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Journal of Modern Optics

Transparency and delay in resonant scattering of gamma photons

S. Gheysen, K. Vyvey, J. Odeurs

Published Oct 25, 2006• 1 citation
Publisher

Abstract

We present a fully quantum mechanical treatment of resonant scattering of gamma radiation in a nuclear Λ-scheme. Simulations of the closed-form solution for the radiation intensity for N effective scatterers contributions are compared with Mössbauer spectra of FeCO3. It is shown that, although the nuclear level mixing scheme does not fulfill EIT conditions, the observable effects are similar. The change in polarization of the scattered radiation, due to level mixing, gives rise to the development of a strong complementary polarization state which is delayed with respect to the incident photon and to a reduction in absorption because this state does not interfere with the incident photon.

DOI
10.1080/09500340600894154

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We present a fully quantum mechanical treatment of resonant scattering of gamma radiation in a nuclear Λ-scheme. Simulations of the closed-form solution for the radiation intensity for N effective scatterers contributions are compared with Mössbauer spectra of FeCO3. It is shown that, although the nuclear level mixing scheme does not fulfill EIT conditions, the observable effects are similar. The change in polarization of the scattered radiation, due to level mixing, gives rise to the development of a strong complementary polarization state which is delayed with respect to the incident photon and to a reduction in absorption because this state does not interfere with the incident photon.
We present a fully quantum mechanical treatment of resonant scattering of gamma radiation in a nuclear medium exhibiting a $\ensuremath{\Lambda}$ scheme through level mixing. A framework is presented to derive the radiation intensity for NNN effective scatterers contributions. A closed-form solution for the radiation intensity is obtained and compared to the generic expression of EIT in an atomic $\ensuremath{\Lambda}$ scheme. Although the nuclear scheme does not fulfill EIT conditions, the observable effects are similar. We show that the change in polarization of the scattered radiation, due to the level mixing, gives rise to the development of a strong complementary polarization state which is delayed with respect to the incident photon to a reduction in absorption because this state does not interfere with the incident photon.
We present a detailed description and a consistent explanation of the transparency observed in the Mössbauer absorption spectra at a nuclear level mixing in FeCO3. We develop a model for scattering in this nuclear Λ system in a Maxwell–Schrödinger approach, taking into account multiple scattering and polarization effects. It is shown that the level mixing scheme not only yields an expected Stark splitting, but, due to the unequal relaxation rates and transition strengths, an additional interference term is present. Therefore, this scheme is equivalent to the Λ scheme considered for EIT in quantum optics. The interference in the absorption of the gamma radiation can be destructive, leading to a partial transparency, but can also be constructive. Both types of interference are present in the observed spectra.
We have observed the effect of electromagnetically induced transparency (EIT) in a nuclear system. A series of Mössbauer measurements was performed on a single crystal of natural FeCO3. When the condition of nuclear level crossing is fulfilled, a clear reduction in absorption or transparency is seen at the point of level crossing. This reduced absorption cannot be ascribed to saturation effects because of the specific geometry of the experiment. We present an explanation in terms of level mixing by a small non-axial component of the electric field gradient. It can be shown that such a scheme is equivalent, at least in principle, with the schemes considered for EIT in quantum optics.
The group velocity of gamma radiation scattered in the forward direction by a nuclear lambda scheme experiencing level mixing induced transparency, which shows some similarity to optical EIT, has been investigated. The equations for the nuclear coherences governing the group velocity have been solved. The group velocity decreases with the density of the resonant nuclei and with a decrease in the intensity of the mixing interaction. A comparison between the group velocity of the gamma radiation and the probe radiation in “classical” optical EIT conditions has been made.
We discuss level mixing induced transparency (LMIT), which is experimentally found in a thick absorber of FeCO3 containing the 57Fe Mössbauer nuclei. LMIT is observed if two hyperfine levels of the excited state nucleus cross. Absorption of gamma radiation drops by about 25% with respect to the sum of two overlapping absorption lines. The absorption deficit is explained by the mixing of the crossing levels with a symmetry breaking interaction. The level mixing induces a polarization change of the scattered radiation. In such a way, the radiation develops in “normal modes,” which are less absorbed in a thick absorber. We show that, in spite of the absorption drop, the area of the absorption line does not change. This confirms the general knowledge that interference phenomena (destructive or constructive) do not change the lifetime of an excited state particle (atom, nucleus, etc).