To achieve this goal, we shape double-pulse sequences from given incident X-ray pulses with a tunable relative phase using the mechanical motion of a resonant absorber (see Fig. Here, we demonstrate the coherent control of the dynamics of Mössbauer nuclei using X-ray light. Although such pulse-shaping techniques are reminiscent of their counterparts in coherent control schemes at lower wavelengths, the application of the shaped X-ray pulses for the coherent control of nuclear quantum dynamics and their phase stability are yet to be demonstrated. The latter works established the possibility of exploiting this shaped X-ray light as a tool. This approach has been used to study polariton dynamics 23, and in particular also to favourably shape X-ray pulses in the temporal 7– 9, 24 or spectral domain 10. Another line of research involves rapid mechanical motions of one or more resonant absorbers to control the interference between different scattering pathways. Fast control of nuclear dynamics was demonstrated, for example, using sudden rotations of a static external magnetic field 6, which allows for selected control operations in sample materials with fast magnetic switching capabilities. These works are concerned with the nuclear excitation dynamics, but did not consider the control thereof or the phases characterizing the nuclear quantum state. It has previously been demonstrated that incoherent light or conversion electrons enable us to study the excitation dynamics of nuclei, for example, to reveal polariton propagation 21 or radiation trapping 22. In this process, we need to be able to shape light pulses, to precisely control their relative phases and to detect the induced dynamics. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science 20.Ĭoherent control refers to the control of quantum dynamics by light, based on coherence and interference phenomena 1, 2. Our results unlock coherent optical control for nuclei, and pave the way for nuclear Ramsey spectroscopy 17 and spin-echo-like techniques, which should not only advance nuclear quantum optics 18, but also help to realize X-ray clocks and frequency standards 19. We present a method of shaping single pulses delivered by state-of-the-art X-ray facilities into tunable double pulses, and demonstrate a temporal stability of the phase control on the few-zeptosecond timescale. Here we demonstrate such control, and use the tunable phase between two X-ray pulses to switch the nuclear exciton dynamics between coherent enhanced excitation and coherent enhanced emission. However, coherent control of atomic nuclei using suitably shaped near-resonant X-ray fields remains an open challenge. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques 6– 16. At hard-X-ray energies (above 5–10 kiloelectronvolts), Mössbauer nuclei feature narrow nuclear resonances due to their recoilless absorption and emission of light, and spectroscopy of these resonances is widely used to study the magnetic, structural and dynamical properties of matter 4, 5.
Recently, coherent control in the extreme-ultraviolet range was demonstrated 3, with a few-attosecond temporal resolution of the phase control. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics 2. Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications 1.
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