Toward Nonlinear Optics with Mössbauer Nuclei Using X-Ray Cavities

Strong excitation of nuclear resonances, particularly of Mössbauer nuclei, has been a longstanding goal and the advance of novel x-ray sources is promising new options in this regard. Here, we map out the necessary experimental conditions for the more general goal of entering the nonlinear optics regime with nuclei and compare with available technology. In particular, we present a comprehensive theory of nonlinear nuclear excitation in thin-film x-ray cavities by focused x-ray pulses. We thereby identify cavity geometries with broad resonances that allow one to boost the nuclear excitation even at moderately tight focusing and offer the possibility to mitigate radiation damage.