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Physical Review A

Radiation burst from a single γ -photon field

R. N. Shakhmuratov, Farit G. Vagizov, Olga A. Kocharovskaya

Published Oct 11, 2011• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.84.043820

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The radiation burst from a single \ensuremathγ\ensuremath{\gamma}\ensuremathγ-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∘{}^{\ensuremath{\circ}}\ensuremath∘ 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 pulsed radiation field propagating in a thick resonant absorber induces the polarization (quantified by the induced atomic dipoles in optical domain or the induced nuclear transition moments in gamma domain), which is distributed oscillatorily along the absorber forming a sandwich of polarization layers with opposite phases. As a result, the reemitted, scattered fields in different layers interfere with the incident input field destructively or constructively, giving rise to the well-known dynamical beats of the output radiation. We propose a method how to force these layers in the sandwich to reemit in phase with the incident field, which results in a strong radiation burst of short duration at the output of the absorber. We demonstrate this method experimentally for the 14.4 keV nuclear transition in 57{}^{57}57Fe.
Single $\ensuremath{\gamma}$ photon propagation in a dense absorptive medium with two widely spaced resonances is experimentally studied. After an initial fast decay, a revival of the photon amplitude in the form of a bump, exceeding the probability amplitude of the incident photon, is observed. The irradiation time of this bump delays approximately by the lifetime of the excited nuclei in the absorber. This effect is explained by the interference of the incoming radiation with the collectively scattered radiation, the phase of which is modulated with the frequency of the doublet splitting. Initially, the destructive interference changes to a constructive one, distinguishing the storage and retrieval stages of the photon propagation in a dense medium, i.e., the collective absorption and collective re-emission processes.
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 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.