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大阪教育大学紀要. III, 自然科学

Shifts of Zeeman Splittings of Quadrupole Spectra due to the Interaction with Nonresonant R.F.Photons

Tarō Itō

Published Jan 1, 1972• 0 citations
Publisher

Abstract

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.

DOI
10.32287/td00010318

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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.
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.
By means of the dressed atom concept examined theoretically by Cohen-Tannoudji and Haroche, the misalignment effects of an oscillating rf-field in optical-rf double resonances are investigated. We present a fully quantum mechanical calculation of higher-order effects in the frequency shifts of new coherence resonance for the general case that a spin-1/2 atom interacts with the oscillating rf-field in optical-pumping. It is analytically shown that the new type resonances can occur even by taking account of higher-order effects in the perturbation theory for the oscillating rf-field whose direction makes a special angle from that of a static field, and that the direction of the shift of the resonance field is not along that of the static field but perpendicular to that of the oscillating field. Theoretical results are compared with optical-pumping experiments of cesium vapor.
Nonlinear phenomena occurring during interaction between an atom and a strong rf field of resonant or nonresonant frequency are reviewed. The account is given in both semiclassical and consistently quantummechanical languages. The concept of an atom "dressed by the radiation field" in which not only the optical-frequency field but also the radio-frequency field is quantized is presented in detail. The results are summarized of theoretical and experimental studies of multiphoton transitions, radiative shifts of normal magnetic resonance lines, parametric resonance, and coherent resonances under the conditions of optical pumping. The influence of nonresonance rf fields on magnetic properties and the rate of magnetic relaxation of atoms is discussed.
We show that second-order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the electric-dipole approximation. A theoretical treatment of quadrupole sum- and difference-frequency generation is given, which includes the effects of spin-orbit and Zeeman splittings. The quadrupole nonlinear susceptibility is evaluated and expressions for phase matching and output power are found. We have generally confirmed the theoretical predictions by observing quadrupole sum-frequency generation of ultraviolet light in sodium vapor. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two-photon saturation, induced index of refraction changes, and single- and multi-photon absorption. Generalization of the dipole forbidden susceptibilities to the case of quadrupole-pumped processes is discussed, with difference-frequency generation in Cs vapor considered as an example.
The coupling of atoms to high Q cavities results in strong modifications of the field and atomic frequencies. These effects are most conveniently analyzed in the ‘‘dressed atom’’ point of view. The vacuum Rabi splitting of the atom‐cavity resonance lines is now being observed in optical and microwave experiments where small samples of atoms resonantly interact with an empty cavity mode. Observation of this effect on a single atom coupled to a cavity vacuum is a realistic goal for experiments. Similar shifts are expected when the cavity mode is weakly excited. The detection of these shifts appears very promising for Quantum nondemolition measurements of very small photon numbers. We propose an experiment in which a microwave field stored in a high Q cavity is continuously monitored with the help of a non‐resonant beam of slow circular Rydberg atoms and we discuss possible applications of this method.
Summary form only given.The present summary reports about a dressed-state approach to optical phase conjugation (OPC) by resonant nearly degenerate four-wave mixing in vapors. The basic idea is to decouple the pump fields from the probe field by first treating the problem of the pump fields interacting with the atom and then consider the interaction with the probe field. From this model, the dip, observed in the OPC yield when the pump fields are tuned to an atomic resonance, can be interpreted as an interference effect between contributions to the polarization originating from two dressed-state transitions.