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Soviet Physics Uspekhi

Nonlinear and parametric effects in atomic rf spectroscopy

L. N. Novikov, G. V. Skrotskiǐ

Published Jul 31, 1978• 7 citations
Publisher

Abstract

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.

DOI
10.1070/pu1978v021n07abeh005666

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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.
The review describes and interprets the basic phenomena recently observed in the interaction between free atoms and laser radiation. Some of these have been known for a long time in magnetic resonance but in the optical range, the situation is strongly modified because of spontaneous emission and the Doppler effect. Therefore, particular attention is paid to resonance fluorescence and Doppler-free spectroscopy but without dwelling on applications. Transient effects are also discussed, but all the phenomena which characterize, not specifically the interaction between atoms and fields, but the free evolution of atoms after coherent excitation are ignored. Pulse propagation experiments are described in detail and multiphoton processes are considered, with special emphasis on Doppler-free multiphoton excitation and resonant multiphoton ionization.
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.
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
In this contribution quantum-effects in the radiation-atom interaction will be reviewed. It is well known that most of the phenomena involving laser light can be described by semi-classical methods however phenomena such as laser noise the spectra and photon statistics of resonance fluorescence and the interaction of atoms in the single-atom maser require a quantization of the radiation field. In this paper we will describe results on the latter two effects. We will start with the discussion of resonance fluorescence. 1. RESONANCE FLUORESCENCE The resonant interaction of laser light with atomic systems has received considerable theoretical and experimental attention over the past decade. Until the advent of the laser light sources for spectroscopy consisted of ordinary spectral lamps excited by DC or RF discharges and produced light having a very broad spectral width and hence very short correlation time and a relatively low intensity. For such fields both the experimental and theoretical results are in general well understood. However the development of the laser made available light sources which are sufficiently intense that an atomic (or molecular) transition can be very easily saturated. In addition the lasers are highly monochromatic having a coherence time much greater than typical natural lifetimes of excited atomic states and finally tunable making it possible to selectively excite particular atomic transitions. The theoretical analysis of this physical situation requires the use of techniques more general than
Behavior of the optically pumped atoms in the oscillating rf field is analized classically in terms of the macroscopic magnetization, in the case that the static magnetic field has components both parallel and perpendicular to the rf field. The theory predicts that the g -factor is modified by the rf field when the Hanle effect and the parametric resonance take place, and that the effect makes its appearance in the variation of width and maxima of lines of the Hanle effect and the parametric resonance. The modification of the g -factor is also derived by the quantum mechanical treatment. The theoretical predictions are quantitatively verified by the experiments with cesium vapor.