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Physical Review A

Shape of the coherent-population-trapping resonances and high-rank polarization moments

S. Gateva, L. Petrov, Emilia A. Alipieva, G. Todorov, V. G. Domelunksen, Vladimir A. Polischuk

Published Aug 22, 2007• 11 citations
Publisher

Abstract

The shape of the coherent-population-trapping (CPT) resonances was investigated theoretically and experimentally at different laser powers. The CPT resonances were observed in fluorescence on the degenerate two-level system of the $({F}_{\ensuremath{\varphi}}=2\ensuremath{\rightarrow}{F}_{f}=1)$ transition of the $^{87}\mathrm{Rb}$ ${D}_{1}$ line by means of a Hanle effect configuration in an uncoated vacuum cell. Numerical simulations based on the density matrix formalism, which take into account the high-rank polarization moment (HRPMs) influence and the velocity distribution of the atoms, were used to calculate the shape of the nonlinear magnetic resonances. The comparison of the theoretical and experimental shapes of the CPT resonances demonstrated that the HRPMs influence the shape at all laser excitation powers, and this influence can be used to explain some peculiarities at the center of the CPT resonance shape.

DOI
10.1103/physreva.76.025401

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The shape of the coherent-population-trapping (CPT) resonances was investigated theoretically and experimentally at different laser powers. The CPT resonances were observed in fluorescence on the degenerate two-level system of the (F\ensuremathφ=2\ensuremath→Ff=1)({F}_{\ensuremath{\varphi}}=2\ensuremath{\rightarrow}{F}_{f}=1)(F\ensuremathφ​=2\ensuremath→Ff​=1) transition of the 87Rb^{87}\mathrm{Rb}87Rb D1{D}_{1}D1​ line by means of a Hanle effect configuration in an uncoated vacuum cell. Numerical simulations based on the density matrix formalism, which take into account the high-rank polarization moment (HRPMs) influence and the velocity distribution of the atoms, were used to calculate the shape of the nonlinear magnetic resonances. The comparison of the theoretical and experimental shapes of the CPT resonances demonstrated that the HRPMs influence the shape at all laser excitation powers, and this influence can be used to explain some peculiarities at the center of the CPT resonance shape.
A model for description of the shapes of the coherent population trapping (CPT) resonances at different geometries of excitation and observation is developed. The numerical calculations, based on the irreducible tensor operator formalism, take into account the experimental geometry, the velocity distribution of the atoms, the Gaussian distribution of the laser beam intensity and the high rank polarization moments (HRPM). The results for different laser beam diameters, aperture of the detection, position of the photodetector etc. are compared with the experimental data. A method for description of the experimental shapes is proposed.
Coherent Population Trapping (CPT) resonance obtained with linearly polarized laser beam through magnetic field sweep (Hanle configuration) was investigated in 87Rb D1 line. Influence of the coherence due to high-rank polarization moment (hexadecapole moment), created in the medium, on the CPT resonance shape was calculated and experimentally detected in fluorescence. It was observed as an inverted structure at a high power of excitation. To distinguish resonances due to coherence between Zeeman sub-levels with ΔmF=2 from that with ΔmF=4, the Larmour frequency ωLmodulated by applying an a.c. magnetic field (a.c. MF). Resonance signal at frequency corresponding to 4ωL observed in a fluorescence, and after lock-in on the frequency corresponding to frequency difference between sub-levels ΔmF=4.
The investigation of the coherent population trapping (CPT) resonance on the degenerate two-level system of the (Fg=2→Fe=1) transition of the 87Rb D1 line by means of Hanle effect configuration in an uncoated vacuum cell (Opt. Lett. 28, 1817, 2003), has shown that the measured in fluorescence resonance has a complex shape: a very narrow (about 1mG) resonance superimposed on a broader one (about few tens mG). In this work the narrow and wide CPT resonances are registered in fluorescence, transmitted light and Faraday rotation. The dependence of the CPT resonances structures width and amplitude are measured at different laser power densities when the registration was in fluorescence and transmission. While the narrow resonance width doesn't change in the limits of the accuracy of our measurements, the wide resonance width dependence is complex and it is different in fluorescence and transmission. The origin of the observed dependencies and the differences between CPT signals observed in fluorescence and transmission are discussed.
The investigation of the coherent-population-trapping (CPT) resonance on the degenerate two-level system of the $({F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1)$ transition of the 87RbD1^{87}\mathrm{Rb}\phantom{\rule{0.3em}{0ex}}{D}_{1}87RbD1​ line by means of a Hanle effect configuration in an uncoated vacuum cell [Opt. Lett. 28, 1817 (2003)] has shown that the measured in fluorescence resonance has a complex shape---a very narrow (about 1 mG) structure superimposed on a broader one (about few tens of mG). In this work, the dependence of the width and amplitude of the CPT resonance structures are measured at different laser power densities when the registration is in fluorescence and transmission. While the narrow resonance width does not change within the limits of the accuracy of our measurements, the wide resonance width dependence is complex and is different in fluorescence and transmission. The origins of the observed resonance width narrowing of the CPT resonance structures registered in fluorescence and transmission are discussed.
Experimental investigation of the width, amplitude and shape of the Coherent Population Trapping (CPT) resonances for magnetic field measurements by means of a Hanle effect configuration (the single frequency CPT resonances) is presented. Different resonance width narrowing effects for increasing the sensitivity of the magnetometers are discussed. Numerical simulations based on density matrix formalism, which take into account the influence of the high rank polarization moments and the velocity distribution of the atoms have been performed for analysis of the shapes of the resonances.
Coherent population trapping (CPT) resonances in the degenerate two-level system of the Fg = 2 → Fe = 1) transition of the 87Rb D1 line were investigated in an uncoated vacuum cell by means of Hanle effect configuration. CPT signals with complex shape (narrow resonance approximately 2 mG superimposed on the wide one approximately 150 mG) were observed. The influence of weak transverse magnetic fields (0-1.2 G) on the amplitude and width of the two components was measured. The observed narrow resonances are interesting for application in high resolution spectroscopy and magnetometry.