The concepts and ideas of coherent, nonlinear and quantum optics deeply penetrate into the range of 10-100 kiloelectronvolt (keV) photon energies, corresponding to soft gamma-ray (hard xray )) radiation. The recent experimental achievements in this frequency range include demonstration of the parametric down-conversion in the Langevin regime [1], cavity electromagnetically induced transparency [2], collective Lamb shift [3], and single-photon revival in the nuclear absorbing sandwiches [4]. Realization of a single photon coherent storage [5] and stimulated Raman adiabatic passage [6] were recently proposed. Still the number of tools for coherent manipulation of gamma-photon -nuclear ensemble interactions remains rather limited. In this work an efficient method to coherently control the waveforms of gamma-photons has been suggested and verified. In particular, the temporal compression of an individual gamma-photon into coherent ultrashort pulse train has been demonstrated. The method is based on the resonant interaction of gamma-photons with an ensemble of nuclei with modulated frequency of the resonant transition. The frequency modulation, achieved by uniform vibration of the resonant absorber due to the Doppler Effect, results in the time-dependence of the resonant absorption and dispersion, which allow shaping of the incident gamma-photons. The developed technique is expected to give a strong ) It is a historic tradition to call a radiation in this range x-ray radiation when it is produced by electron motion and to call it gamma-ray radiation if it is produced by nuclear transitions. 2impetus on emerging fields of coherent and quantum gamma-optics, providing a basis for realization of the gamma-photon -nuclear ensemble interfaces and quantum interference effects at the nuclear gamma-ray transitions.Quantum optics is the field of research dealing with interactions of quanta of electromagnetic radiation with quantum transitions of matter. It provides the basis for new fast growing fields of quantum cryptography, communication, and information. So far the experiments in these fields have been implemented either with microwave or optical photons, interacting with atomic electron transitions, and typically required cryogenic temperatures. The gamma-photons in the range of 10-100keV and the corresponding nuclear quantum transitions are the most suitable for realization of such experiments due to nearly 100% detector efficiency, extremely high Q-factor (~10 12 for 14.4keV transition in 57 Fe) of recoilless nuclear transitions even at room temperature, existence of radioactive materials (representing themselves the natural sources of single gamma-photons) and the cascade scheme of radiative decay of some radioactive sources (Fig.1a), allowing one to study the photon temporal shape via time-delayed coincidence measurement technique [7]. Moreover, the gamma-photons have important potential advantages over the microwave and optical photons for applications in cryptography, communication and information due to extremely...

A significant reduction of absorption for single gamma photons has been experimentally observed by studying Mössbauer spectra of 57 Fe in a FeCO 3 crystal. The experimental results have been explained in terms of a quantum interference effect involving nuclear level anticrossing due to the presence of a combined magnetic dipole and electric quadrupole interaction. [16] in Mössbauer spectra, gamma-microwave double resonance [13,17,18], or gamma-optical double resonance [19]. Recently, interesting proposals have been discussed to obtain lasing for gamma rays by utilizing coherent effects [20][21][22][23]. In this Letter, we report on experiments demonstrating the EIT effect at the singlephoton level via the level (anti)crossing technique. A theory of the one-photon interaction with a nucleus has been developed to describe the experimental results. The obtained results open an interesting perspective to extend coherent effects to nuclear transitions. Figure 1 represents the main results of the paper. It shows the observed Mössbauer spectrum of a single crystal of FeCO 3 at a temperature of 30.5(5) K which corresponds to a magnetic hyperfine field of B 15:1 3 T. At this field the hyperfine levels jm 1=2i and jm ÿ3=2i anticross. For the transitions connected to the anticrossing levels, a deficit of absorption of 25% is observed at the peak velocity. It means that some transparency is induced by interference, similar to EIT observed in optics.The experiments were performed by using a conventional Mössbauer setup. It includes a source of gamma radiation ( 57 CoRh), an absorber of FeCO 3 cleaved on the f1014g faces (optical thickness is of the order 10), and a detector. The absorber was mounted on a target holder which allows for a precise temperature control at the target position in the interval 4-600 K. Besides the magnetic hyperfine field, the Fe 2 nucleus in the FeCO 3 crystal [24,25] is subjected to a large axially symmetric electric field gradient (EFG) which results in a well-resolved quadrupole doublet. The level structures of the source and the absorber are shown in Fig. 2. In a magnetic field, the levels might shift to the position where their energies coincide; this situation is referred to as level crossing. But due to the presence of additional fields, the energies of levels might never be equal, and it is the case of level anticrossing.If the magnetic field is collinear with the EFG axis, the axial symmetry is preserved and the m states are eigenfunctions of the total nuclear Hamiltonian if the z axis is chosen along the symmetry axis. However, in such a mineral containing impurities and defects, one can expect a small distribution of fields which are responsible for the