resonance (Fig. 1A) (24). Related piezo techniques
have been used before to shape single narrow-band
g-ray photons in the time domain (10, 19, 21, 26, 27).
Broadband x-ray pulses (20) have also been considered, but spectral shaping (28) has received
little attention so far.
We implemented our scheme using the
Mössbauer isotope 57Fe with its nuclear transition
at energy h –w0 = 14.4 keV. The resonance width of
h –g = 4.7 neV corresponds to a lifetime of 141 ns,
during which a controlled piezo displacement is
experimentally feasible. The experiments were
performed at the synchrotron sources ESRF
(Grenoble, France) and PETRA III (DESY, Hamburg,
Germany). The target mounted on the piezo consists
of a-iron with thickness 2 mm, enriched in the
resonant isotope 57Fe to 95%. The magnetization
was externally aligned such that two magnetic
hyperfine transitions were driven by the x-rays.
The piezo motion was controlled via an arbitrary-function generator (24). Triggered by the synchrotron bunch clock, each x-ray pulse is manipulated
by the same piezo motion, such that the desired
resonant brilliance boost can be observed in the
data averaged over all x-ray pulses.
For energy analysis of the radiation transmitted
through the piezo target, we used a single-line
reference absorber consisting of 57Fe-enriched
stainless steel, mounted on a Doppler drive, and
scanned it across the 57Fe resonance (Fig. 2A)
(24). The analysis of the combined temporal response of target and analyzer provides access
to both the piezo motion and the generated
x-ray spectra. A subset of such time- and energy-dependent measurements integrated over different detection time windows is shown in Fig. 2C.
The actual motion of the target on the piezo does
not directly follow the applied voltage signal,
most likely because of signal dispersion and
bandwidth limitations in the transmission from
electric voltage to mechanical motion. To deter-
mine the piezo motion without assuming a par-
ticular motional pattern, we used an evolutionary
algorithm in which an initially random motion
was successively optimized toward best agree-
ment between simulation and measured data
(24). The resulting converged piezo motions are
depicted in Fig. 2B, and corresponding theory
fits to the data are shown as solid lines in Fig.
2C. The reconstructed motion then allows us to
calculate the generated x-ray spectra via a Fourier
transform of the phase-modulated pulses.
In the x-ray pulse spectra normalized to the
input spectra (Fig. 2D), obtained for the displacements shown in Fig. 2B, the spectrum plotted in
black is a reference without piezo motion. Off
resonance, its normalized spectral intensity is
below unity because of electronic absorption.
With motion of the target, the resonant intensity clearly exceeds that of the incident pulse by
more than a factor of 3. The spectral rearrangement is confirmed by the fact that the motion
shown in blue rearranges lower spectral regions
onto the respective resonances, whereas the
opposite motion shown in red shuffles higher
frequencies onto resonance (Fig. 2D, dashed arrows). These main spectral features are already
well visible in the experimental raw data integrated
over late photon arrival times (Fig. 2C, bottom),
which approximates the spectrum of the piezo
target alone (8, 13). The properties of the generated
x-rays closely resemble those of ideal narrow-band
pulses, as can be seen in their respective Wigner
representations (fig. S7). Our theoretical analysis
(24) shows that an enhancement factor of 12 is
possible for a single a-iron foil with optimized
To investigate the possibility of further en-
hancement, we performed proof-of-principle ex-
periments with two piezo stages, which also
allowed for stringent tests of the recovered piezo
motions. Enhancements beyond the single piezo
capabilities are possible if multiple piezos har-
vest intensity from different off-resonant spectral
regions. In our experiment (Fig. 3A), the two
piezos harvest from spectral regions above and
below the resonance, respectively. We first indi-
vidually reconstructed the respective motions of
each of the two piezos (Fig. 3B). Then, we theo-
retically optimized the resonant intensity boost
expected for both piezos combined by temporally
shifting their motions relative to the synchrotron
bunch clock. The subsequent optimized measure-
ment with two piezo stages shows good agree-
ment with the theoretical predictions (Fig. 3C).
This also confirms the recovered piezo motions,
because the theoretical predictions for two piezos
were based on the single-stage measurements
only. Note that multiple piezos have also been
studied with narrow-band g-ray sources (29).
These results readily open the way for more
general manipulations of the spectrum. Similar
brilliance enhancements with a single-line spec-
trum as in Fig. 1 are feasible with suitable single-
line targets (e.g., stainless steel enriched in 57Fe).
We have verified this by calculating the resonant
enhancement expected with the single-line ab-
sorber and the motional pattern used in our
experiment. In additional experiments, we inves-
tigated piezo motions with larger amplitude,
which redistribute intensity over a wider spec-
tral range (24). Note that the partial longitudinal
coherence of synchrotron or x-ray free electron
laser pulses is not a limitation for switching times
on the order of nanoseconds (24). It may be pos-
sible to cascade even more piezo stages, further
increasing the resonant x-ray brilliance. Exten-
sions of this scheme can be envisioned by replacing
the piezo-based mechanical displacement with
faster laser-induced phononic control of the posi-
tions of the nuclei.
More general time-dependent displacements
could facilitate the engineering of arbitrary spectra.
This provides a direct link to laser pulse shaping,
a widespread technique in ultrafast optics with
many applications (30). Ultimately, closed-loop
feedback setups could be envisioned to optimize
the x-ray pulse spectra for specific applications,
such as selective excitations in compound materials or enhanced nonlinear light-matter interactions. These perspectives reach beyond Mössbauer
resonances, as our method applies to spectroscopy
in general. Alternatively, in combination with short
and focused x-ray beams, the tracking of motion
on sub-angstrom scales developed here could
serve as a valuable tool to study laser-induced
mechanical excitations or distortions with high
spatial and temporal resolution, among other possible applications.
REFERENCES AND NOTES
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3. R. V. Pound, G. A. Rebka, Phys. Rev. Lett. 3, 439–441 (1959).
4. D. C. Champeney, G. R. Isaak, A. M. Khan, Nature 198,
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SCIENCE sciencemag.org 28 JULY 2017 • VOL 357 ISSUE 6349 377
− 100 − 50 0 50 100
Frequency detuning Δ[γ ]
Piezo 1 & 2
Time t [ns]
− 50 0 50
M ¨ ossbauer detuning ΔD [γ ]
Fig. 3. Cascading of two piezo stages. (A) Spectrum generated with two 57Fe targets on separate piezo
stages (green) and the corresponding spectra for the respective single piezo stages (red, blue).
(B) The two respective motional patterns redistribute spectral power from different off-resonant regions
onto resonance [dashed arrows in (A)]. Thus, the combination of the two stages increases the
resonant intensity beyond what is achieved with a single piezo (red, blue). (C) Measured spectrum
for the two-piezo setup. The solid line shows the corresponding theoretical prediction. Photon shot-noise
errors are within the marker size.