Towards Flexible Intensity Control of Resonantly Scattered $\gamma$-Rays Using Multi-Frequency Vibrating Resonant Absorber

We report a method for coherent control of $\gamma$-photons, enabling the shaping of $\gamma$-ray intensity in nearly arbitrary waveforms. Different intensity waveforms are created by adjusting the motion profile of a resonant absorber (an ensemble of M\"{o}ssbauer nuclei) and tuning the energy of the incident radiation. A crucial aspect of this method is the use of a low fundamental frequency of vibrations, which broadens the possibilities for $\gamma$-ray control. The results of numerical simulations are experimentally validated by generating single and double $\gamma$-pulses and inducing short-term absorption. For this, a resonant absorber containing $^{57}$Fe nuclei was vibrated with different motion profiles composed of 12 harmonics with a fundamental frequency of 1\,MHz. The proposed technique represents an advancement in the manipulation of $\gamma$-rays and potentially X-rays, paving the way for the performance of unique types of $\gamma$-ray or X-ray quantum experiments and the development of tools such as adjustable tabletop $\gamma$-pulse sources or $\gamma$-ray or X-ray delays and gates. Moreover, inverse application of the method enables investigation of motion at the picometer scale.