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Journal of Experimental and Theoretical Physics Letters

Shape of the signal of double radio-optical resonance in 85Rb atomic vapors in strong fields

Alexander S. Zibrov, AA Zhukov, VP Yakovlev, Vladimir L Velichansky

Published Apr 1, 2006• 7 citations
Publisher

Abstract

A transmission peak has been experimentally observed in the center of the signal of double radio-optical resonance in rubidium atomic vapors at the hyperfine splitting frequency of the ground state. It has been shown that this structure appears due to the Doppler detuning of the optical field and the corresponding optical shift of the microwave field. An analytical expression has been obtained for the shape of this resonance and the effect has been qualitatively explained.

DOI
10.1134/s0021364006040023

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Journal of Experimental and Theoretical Physics•Dec 1, 2021•7 citations
A transmission peak has been experimentally observed in the center of the signal of double radio-optical resonance in rubidium atomic vapors at the hyperfine splitting frequency of the ground state. It has been shown that this structure appears due to the Doppler detuning of the optical field and the corresponding optical shift of the microwave field. An analytical expression has been obtained for the shape of this resonance and the effect has been qualitatively explained.
The absorption of a light wave interacting with optical transitions in the D1line of an alkali metal atom subjected to microwave radiation that is in resonance with magnetic dipole transitions between hyperfine ground-state components, has been investigated. It is known that when scanning a longitudinal magnetic field (B||k, wherekis the wavevector), one may observe a magneto-optical resonance due to the ground-state Hanle effect. In addition, the effect of double radio-optical resonance takes place because of the presence of the resonance microwave field. The joint influence of these effects on the formation of a narrow magneto-optical resonance in light wave absorption has been studied theoretically and experimentally. It has been shown analytically that the effects compete with each other and destructively act on the resonance formation. As a result, the amplitude of the resonance is small and its shape is complicated. However, in the presence of a buffer gas the pressure of which is such that the hyperfine splitting of the ground state remains spectrally unresolved, it becomes possible to observe a magneto-optical resonance with a relatively large amplitude. Experiments have been carried out with the use of a miniature glass cell (V~ 0.1 cm3) filled with87Rb vapor and a buffer gas argon (a pressure of about 95 Torr). In particular, the theoretically predicted resonance narrowing with increasing light field intensity has been experimentally observed. A configuration for magneto-optical resonance excitation suggested here may be applied in quantum magnetometry to measure weak permanent magnetic fields and resonance microwave fields using cells filled with alkali metal vapor.
Abstract The absorption of a light wave interacting with optical transitions in the D1 line of an alkali metal atom subjected to microwave radiation that is in resonance with magnetic dipole transitions between hyperfine ground-state components, has been investigated. It is known that when scanning a longitudinal magnetic field (B || k, where k is the wavevector), one may observe a magneto-optical resonance due to the ground-state Hanle effect. In addition, the effect of double radio-optical resonance takes place because of the presence of the resonance microwave field. The joint influence of these effects on the formation of a narrow magneto-optical resonance in light wave absorption has been studied theoretically and experimentally. It has been shown analytically that the effects compete with each other and destructively act on the resonance formation. As a result, the amplitude of the resonance is small and its shape is complicated. However, in the presence of a buffer gas the pressure of which is such that the hyperfine splitting of the ground state remains spectrally unresolved, it becomes possible to observe a magneto-optical resonance with a relatively large amplitude. Experiments have been carried out with the use of a miniature glass cell (V ~ 0.1 cm3) filled with 87Rb vapor and a buffer gas argon (a pressure of about 95 Torr). In particular, the theoretically predicted resonance narrowing with increasing light field intensity has been experimentally observed. A configuration for magneto-optical resonance excitation suggested here may be applied in quantum magnetometry to measure weak permanent magnetic fields and resonance microwave fields using cells filled with alkali metal vapor.
An investigation was made of a double radio–optical resonance (DROR) in a multilevel system of the alkali metal type. Equations for the density matrix were solved to obtain expressions for the signal, DROR line width, and shift of the maximum of DROR line peak. A study was made of the principal characteristics of a DROR in an optically dense medium in the form of a rubidium vapor. The ultimate short-term frequency instability of a rubidium discriminator was estimated to be 2 × 10 − 14 t − 1/2 . Several experiments were carried out using an injection laser as an optical pump source. The results of the measurements yielded a short-term instability of 3 × 10 − 12 t − 1/2 . An investigation was made of the optical frequency shift and an anomalous dependence of the shift on the intensity was observed. The results of the experimental and theoretical investigations were compared. The requirements for stabilization of the DROR parameters needed to reduce the frequency instability of a rubidium discriminator to the 10 − 14 level were identified.
The interaction of a four-level atomic system with two electromagnetic radiations has been studied. The two intermediate levels are closely spaced such that a single radiation frequency can induce transitions from the ground state to both of them. In a cascade-type double resonance, the pump electric-field amplitude is much stronger than the amplitude of the signal field, which can induce transitions from both of the intermediate levels to the upper state. The 15 optical Bloch equations obtained from the Liouville equations are solved analytically to obtain the Doppler-free signal line shape. The computed signals, exhibiting two Lorentzian line profiles, are presented for different pump frequencies. In addition to these one-photon transitions, we obtain a weak two-photon resonance peak. The two-photon resonance becomes weaker when the detuning of the pump frequency from a resonance frequency is increased. When the pump frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$ is intermediate between the pump resonance frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, the two-photon resonance is very weak and almost vanishes when ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$=(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$)/2. When the pump frequency is on resonance with one of the transition frequencies, the Rabi splitting of the signal shows asymmetry because of the presence of a close-lying transition which is pumped off resonance. The intensity-dependent shifts of the transitions are such that they repel each other more and more as the intensity of the pump field is increased. These shifts arise from the nonresonant interaction between the atom and the field.
Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.