Quantum and Nonlinear Optics with Hard X-Rays

With the increasing brilliance of modern synchrotron radiation sources and free-electron lasers, the observation of nonlinear and quantum optical phenomena at x-ray wavelengths has come into reach. Single-photon x-ray detectors with quantum efficiency near unity and photon-number resolving capabilities are commercially available. Consequently, fundamental concepts in quantum optics can now also be studied in the x-ray portion of the electromagnetic spectrum. A key role in theoretical and experimental studies in x-ray quantum optics is played by the nuclear resonances of Mössbauer isotopes, the excitation of which became more and more efficient with increasing spectral flux delivered by these sources. The narrow resonance bandwidth facilitates to probe fundamental aspects of the light-matter interaction. A very sensitive manipulation of this interaction is possible by embedding Mössbauer nuclei in x-ray cavities. This allows one to prepare collective radiative eigenstates which open new avenues to establish concepts of quantum control in the x-ray regime via generation of coherences between nuclear levels. Moreover, the large number of vacuum field modes in the x-ray regime enables one to produce and probe nonclassical states of x-ray radiation and has opened the field of nonlinear x-ray optics