162
R. Röhlsberger and J. Evers
approaches encompass both the generation of X-ray photon entanglement and its
applications, and the exploration of quantum states in the nuclei by subsequent spectroscopic detection of scattered X-ray photons [153]. The availability of multiple
coherent photons per pulse in turn enables detection of multiple correlated X-ray
photons, providing access to higher-order correlation functions characterizing, e.g.,
density fluctuations, phonons or similar excitations. This will fuel the development
of a broad class of new detection and analysis techniques. With multiple potentially
phase-locked driving fields, multi-dimensional spectroscopy techniques come within
reach, providing further insight into the dynamics. 2D nuclear spectroscopy might
reveal couplings among nuclear transitions that could provide fundamental insight
into intra-nuclear interactions, analogous to what is revealed in two-dimensional
spectroscopy throughout radio frequency to optical spectral ranges [154, 155]. This
and the other 2D measurements mentioned above will require at least phase-related
X-ray pulse pairs, which could be generated by splitting one XFELO output pulse by
an X-ray split-and-delay line or by applying temporal control of resonantly scattered
photons via ultrafast piezo modulation [84].
Further progress is anticipated in the engineering of advanced nuclear level
schemes. First steps have recently been demonstrated at 3rd generation light sources,
by designing suitable target structures utilizing Mössbauer nuclei embedded in superlattices [38] and planar X-ray cavities [27, 29, 39]. The XFELO will enhance these
capabilities by its unique source properties, which, aside from the spectral brightness also includes coherent multi-pulse or multi-color excitation. The XFELO could
also facilitate novel nuclear resonance excitation processes, such as non-linear twophoton excitation [156] or four-wave mixing.
The pulse-to-pulse coherence of an energy stabilized XFELO enables one to
realize a hard X-ray frequency comb (see Sect. 3.6), facilitating ultrahigh-resolution
X-ray spectroscopy of nuclear transitions. Examples include multi-level nuclear transition measurements, probing ultra-narrow X-ray Mössbauer resonances, dynamics
of X-ray driven nuclear—electronic transitions, and X-ray + laser double resonance
experiments. Facilitated by X-ray comb spectroscopy, fascinating possibilities come
into reach: X-ray frequency and wavelength metrology would be enabled by extending the optical frequency comb technologies and techniques to X-ray wavelengths.
In addition to probing nuclear physics with unprecedented precision, linking nuclear
transitions to the Cs standard can be used to search for the variation of fundamental
constants with improved sensitivity [158, 159]. Nonlinear phase-coherent driving
and probing at X-ray wavelengths will be possible over long times >10 s. Highquality-factor nuclear transitions like the 12.4 keV level of
45 Sc with a lifetime of
∼300 ms and 0 /E 0 ∼ 10
−19 (see Fig. 3.27) can be established as new and improved
frequency standards. Importantly, the pulse-to-pulse coherence allows to excite these
narrow resonances using a sequence of pulses, offering the possibility of orders of
magnitude higher excitation fraction than expected from SASE [153].
With sufficient temporal coherence and high intensity, coherent processes including nuclear coherent population transfer in the stimulated Raman adiabatic passage
(STIRAP) technique [160, 161] or nuclear Rabi oscillations [162] are rendered pos-
R. Röhlsberger and J. Evers
approaches encompass both the generation of X-ray photon entanglement and its
applications, and the exploration of quantum states in the nuclei by subsequent spectroscopic detection of scattered X-ray photons [153]. The availability of multiple
coherent photons per pulse in turn enables detection of multiple correlated X-ray
photons, providing access to higher-order correlation functions characterizing, e.g.,
density fluctuations, phonons or similar excitations. This will fuel the development
of a broad class of new detection and analysis techniques. With multiple potentially
phase-locked driving fields, multi-dimensional spectroscopy techniques come within
reach, providing further insight into the dynamics. 2D nuclear spectroscopy might
reveal couplings among nuclear transitions that could provide fundamental insight
into intra-nuclear interactions, analogous to what is revealed in two-dimensional
spectroscopy throughout radio frequency to optical spectral ranges [154, 155]. This
and the other 2D measurements mentioned above will require at least phase-related
X-ray pulse pairs, which could be generated by splitting one XFELO output pulse by
an X-ray split-and-delay line or by applying temporal control of resonantly scattered
photons via ultrafast piezo modulation [84].
Further progress is anticipated in the engineering of advanced nuclear level
schemes. First steps have recently been demonstrated at 3rd generation light sources,
by designing suitable target structures utilizing Mössbauer nuclei embedded in superlattices [38] and planar X-ray cavities [27, 29, 39]. The XFELO will enhance these
capabilities by its unique source properties, which, aside from the spectral brightness also includes coherent multi-pulse or multi-color excitation. The XFELO could
also facilitate novel nuclear resonance excitation processes, such as non-linear twophoton excitation [156] or four-wave mixing.
The pulse-to-pulse coherence of an energy stabilized XFELO enables one to
realize a hard X-ray frequency comb (see Sect. 3.6), facilitating ultrahigh-resolution
X-ray spectroscopy of nuclear transitions. Examples include multi-level nuclear transition measurements, probing ultra-narrow X-ray Mössbauer resonances, dynamics
of X-ray driven nuclear—electronic transitions, and X-ray + laser double resonance
experiments. Facilitated by X-ray comb spectroscopy, fascinating possibilities come
into reach: X-ray frequency and wavelength metrology would be enabled by extending the optical frequency comb technologies and techniques to X-ray wavelengths.
In addition to probing nuclear physics with unprecedented precision, linking nuclear
transitions to the Cs standard can be used to search for the variation of fundamental
constants with improved sensitivity [158, 159]. Nonlinear phase-coherent driving
and probing at X-ray wavelengths will be possible over long times >10 s. Highquality-factor nuclear transitions like the 12.4 keV level of
45 Sc with a lifetime of
∼300 ms and 0 /E 0 ∼ 10
−19 (see Fig. 3.27) can be established as new and improved
frequency standards. Importantly, the pulse-to-pulse coherence allows to excite these
narrow resonances using a sequence of pulses, offering the possibility of orders of
magnitude higher excitation fraction than expected from SASE [153].
With sufficient temporal coherence and high intensity, coherent processes including nuclear coherent population transfer in the stimulated Raman adiabatic passage
(STIRAP) technique [160, 161] or nuclear Rabi oscillations [162] are rendered pos-