The so-called gamma-echo effect has been observed experimentally and analyzed using the semiclassical optical theory. Here the effect is reinterpreted using a new 1D quantum mechanical model. This leads to a different interpretation of the effect as a π phase-shift induced transparency. In the basic time-differential Mössbauer spectroscopic technique the forward-scattered recoil-free radiation is observed, in delayed coincidence, after passing through a nuclear-resonant absorber. The effect in question is produced most efficiently when the source of recoil-free radiation is moved abruptly causing a π phase shift of the source radiation during its radiative lifetime. Using the 1D model the effect is seen to arise from the constructive interference between the source radiation at a later time, and the radiation coming from the absorber excited at an earlier time. The exact form of the source modulation and the nuclear-resonant thickness of the resonant absorber determines the shape of the time-differential resonant gamma ray transmission spectrum. Numerical results are given using the familiar 57Fe recoil-free resonant transition. The π phase-shift-induced transparency allows the resonant gamma radiation, incident on the resonant absorber, to be transmitted through the absorber without appreciable attenuation.
The purpose of this paper is to describe a method for observing stimulated emission of gamma radiation. Stimulated emission of gamma radiation has never been observed. Stimulated emission of gamma radiation will be essential for developing gamma-ray lasers. The method uses the ‘π phase-shift induced transparency’ of gamma radiation, previously called the ‘gamma echo’. The gamma-echo technique is based on a modification of the time-differential Mössbauer spectroscopic method, i.e. the source is moved ‘instantaneously’ during the lifetime of the excited state. Then a resonant absorber becomes transparent to the resonant gamma radiation. There is a type of ‘self-stimulated’ emission in which the radiation ‘absorbed’, before the phase shift, is stimulated to emit after the phase shift. To observe stimulated emission of the resonant gamma radiation, one performs the same gamma-echo experiment except the resonant absorber is replaced by another source. This secondary source is chosen to be in resonance with the original source. Under these conditions there will be no stimulated emission, in the secondary source, before the π phase shift because the incident radiation is absorbed. However, after the phase shift, the secondary source becomes transparent to the incident radiation. If one uses a matched pair of Co57 sources and the secondary source is 2mCi, there will be about 3 nuclei in the secondary source, in the first excited state of Fe57, that are available to be stimulated during the 97.8ns lifetime of the primary source radiation.
Classical phase-modulation theory is applied to describe the interference of the recoil-free gamma-radiaton fields emitted by a M\"ossbauer source and a resonant absorber in forward-scattering geometry. During the exponential decay of the excited state in the source the resonant absorber develops and emits a coherent field, which interferes destructively with the source field. A stepwise phase change of the source field relative to the absorber field is introduced by a fast mechanical displacement of the source. As a result, an intense pulse of gamma rays is observed in the time dependence of the resonantly filtered radiation. This coherent transient phenomenon is called a gamma echo. The time reference of the gamma-echo experiment is the moment of formation of the excited state in the source. This is in contrast to earlier transient M\"ossbauer experiments in which the measurements were synchronized to the phase of the modulation and averaging occurred over all possible times of formation of the excited state. By choosing a suitable shape for the phase-modulation function in the echo experiment, short pulses of gamma radiation with desired duration and amplitude can be generated within a time frame defined by the lifetime of the excited nuclear state. Here, a detailed description of the experimental and theoretical aspects of stepwise phase modulation in a coincidence scheme is given. Theoretical results are presented in a general form, taking into account the experimental nonidealities. The properties of the mechanical drive system are discussed in detail. Gamma-echo data are presented. Good agreement between the theoretical calculations and the experimental data has been established.
The radiation burst from a single $\ensuremath{\gamma}$-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, 2037 (1991)] and it was named the ``gamma echo.'' The echo is generated by a 180${}^{\ensuremath{\circ}}$ 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 the 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 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 the three fields interfere constructively and the amplitude of the radiation burst is three times larger than the amplitude of the input radiation field.
The radiation from a Mössbauer source of 57Co in a copper matrix is frequency-modulated by vibrating the source with a quartz piezo-crystal driven by an oscillator. If the radiation passes through a resonant absorber (a "filter"), a time structure containing the oscillator frequency and its harmonics appears in the resulting counting rate. It may be seen by sorting the time of each count with respect to the cross-over time of a subharmonic of the oscillator. These quantum beats are caused by interferences between the frequency components of the photon amplitude, and vanish unless there is some alteration of relative phase or amplitude of the original radiation by the filter. The harmonic constitution of the beats is a sensitive function of the relative shift of source and filter and may be used as a sensitive probe of small shifts. This is demonstrated by measuring the temperature shift in 57Fe-Be. If a velocity spectrum is made with counts collected during only a part of the vibration cycle, prominent dispersion effects are seen, with counting rates higher than background in some portions of the spectrum. A classical optical theory of the phenomenon is presented in summary. It explains the beats, the dispersion effects, and the sensitivity of the harmonic ratios to relative shifts.
A classical optical theory is given for the phenomenon of $\ensuremath{\gamma}$-ray quantum beats observed by Perlow in a study of the M\"ossbauer effect of a frequency-modulated source. The intensity $I({\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}},t)$ of the radiation from such a source transmitted through a resonant absorber is obtained as a function of ${\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}}$ and
t, where ${\ensuremath{\omega}}_{0}^{\ensuremath{'}}$ is the frequency of an absorber resonance, ${\ensuremath{\omega}}_{0}$ is the central frequency of the frequency-modulated source, and
t is the laboratory time. An average is taken over the unobserved initial formation time of the excited nuclear state in the source. When viewed at fixed ${\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}}$, the calculated intensity displays beats in the time spectrum, and when viewed at fixed
t, the intensity shows dispersion at appropriate values of ${\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}}$, responsible for the observed enhancement of intensity above background. The harmonic content of the quantum beats is calculated explicitly in the thin-absorber limit, and the observed linear variation about ${\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}}=0$ of the ratio of Fourier components
D2D1 is explained. The use of
D2D1 to measure small frequency shifts is analyzed by a statistical comparison with the method of switching between steepest points of the line, as used in gravitational-red-shift measurements. The variances are comparable. The effect on $I({\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}},t)$ of line broadening due to sample inhomogeneities is calculated for a Lorentz distribution of center frequencies in source and absorber, and a prescription is given for modifying the various terms in $I({\ensuremath{\omega}}_{0}\ensuremath{-}{\ensuremath{\omega}}_{0}^{\ensuremath{'}},t)$ accordingly. Finally, the effect of a distribution of phase and amplitude of the motion of the vibrating source is discussed.
Abstract The induced transparency of opaque medium for resonant electromagnetic radiation is a powerful tool for manipulating the field-matter interaction. Various techniques to make different physical systems transparent for radiation from microwaves to x-rays were implemented. Most of them are based on the modification of the quantum-optical properties of the medium under the action of an external coherent electromagnetic field. Recently, an observation of acoustically induced transparency (AIT) of the 57Fe absorber for resonant 14.4-keV photons from the radioactive 57Co source was reported. About 150-fold suppression of the resonant absorption of photons due to collective acoustic oscillations of the nuclei was demonstrated. In this paper, we extend the AIT phenomenon to a novel phase-locked regime, when the transmitted photons are synchronized with the absorber vibration. We show that the advantages of synchrotron Mössbauer sources such as the deterministic periodic emission of radiation and controlled spectral-temporal characteristics of the emitted photons along with high-intensity photon flux in a tightly focused beam, make it possible to efficiently implement this regime, paving the way for the development of the acoustically controlled interface between hard x-ray photons and nuclear ensembles.