Two-center Interference in the Photoionization Delays of Kr 2 Saijoscha Heck1Meng Han1Denis Jelovina1Jia-Bao Ji1Conaill Perry1 Xiaochun Gong2Robert Lucchese3Kiyoshi Ueda1 4and Hans Jakob W orner1y

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Two-center Interference in the Photoionization Delays of Kr2

Saijoscha Heck,1Meng Han,1, ∗Denis Jelovina,1Jia-Bao Ji,1Conaill Perry,1

Xiaochun Gong,2Robert Lucchese,3Kiyoshi Ueda,1, 4 and Hans Jakob W¨orner1, †

1Laboratorium f¨ur Physikalische Chemie, ETH Z¨urich, 8093 Z¨urich, Switzerland.

2State Key Laboratory of Precision Spectroscopy,

East China Normal University, Shanghai, China

3Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

4Department of Chemistry, Tohoku University, Sendai, 980-8578, Japan

(Dated: October 21, 2022)

We present the experimental observation of two-center interference in the ionization time delays

of Kr2. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the pho-

toionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a

function of the electron kinetic energy, an eﬀect that is traced back to constructive and destructive

interference of the photoelectron wave packets that are emitted or scattered from the two atomic

centers. Our interpretation of the experimental results is supported by solving the time-independent

Schr¨odinger equation of a 1D double-well potential, as well as coupled-channel multiconﬁgurational

quantum-scattering calculations of Kr2. This work opens the door to the study of a broad class of

quantum-interference eﬀects in photoionization delays and demonstrates the potential of attosecond

coincidence spectroscopy for studying weakly bound systems.

Two-center interference is one of the most prominent

manifestations of the wave character of matter. The sim-

plest demonstration consists of a double slit as it was ﬁrst

done in 1801 by Thomas Young with light waves [1] and

in 1961 by Claus J¨onsson with electrons [2]. Soon after

that it was noted by Cohen and Fano [3] that the electron

wave from photoionization of diatomic molecules resem-

bles the one behind the double slit. Since then, there

have been numerous investigations of the molecular dou-

ble slit in diatomic molecules [4–13]. The interference

can be simply described with the superposition of two

spherical waves departing from each atom of a diatomic

molecule:

Ψ1,2=1

|r|·ei(k(r±R/2)+Φ),(1)

with an internuclear distance R, momentum kand ini-

tial phase shift Φ [14]. So far, most of the experi-

ments have studied the photoionization cross section of

aligned [4, 6, 7, 9, 11, 13, 15] and unaligned [3] diatomic

molecules. More recently the inﬂuence of two-center in-

terference on high-harmonic generation (HHG) was in-

vestigated in CO2[5, 16–19] and H2[8, 20].

Owing to the fact that photoionization delays are in-

deed closely linked with the variation in the cross section

[21], it is expected that two-center interference also has a

signiﬁcant impact on the ionization dynamics in the time

domain. Vladislav Serov and other theoretical physicists

made several pioneering predictions of such eﬀects [22–

28] on H2and H+

2molecules. However, until now there

has been no experimental observation of the inﬂuence of

the two-center interference on the photoionization delays.

∗menhan@ethz.ch

†hwoerner@ethz.ch

Here, we report the photoionization delay of the krypton

dimer relative to its monomer and observe oscillations in

the delay that can be traced back to the interference of

the electron wave packets that are emitted or scattered

from the two weakly bound atoms in Kr2.

The experiment was performed by combining an

XUV attosecond pulse train (APT) generated via high-

harmonic generation (HHG) in a 3 mm long gas cell ﬁlled

with 20 mbar of xenon, covering the odd-order harmon-

ics from H9 to H21, with an electron-ion coincidence

spectrometer. The APT is focused into a cold krypton

gas beam which is produced via supersonic expansion,

where it is spatially and temporally overlapped with a

near-infrared (NIR) pulse of co-linear polarization. The

APT and NIR pulses are phase locked in an actively-

stabilized Mach-Zehnder interferometer and their delay

is controlled with a piezo-electric translation stage. Upon

photoionization, the electrons and ions are detected in

coincidence using COLd Target Recoil Ion Momentum

Spectroscopy (COLTRIMS) [29, 30], which measures the

three-dimensional momentum vectors of electrons and

ions. A more detailed account of the experimental ap-

paratus can be found in [31]. The photoelectron spectra

of Kr and Kr2are measured simultaneously for XUV-

NIR delays between 0 to 7 fs, using the Reconstruction

of Attosecond Beating By two-photon Transitions (RAB-

BIT) technique [32–35]. In RABBIT the intensity of the

sidebands, which are the photoelectron bands generated

by the additional absorption or emission of a single NIR

photon by a photoelectron, oscillates as a function of the

XUV-NIR delay τas

ISB =A+B∗cos(2ωNIRτ−ΦXUV −Φsys),(2)

where A and B are constants, ωNIR is the center fre-

quency of NIR. ΦXUV is the spectral phase diﬀerence

between the two adjacent harmonic orders (which char-

acterizes the attochirp) and Φsys is the system-speciﬁc

arXiv:2210.11136v1 [physics.atom-ph] 20 Oct 2022

50 100 150 200

Mass-over-charge ratio

-10

Position (mm)

XUV-IR time delay (fs)

lectron energy (eV)

0.2

0.4

0.6

0.8

(a)

(b) (c)

0246

0 2 4 6

SB10

SB12

SB14

SB16

SB18

SB20

3/2

1/2

Fig. 1. (a) Measured ionic distribution as a function of the

mass-over-charge ratio and the hit position on the detector

along the direction of the supersonic molecular beam. The

counts are shown on a logarithmic scale and displayed in

false color. (b,c) RABBIT spectrograms for electrons

detected in coincidence with undissociated Kr+and Kr+

corresponding to the sharp distributions labeled with dashed

ellipses in (a), respectively. Counts are normalized and

shown in false color. In (b), the red and green arrows

indicate the energy positions ionized by harmonic 11 for the

two spin-orbit-coupling split states 2P3/2and 2P1/2of Kr+

respectively.

phase term. The latter is what we are interested in.

In Figure 1a, we illustrate the measured ionic distri-

bution as a function of the mass-over-charge ratio and

the hit position on the detector. The sharp distributions

of Kr+and Kr+

2(see dashed ellipses in Fig. 1a) indi-

cate that these ions are from the undissociated channel,

and their surrounding diﬀuse distribution of ions orig-

inates from the dissociative ionization channels of the

larger clusters due to the kinetic-energy release in frag-

mentation. Figures 1b and 1c show the RABBIT spectro-

grams for photoelectrons measured in coincidence with

the undissociated Kr+and Kr+

2, respectively. The pho-

toelectrons were detected for an emission cone angle of

θLab = 0 −25◦between the electron momentum vector

and the XUV polarization, where the molecular axis with

respect to the XUV polarization is randomly oriented.

Six sidebands ranging from SB10 to SB20 can clearly be

seen in both spectra, as labeled. There is also the sig-

nature of spin-orbit splitting, which can be observed in

Kr [36], as well as in Kr2(see the arrows in Fig. 1b).

4 6 8 10

R (a.u.)

-1

Energy (eV)

(a) (b)

( )

* 4

( )

* 2

( )

Fig. 2. Schematic illustration of the outermost valence

molecular orbitals (a) for Kr2and the corresponding

potential energy curves (b) for Kr+

2, neglecting spin-orbit

interaction for simplicity. In (b), the data is taken from Ref.

[37] and the vertical dashed line indicates the equilibrium

internuclear distance (7.578 a.u.) for the ground state of

neutral Kr2.

In the analysis of the sideband oscillations the energy

range of each sideband was chosen to include both spin-

orbit states. Due to the direct comparison of the same

sidebands of Kr and Kr2, the XUV spectral phase ΦXUV

cancels out and the relative photoionization delays are

determined by

∆τKr2−Kr =~∂ΦKr2

sys

∂E −~∂ΦKr

sys

∂E '~∆ΦKr2

sys −∆ΦKr

sys

∆E,(3)

where ∆E= 2~ωNIR is the oscillation frequency of the

sidebands. The most fundamental diﬀerence between

monomer and dimer is that the two-center potential of

the dimer will cause additional eﬀects on its photoioniza-

tion delay.

In Kr2, the conﬁguration of the outermost valence elec-

trons is (σg)2(πu)4(π∗

g)4(σ∗

u)2. The removal of one elec-

tron from one of these four molecular orbitals gives rise

to the ionic states of 2Σ+

g,2Πu,2Πgand 2Σ+

u, respec-

tively, which are graphically illustrated in Fig. 2a. The

diﬀerent ionic states will have diﬀerent nuclear dynam-

ics after photoionization, resulting in diﬀerent fragments.

In Fig. 2b, we show the potential energy curves of the

four ionic states as a function of the internuclear dis-

tance. 2Πgand 2Σ+

ustates (corresponding to ionization

of the anti-bonding orbitals) have a potential well, allow-

ing the Kr+

2to remain bound. Thus, our experimental

coincidence measurements, performed with the undisso-

ciated Kr+

2, rule out the contributions from the other

two states (2Π+

uand 2Σg). In spite of this important

simpliﬁcation, one still needs to consider two ionic states

of opposite parities. The parity of the molecular orbital

controls the initial phase diﬀerence between the emitted

electron wavepackets from the two centers. The gerade

orbital launches wavepackets with a equal initial phase,

whereas the wavepackets released from the two centers

in the ungerade orbital have an initial πphase shift.

To demonstrate the parity eﬀect in two-center inter-

ference on the photoionization delays, we ﬁrst resort to

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Two-centerInterferenceinthePhotoionizationDelaysofKr2SaijoschaHeck,1MengHan,1,DenisJelovina,1Jia-BaoJi,1ConaillPerry,1XiaochunGong,2RobertLucchese,3KiyoshiUeda,1,4andHansJakobWorner1,y1LaboratoriumfurPhysikalischeChemie,ETHZurich,8093Zurich,Switzerland.2StateKeyLaboratoryofPrecisionSpectroscopy...

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Two-center Interference in the Photoionization Delays of Kr 2 Saijoscha Heck1Meng Han1Denis Jelovina1Jia-Bao Ji1Conaill Perry1 Xiaochun Gong2Robert Lucchese3Kiyoshi Ueda1 4and Hans Jakob W orner1y.pdf

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Two-center Interference in the Photoionization Delays of Kr 2 Saijoscha Heck1Meng Han1Denis Jelovina1Jia-Bao Ji1Conaill Perry1 Xiaochun Gong2Robert Lucchese3Kiyoshi Ueda1 4and Hans Jakob W orner1y

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