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Journal of the Physical Society of Japan

The Mechanism of Frequency Shifts in New Coherence Resonances

Shigeru Nakayama, Toru Ogawa

Published Sep 15, 1976• 2 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.41.950

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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.
By means of the recursive perturbation method developed by Hioe and Eberly, we present an analytic expression of general fourth-order effects in the frequency shifts of new coherence resonances and multiphoton transitions for the general case that a spin-1/2 atom interacts with an oscillating rf field in optical pumping. Moreover, the validity of the theoretical results is checked by an optical-rf double resonance experiments with cesium vapor, and agreement between observed and calculated results becomes close.
By means of a theoretical approach recently developed by Pegg and Series, the consequences of misalignment of an oscillating rf field in optical-rf double resonances are investigated. Effects of both the longitudinal pumping and the transverse pumping are considered. We show that the single (or ordinary) or multiple quantum resonances and the transverse resonance appear at integral multiples of the oscillating field frequency simultaneously. It is also shown that there is no essential difference between the parametric resonance and the Haroche resonance, namely the transverse resonance becomes the parametric resonance for misalignment angle θ=90° and becomes the Haroche resonance for θ=0°.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
A theoretical and experimental study has been made of the effect of transverse optical pumping in the optical-rf double resonance of cesium atoms. The solution of Bloch type equations shows that the Hanle effect and new type resonances become notable in the weak magnetic field or for strong rf field, as the effect of the transverse pumping. The new type resonances appear in the unmodulated component and the components modulated at the first and the second harmonics of the applied rf frequency in the pumping light beam transmitted through the sample cell. It is predicted that the new type resonances are not only shifted but also broadened as the intensity of rf field increases. The shift, broadening and the intensity for observed new type resonances are in good agreement with the theoretical prediction.
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.
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.