(G¼170 meV) was consistent with previous
x-ray absorption measurements ( 27 ). The rela-
tive amplitude between transitions to the
bound, core-excited states and direct photo-
ionization of valence electrons to the continuum
was represented by the Fano parameter,qi(see
supplementary materials) ( 28 ). We choose the
value forqiaccording to the measured absorp-
tion spectrum of NO ( 27 ).
The coherent bandwidth of the exciting x-ray
source was∼5 eV ( 12 ), which was sufficient to
span all core-excited bound states in the model.
Symmetry constraints did not allow for the
coherent population of the^2 S and^2 Sþstates
because the^2 S and^2 Sþstates each coupled to
a different component of the doubly degenerate
ground state ( 14 ). Moreover, each component of
the ground state coupled to a different compo-
nent of the degenerate^2 Dstate ( 14 ). Thus, the
model only included coherence between the
(^2) S and one of the (^2) Dstates and the (^2) Sþand
the other^2 Dstate, but not the^2 S and^2 Sþ
states. In both simulation and experiment, we
tune the central wavelength of the x-ray source
across the 1s→2ppresonance (red, green,
and blue shaded curves in Fig. 3, bandwidth
drawn to scale with energetic separation of
core-excited states).
In the simulation, we could calculate the
energy-resolved continuum wave function in
the absence of the streaking-field, shown in
Fig. 2D, demonstrating the build-up of reso-
nant features. The rate of electron emission
(integrated over electron kinetic energy) is
showninFig.2E),andweclearlyobservean
oscillatory emission rate. Finally, in Fig. 2F
we show the population of each core-excited
state as a function of time, which again shows
oscillatory behavior. The periodic modulation
of the electron emission rate resulted from
the coherent population of the two pairs of
excited states^2 S and^2 D, and^2 Dand^2 Sþ.
Electronic coherence between the pairs of
excited states resulted in consecutive minima
or maxima in the time-dependent ionization
rate, owing to destructive or constructive in-
terference between emission from the core-
excited states. Because the core-excited wave
packet consisted of states with different an-
gular momentum projections along the mo-
lecular axis, the excited state wave packet
produced an excited electron density that
rotated around the molecular axis, as shown
in Fig. 2C.
Results
We directly modeled our experimental observ-
able by computing the asymptotic (t→∞) mo-
mentum distribution of ionized electrons within
the strong-field approximation (SFA) ( 26 ) (Fig.
2B) and performing the same analysis routine
as the one we applied to the experimental
data. The asymmetry parameters describing
emission from the oxygen 1s→^2 S , O1s→^2 D,
and O 1s→^2 Sþexcitations were expected to be
different for each of the electronic states ( 24 )
and have not previously been measured, mean-
ing the contribution of each channel to emis-
sion in the direction of our observation window
was not well defined. We fit the simulation to
the experimental data using the lower kine-
tic energy limits of the small detector region
defined in Fig. 1E, and the relative contribu-
tion from each decay channel at the precise
region on the detector, as free parameters.
With a separate measurement taken concur-
rent with the presented data, we determined
an error distribution ofs= 30° for single-shot
vector potential determination. We accounted
for this experimental error by convolution
of the time-dependent electron yield with a
Gaussian kernel ofs= 30°. Further details are
provided in the supplementary materials. We
also accounted for the possibility of a small
systematic error int 0 determination between
experiment and theory, resulting from the
finite temporal profile of the reference nitro-
gen K-shell photoline produced by the atto-
second x-ray pulse ( 12 ). We identified an offset
of∼1.7% of the full detector angle.
Figure 3A shows the vector-potential direction–
dependent electron yield measured at different
x-ray excitation energies (black dots) compared
with the simulated yield (solid line). The tran-
sient revival att∼ 3 :5 fs resulting from electronic
coherence in the core-excited state is indicated
by the black arrow and is observed in both ex-
periment and simulation. This feature is a
quantum beat, occurring at the moment when
the quantum phases of the coherently excited
(^2) S and (^2) Dexcitations realigned. This align-
ment caused constructive interference between
the two core-excited states, and an increase in
AM emission rate. The feature at∼1.3 fs mea-
sured at central photon energy 536 eV was
possibly due to the temporal build-up of the
Fano interference between the resonant and
direct excitation channels and has been qual-
itatively reproduced in further simulation.
Analysis of the energetic positions of the
Rydberg series converging to the oxygen K-edge
( 27 ) was not consistent with the interpretation
that this modulation was due to further coherent
excitation involving Rydberg states.
Figure 3B shows a magnified image of the
revival feature. By tuning the central x-ray
photon energy away from the center of the
1s→2ppresonance, we could suppress the
quantum beat in both experiment (left) and
simulation (right), demonstrating control over
the coherent evolution of the core-excited states.
The beat was suppressed at higher photon en-
ergy because of an increased relative contri-
bution from the direct channel versus the
coherently excited resonant decay pathways.
In Fig. 3C, we compare our measurement, for
a central x-ray excitation energy of 533 eV, to
our simulation, including (deep red) and ex-
cluding (pale red) the coherence between the
core excited states. As expected, the revival
feature could be reproduced only by including
the coherence between the different core-excited
electronic states. The result from incoherent
summation of the AM emission from the dif-
ferent core-excited states failed to reproduce
the feature at 150° streaking angle.
Conclusion
This work reports the real-time measurement
of electronic coherence in the temporal evolution
of a core-excited molecule. Electronic coherence
imparted a modulation in the time-dependent
emission rate of AM electrons, driven by an
isolated attosecond soft x-ray pulse from a free-
electron laser. The AM emission occurred on a
few-femtosecond time scale, and we time-
resolved it using angular streaking. Our mea-
surement provides a testbed for exploring the
effect of electronic coherence in the photo-
excitation dynamics and subsequent photo-
chemical behavior of molecular systems. The
existence of this electronic coherence provides
the opportunity to explore interatomic site
electronic wave packet coupling, which can
reveal interactions between different parts of
an extended system ( 29 – 31 ). Measuring this
coupling can reveal important information on
the system’s fundamental physical properties
( 32 , 33 ). For example, the spectral makeup of
the observed modulations provides rich infor-
mation on the composition of the excited super-
position state. This information opens the
possibility for resolving in time the evolution
and decay of coherent electronic states, as they
evolve and couple to subsequent nuclear mo-
tion in the first stages of a photochemical
reaction ( 34 – 37 ).
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