprocesses.Phys.Rev.A82,023406(2010).

13 Pabst,S.,Greenman,L.,Mazziotti,D.A.&Santra,R.ImpactofmultichannelandmultipoleeffectsontheCooperminimuminthehigh-order-harmonicspectrumofargon.Phys.Rev.A85,023411(2012).






17

14 Keldysh,L.V.Ionizationinthefieldofastrongelectromagneticwave.Sov.Phys.JETP20,1307-1314(1965).

15 Perelomov,A.M.,Popov,V.S.&Terent'ev,M.V.Ionizationofatomsinanalternatingelectricfield.Sov.Phys.JETP23,924-934(1966).

16 Faisal,F.H.M.Multipleabsorptionoflaserphotonsbyatoms.J.Phys.B6,L89-L92(1973).

17 Reiss,H.R.Effectofanintenseelectromagnetic-fieldonaweaklyboundsystems.Phys.Rev.A22,1786-1813(1980).

18 Popruzhenkoab,S.V.&Bauera,D.StrongfieldapproximationforsystemswithCoulombinteraction.J.Mod.Opt.55,2573-2589(2008).

19 Smirnova,O.,Spanner,M.&Ivanov,M.Coulombandpolarizationeffectsinsub-cycledynamicsofstrong-fieldionization.J.Phys.B:At.Mol.Opt.Phys.39,S307(2006).

20 Szabo,A.&Ostlund,N.S.ModernQuantumChemistry:IntroductiontoAdvancedElectronicStructureTheory.DoverPublicationsInc.,Mineola,NewYork(1996).





Documents

SUPPLEMENTARY INFORMATION · PDF fileThe synthesis of these sub-femtosecond pulses is achieved by high-harmonic generation in a 2 mm gas cell a hole diwith ameter