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Physical Review A

Two-dimensional optical spectroscopy by periodic excitation of sublevel coherence with sub-Doppler resolution

Gerhard Wäckerle, Stephan Appelt, M. Mehring

Published Jan 1, 1991• 9 citations
Publisher

Abstract

The response of ground-state spin coherence to narrow-band periodic optical excitation is studied theoretically and experimentally. The dependence of the induced oscillating magnetization on the transverse magnetic field and on the frequency of the laser radiation is calculated for a four-level model system from a Bloch-type equation, yielding a two-dimensional resonance line. The application of this two-dimensional high-resolution Zeeman and optical spectroscopy is demonstrated experimentally in the case of the ${\mathit{D}}_{1}$ line of atomic rubidium vapor. Resolution in the kilohertz range is achieved, which allows clear spectral separation of the two isotopes $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$, showing overlapping lines in the conventional optical absorption spectrum.

DOI
10.1103/physreva.43.242

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 8, 2010•1 citation
The response of ground-state spin coherence to narrow-band periodic optical excitation is studied theoretically and experimentally. The dependence of the induced oscillating magnetization on the transverse magnetic field and on the frequency of the laser radiation is calculated for a four-level model system from a Bloch-type equation, yielding a two-dimensional resonance line. The application of this two-dimensional high-resolution Zeeman and optical spectroscopy is demonstrated experimentally in the case of the D1{\mathit{D}}_{1}D1​ line of atomic rubidium vapor. Resolution in the kilohertz range is achieved, which allows clear spectral separation of the two isotopes 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb, showing overlapping lines in the conventional optical absorption spectrum.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1{D}_{1}D1​ line of the Rb\mathrm{Rb}Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with FFF and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s1\phantom{\rule{0.1em}{0ex}}\mathrm{s}1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s{10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.
It is experimentally demonstrated that use of an extremely thin cell (ETC) with the thickness of a Rb atomic vapor column of ∼400 nm allows one to resolve a large number of individual transitions between Zeeman sublevels of the D1 line of 87Rb and 85Rb in the sub-Doppler fluorescence excitation spectra in an external magnetic field of ∼200 G. It is revealed that due to the peculiarities of the Zeeman effect for different hyperfine levels of Rb, all allowed transitions between magnetic sublevels can be clearly resolved for 87RbF_g = 1 --> F_e = 1, 2 and F_g = 2 --> F_e = 1, 2 fluorescence excitation. Also, relatively good spectral resolution can be achieved for 85RbF_g = 2 --> F_e = 2, 3 fluorescence excitation. Some partial resolution of transitions between magnetic sublevels is achieved for 85RbF_g = 3 --> F_e = 2, 3 fluorescence excitation. The spectral resolution of individual transitions allows one to easily observe both linear and nonlinear Zeeman effects in the fluorescence excitation spectra obtained with the help of the ETC. In the fluorescence spectra of a cell of usual length there is no evidence of a spectral resolution of individual transitions at B ∼ 200 G. A simple magnetometer based on ETC with Rb with a submicrometer spatial resolution is described.
Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1{D}_{1}D1​ transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground-state total angular momentum Fg{F}_{g}Fg​ was greater than or equal to the excited-state total angular momentum Fe{F}_{e}Fe​. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model, which had been developed previously for ordinary vapor cells, averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. However, to describe the resonances in the ETC, key parameters such as the ground-state relaxation rate, excited-state relaxation rate, Doppler width, and Rabi frequency had to be modified significantly in accordance with the ETC's unique features. The level of agreement between the measured and calculated resonance curves achieved for the ETC was similar to what could be accomplished for ordinary cells. However, in the case of the ETC, it was necessary to fine-tune parameters such as the background and the Rabi frequency for different transitions, whereas for the ordinary cells, these parameters were identical for all transitions.
The spectra of the three-photon laser excitation 5 S 1/2 → 5 P 3/2 → 6 S 1/2 nP of cold Rb Rydberg atoms in an operating magneto-optical trap based on continuous single-frequency lasers at each stage are studied. These spectra contain two partly overlapping peaks of different amplitudes, which correspond to coherent three-photon excitation and incoherent three-step excitation due to the presence of two different ways of excitation through the dressed states of intermediate levels. A four-level theoretical model based on optical Bloch equations is developed to analyze these spectra. Good agreement between the experimental and calculated data is achieved by introducing additional decay of optical coherence induced by a finite laser line width and other broadening sources (stray electromagnetic fields, residual Doppler broadening, interatomic interactions) into the model.
We studied magneto-optical resonances caused by excited-state level crossings in a nonzero magnetic field. Experimental measurements were performed on the transitions of the D2{D}_{2}D2​ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Good agreement between the experimental measurements and the theoretical model could be achieved over a wide range of laser power densities. We further showed that the contrasts of the level-crossing peaks can be sensitive to changes in the frequency of the exciting laser radiation as small as several tens of megahertz when the hyperfine splitting of the exciting state is larger than the Doppler broadening.
Laser spectroscopy experiments are reported on rubidium atoms by using two or three external cavity diode lasers to study multiple resonance transitions in Λ- and V-type systems as well as on (Λ+V)-type system. Electromagnetically induced transparency (EIT) peaks having sub-natural line-widths are found on the Doppler broadened transmission backgrounds with velocity selective enhanced absorption dips. In the presence of a pump laser, probe spectrum shows enhancement of EIT signal by tuning the control laser frequency when the Λ- and V-type EIT signals are made to overlap. Theoretical analysis is carried out by solving the optical Bloch equations for five-level atomic model under Λ configuration. With the numerically simulated spectra, variation of EIT transmission peak with ground state decay rate and excited state spontaneous decay rate are investigated. Effect of pump Rabi frequency on the transmission peak is also shown.