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Journal of Physics Condensed Matter

Mössbauer-Zeeman spectroscopy using nuclear ground states dressed with RF photons

J. Odeurs, Gilbert R. Hoy

Published Oct 26, 1998• 1 citation

Abstract

As part of our general programme to develop the field of quantum nucleonics, we have studied Mössbauer spectroscopy when there is Zeeman splitting of the nuclear levels and a further interaction due to an applied rf-radiation field. We have applied the `dressed' state concept, developed in quantum electronics, to this situation. In particular, we have studied the case when the rf frequency is in the neighbourhood of the ground state (spin =1/2) splitting. The dressed-state approach in this case treats the coupling of nuclear Zeeman levels, due to an rf field, by considering the total system made up of nucleus, static magnetic field and rf field as one global quantum system. This allows the time evolution of the system to be handled straightforwardly. The energy levels and corresponding eigenstates of the system are calculated as a function of the rf frequency and the magnitude of the rf magnetic flux density. Mössbauer spectra are calculated for the case in which the source is subjected to both the static and radiation fields while the absorber nuclear levels are unsplit. Spectra are given as a function of the rf frequency, the magnitude of rf-field magnetic flux density, as well as the photon direction.

DOI: 10.1088/0953-8984/10/42/016

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As part of our general programme to develop the field of quantum nucleonics, we have studied Mössbauer spectroscopy when there is Zeeman splitting of the nuclear levels and a further interaction due to an applied rf-radiation field. We have applied the `dressed' state concept, developed in quantum electronics, to this situation. In particular, we have studied the case when the rf frequency is in the neighbourhood of the ground state (spin =1/2) splitting. The dressed-state approach in this case treats the coupling of nuclear Zeeman levels, due to an rf field, by considering the total system made up of nucleus, static magnetic field and rf field as one global quantum system. This allows the time evolution of the system to be handled straightforwardly. The energy levels and corresponding eigenstates of the system are calculated as a function of the rf frequency and the magnitude of the rf magnetic flux density. Mössbauer spectra are calculated for the case in which the source is subjected to both the static and radiation fields while the absorber nuclear levels are unsplit. Spectra are given as a function of the rf frequency, the magnitude of rf-field magnetic flux density, as well as the photon direction.

In this paper we derive a complete semiclassical description of M\"ossbauer spectroscopy with arbitrary external or internal perturbations of the active levels. The \ensuremath{\gamma} rays are taken to be weak enough to allow us to evaluate the linear M\"ossbauer response to lowest order in the intensity, in which case the \ensuremath{\gamma}-ray field can be treated classically. It induces transitions between level manifolds that can have arbitrary interactions inside themselves. The nuclear system is described by a density matrix. In principle, time-dependent perturbations can be handled by the formalism, but the equations are easier to solve for systems that display steady-state behavior. We consider, in particular, the case of magnetic radio-frequency modulation of the M\"ossbauer levels. Utilizing a matrix-continued-fraction technique, we solve for the absorption spectrum, and we choose numerical illustrations with parameters such that they describe the nucleus

^{57}\mathrm{Fe}

. In this paper we treat mainly the case of magnetic modulation, but other experimental arrangements are discussed too. The calculations are able to treat both saturation and interference effects, which become important when the radio-frequency modulation is very strong. The new feature that emerges is the occurrence of resonances arising from the interference of different physical processes. The calculational method and its results are discussed and compared with other works.

We study theoretically resonance absorption of \ensuremath{\gamma} rays by nuclei exposed to an external radio-frequency (rf) magnetic field. The external field is taken to couple directly to the nuclear magnetic moments. Perturbation theory is developed for M\"ossbauer spectroscopy in terms of Floquet eigenstates that incorporate the rf field exactly. The present treatment allows for calculation of the conventional time-averaged absorption spectrum, as well as analysis of the time dependence of absorption, resolved on the scale of a period of the rf field. An efficient numerical implementation of the theory is described and comparisons with the equally general approach of Salkola and Stenholm [M. Salkola and S. Stenholm, Phys. Rev. A 41, 3838 (1990)] are made. We demonstrate that even at off-resonance frequencies a strong modulation leads to shifts of the original static hyperfine lines. Examples of line splittings of NMR's associated with Rabi flopping are also shown. \textcopyright{} 1996 The American Physical Society.

The ”dressed atom” concept has been introduced by Cohen-Tannoudji et al. in relation to the interpretation of the multiple quantum transitions observed in optically pumped vapors. Using this concept, a proposal for its application to solids is given. We have calculated the shifts of the Zeeman splittings of quadrupole spectra due to the interaction with nonresonant r. f. photons in the case of nuclear spin I=3/2. The possibility of detecting the calculated result has been discussed for the Cl atoms in paradichlorobenzene.

Dressed states are eigenstates of the full Hamiltonian which also includes the interaction of the atoms with the driving field. From this point of view, photons of the field interacting with the atom externally induce quantum coherence, and thus modify the inherent properties of atomic system, such as Mollow triplets in the resonance fluorescence spectrum. Because of the rigorous requirement on the ratio of driving strength to the intrinsic linewidth, the associated demonstrations in neutral atoms are restricted to optical dressing in a cavity quantum electrodynamics system and microwave dressing in the Rydberg excitation. Here, we report the realization of coherent dressing of a ground state driven by a radio-frequency magnetic field in an antirelaxation coated warm vapor cell. We reveal the properties of the radio-frequency dressed states, a linear scaling in the resonance splitting, and the improved resonance linewidth. Such a system is robust to the variation of detection frequency and atom number and is able to determine the driving frequency. It thus may emerge as a unique and versatile tool in quantum metrology, for instance, rf atomic magnetometry in a large detection frequency range. Published by the American Physical Society 2024

We present the first experimental observation of the Rabi splitting of M\"ossbauer resonance lines. A radio-frequency magnetic field is tuned to induce transitions between hyperfine sublevels of the Zeeman-split excited or ground state of

^{57}\mathrm{Fe}

nuclei. The line splitting corresponding to the Rabi flopping frequency is observed using a magnetically soft

^{57}\mathrm{FeNi}

absorber foil of composition with almost zero magnetostriction.