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R. Röhlsberger and J. Evers
the regime of hard x-rays. However, it is not only the sharpness of the nuclear resonances and their favorable coherence properties which render Mössbauer nuclei an
ideal candidate to experimentally explore cooperative phenomena at x-ray energies.
Also, the possibility to engineer the interaction of x-rays with nuclei and the coupling
between nuclei via their geometric arrangement or by embedding them into photonic
nanostructures opens many fascinating routes to realize quantum optical concepts
with nuclei. In this respect, thin-film x-ray cavities and multilayers have become an
enabling technology for nuclear quantum optics. These cavities transform the propagating x-ray field delivered by the source into a standing wave field structure, and
the precise placement of the nuclei within this standing wave allows for an accurate tuning of the interaction of the nuclei with the x-rays. Another decisive aspect
is that the cavity geometry facilitates the excitation of single cooperative radiative
eigenstates of the embedded nuclei, and to tailor the superradiant enhancement of the
resonant emission as well as the collective Lamb shift. The possibilities are further
enriched if the magnetic substructure of the nuclei is exploited, or if different nuclear
ensembles are embedded within a single thin film structure. Then, the cavity fields
can be employed to generate atomic coherences between different nuclear states,
and to induce couplings between nuclear states up to the regime of strong collective
coupling, opening additional new possibilities. This enabled the implementation of
archetype quantum optical phenomena such as electromagnetically induced transparency, spontaneously generated coherences, Fano resonances and others. While
much progress has already been achieved on the level of single excitations, we anticipate further enrichment of this fascinating field of physics facilitated by the ongoing
development of modern x-ray sources like high-brilliance synchrotrons and x-ray
lasers, see Fig. 3.1. These sources are capable of delivering many resonant photons
in each single radiation pulse, providing a direct route towards multiphoton x-ray
optics, and opening perspectives for associated effects like stimulated emission, x-ray
lasing, nonlinear optics and more.
3.1.5 Outline of this Review
This review is organized as follows. In Sect. 3.2 of this chapter we review the properties of nuclear resonances as almost ideal two-level systems that can be prepared as
identical emitters in various structural arrangements. This leads us then in Sect. 3.3 to
discuss general properties of ensembles of Mössbauer isotopes forming a cooperative
atomic environment concerning their radiative properties. Specifically, in Sect. 3.4
we will discuss the properties of the nuclear exciton, i.e., the state that is formed after
impulsive excitation of a nuclear ensemble by a radiation pulse, the duration of which
is much shorter than the collective nuclear lifetime. Section 3.5 describes the most
fundamental effect of cooperative emission, the collective Lamb shift, the observation
of which was enabled via the application of planar x-ray cavities. While this section
contains a semiclassical description of the underlying physics to illustrate the basic
concepts of x-ray cavities as ‘enabling technology’ for this field, the following Sect.
R. Röhlsberger and J. Evers
the regime of hard x-rays. However, it is not only the sharpness of the nuclear resonances and their favorable coherence properties which render Mössbauer nuclei an
ideal candidate to experimentally explore cooperative phenomena at x-ray energies.
Also, the possibility to engineer the interaction of x-rays with nuclei and the coupling
between nuclei via their geometric arrangement or by embedding them into photonic
nanostructures opens many fascinating routes to realize quantum optical concepts
with nuclei. In this respect, thin-film x-ray cavities and multilayers have become an
enabling technology for nuclear quantum optics. These cavities transform the propagating x-ray field delivered by the source into a standing wave field structure, and
the precise placement of the nuclei within this standing wave allows for an accurate tuning of the interaction of the nuclei with the x-rays. Another decisive aspect
is that the cavity geometry facilitates the excitation of single cooperative radiative
eigenstates of the embedded nuclei, and to tailor the superradiant enhancement of the
resonant emission as well as the collective Lamb shift. The possibilities are further
enriched if the magnetic substructure of the nuclei is exploited, or if different nuclear
ensembles are embedded within a single thin film structure. Then, the cavity fields
can be employed to generate atomic coherences between different nuclear states,
and to induce couplings between nuclear states up to the regime of strong collective
coupling, opening additional new possibilities. This enabled the implementation of
archetype quantum optical phenomena such as electromagnetically induced transparency, spontaneously generated coherences, Fano resonances and others. While
much progress has already been achieved on the level of single excitations, we anticipate further enrichment of this fascinating field of physics facilitated by the ongoing
development of modern x-ray sources like high-brilliance synchrotrons and x-ray
lasers, see Fig. 3.1. These sources are capable of delivering many resonant photons
in each single radiation pulse, providing a direct route towards multiphoton x-ray
optics, and opening perspectives for associated effects like stimulated emission, x-ray
lasing, nonlinear optics and more.
3.1.5 Outline of this Review
This review is organized as follows. In Sect. 3.2 of this chapter we review the properties of nuclear resonances as almost ideal two-level systems that can be prepared as
identical emitters in various structural arrangements. This leads us then in Sect. 3.3 to
discuss general properties of ensembles of Mössbauer isotopes forming a cooperative
atomic environment concerning their radiative properties. Specifically, in Sect. 3.4
we will discuss the properties of the nuclear exciton, i.e., the state that is formed after
impulsive excitation of a nuclear ensemble by a radiation pulse, the duration of which
is much shorter than the collective nuclear lifetime. Section 3.5 describes the most
fundamental effect of cooperative emission, the collective Lamb shift, the observation
of which was enabled via the application of planar x-ray cavities. While this section
contains a semiclassical description of the underlying physics to illustrate the basic
concepts of x-ray cavities as ‘enabling technology’ for this field, the following Sect.