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

We show here that taking into account the contribution of the nearest satellites of the resonant component removes misfit of our analytical approximation with the exact result for the probability amplitude of the photon, transmitted through the vibrating absorber. We analyze time evolution of the phase difference of the scattered field and the comb. We discuss the scheme how single and two-pulse bunches can be used to simulate spin 1/2 qubit and ququad.

The anomalous behavior of transient nutations is experimentally investigated in a set of two-level (Sϭ 1 2 ) spin systems differing only in spin concentration. Our results show that the non-Bloch power dependence of the decay rate of transient nutations is a concentration-dependent effect, which is more and more pronounced in more and more concentrated samples. The experimental results are interpreted in the framework of the recent theory by Shakhmuratov et al. ͓Phys. Rev. Lett. 79, 2963 ͑1997͔͒ and support the hypothesis that the anomalous decay of transient nutations in solids originates from radiation-induced changes of the dipolar field, rather than from residual fluctuations of the nominally coherent field. ͓S1050-2947͑99͒03905-0͔ PACS number͑s͒: 42.50. Md, 76.30.Mi, 76.90.ϩd

We consider the propagation of a Gaussian probe pulse in an absorptive, optically dense, two-level medium if a deep, persistent hole is created in advance by another pump field in the inhomogeneously broadened absorption spectrum of this medium. Both fields are well separated in time and the lifetime of the hole is assumed to be long with respect to the delay time between the pump and probe pulses. We show that the group velocity of the Gaussian probe pulse reduces several orders in magnitude, similarly to the reduction of the group velocity for the probe field in electromagnetically induced transparency ͑EIT͒ phenomena. In contrast to EIT, the width of the transparency window can be made very wide because of the saturation broadening of the hole.

The radiation burst from a single gamma-photon field interacting with a dense resonant absorber is studied theoretically and experimentally. This effect was discovered for the fist time by P. Helisto et al., Phys. Rev. Lett. 66, 2037Lett. 66, (1991 and it was named "gamma echo". The echo is generated by 180-degree phase shift of the incident radiation field, attained by an abrupt change of the position of the absorber with respect to the radiation source during the coherence time of the photon wave packet. Three distinguishing cases of "gamma echo" are considered, i.e., the photon is in exact resonance with the absorber, close to resonance (on the slope of the absorption line), and far from resonance (on the far wings of the resonance line). In resonance the amplitude of the radiation burst is two times larger than the amplitude of the input radiation field just before its phase shift. This burst was explained by P. Helisto et al. as a result of constructive interference of the coherently scattered field with the phase shifted input field, both having almost the same amplitude. We found that out of resonance the scattered radiation field acquires an additional component with almost the same amplitude as the amplitude of the incident radiation field. The phase of the additional field depends on the optical thickness of the absorber and resonant detuning.Far from resonance this field interferes destructively with the phase-shifted incident radiation field and radiation quenching is observed. Close to resonance three fields interfere constructively and the amplitude of the radiation burst is three times larger than the amplitude of the input radiation field.

Free induction decay and transient nutations are investigated in a system of two-level particles with an inhomogeneously broadened spectrum. The influence of the x (real) and y (imaginary) parts of the complex amplitude of the noise, induced by the driving field in the sample, is considered. It is shown that both noises affect T 1 and T 2 relaxation processes. When field-noise contributions to 1͞T 2 and 1͞T 1 relaxation rates are dominant and equal to each other, Bloch's saturation is changed to Redfield's saturation. This effect also accelerates transient nutation decay. Comparison with experimentally observed free induction decay and transient nutation in color centers in quartz is discussed.[S0031-9007(97)04230-0]

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