Science - USA (2022-01-21)

electron emitted attiwill experience a mo-
mentum shift in the direction ofA

→
ðÞti. Because
the periodTLof the circularly polarized laser is
well known, if two photoemission features are
found to have momentum shifts that differ by
an amountDq, this difference implies that
the photoemission events were separated by
a timeDt:

Dt¼

Dq

2 p

TL ð 2 Þ

This mapping of angle-to-time resembles
the face of a clock, which has led to the term
“attoclock”being used to describe this type of
time-resolved measurement ( 17 – 19 ).

Our method for extracting the temporal pro-

file of the AM electron yield is illustrated in

Fig. 1, D and E. Figure 1D shows the var-

iation in the differential electron yield for

measurements with three different x-ray ar-

rival times, or directions of the streaking laser

vector potential,A

→

0. The differential images

show the difference between the averaged

electron image when the vector potential of

the IR laser was chosen to lie along the line

labeledA

→

0 on the figure (and labeled as“0 fs”

on the clock face) and the averaged electron

image where the IR laser was intentionally

mistimed with the x-rays to ensure that there

was no effect from the streaking field. To

extract the time-dependent emission rate of

resonant AM electrons, we monitored a small

angular region on the detector (black wedge

in Fig. 1D) and plot this yield as a function

of streak angle, or the angle between the

observation bin and the streaking laser vector

potential, in Fig. 1E. The observation region

was chosen to be slightly higher in momen-

tum than the center of the field-free resonant

emission spectrum shown in Fig. 1B. The elec-

tron yield in this radial bin therefore mapped

to the number of electrons released into the

continuum at the time the vector potential

A

→

0 ðÞt is pointed in the angular direction of

the observation region. The lower momentum

SCIENCEscience.org 21 JANUARY 2022•VOL 375 ISSUE 6578 287

Fig. 2. Model for Auger-Meitner emission.(A) Schematic representation of
the model used for AM emission. Subfemtosecond x-ray pulses coherently
excite four resonances (labeled^2 Sþ;^2 S, and a doubly degenerate^2 D).
In addition to the resonant pathway, electrons can be directly ionized by the
x-ray pulse, leading to interfering paths from the ground state to the field-
dressed continuum [although the direct ionization pathway is a minor channel
( 14 )]. (B) Calculated photoelectron momentum spectrum for 0:5-fs x-ray
pulses centered at 533-eV photon energy in the presence of a 2:3-mm laser
field. The blue arrow shows the direction of IR laser vector potential, A(t), at
the x-ray arrival time,t 0 .(C) Kinetic energy distribution of the continuum

electron as a function of time in the absence of the streaking laser field.

(D) Time-dependent ionization rate for this wave function, summed over electron

kinetic energy, for a central photon energy of 533 eV (red), 534:5 eV (green),

and 536 eV (blue). (E) Total population of the core-excited states as a

function of time delay for the same photon energies as in (D). (F) Time

evolution of the electron density of the bound electronic states. The three-

dimensional contour is drawn at 20% of the maximum electron density,

and its transparency represents the overall bound-state population, which

decays via AM emission. The blue and red dots in the rightmost panel show

the positions of the nitrogen and oxygen atoms, respectively.

RESEARCH | RESEARCH ARTICLES