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Optics Express

On non-vanishing amplitude of Hanle electromagnetically induced absorption in Rb

Marina M. Mijailović, Jelena Dimitrijević, Aleksandar J. Krmpot, Z. D. Grujić, Bratimir M. Panic, D. Arsenović, Dejan Pantelić, B. M. Jelenkovic

Published Jan 1, 2007• 10 citations
Publisher

Abstract

Amplitude and linewidts of the Hanle EIA, obtained from transmission of the laser locked to closed F(g) ? F(e) = F(g) +1 transitions in (85)Rb and(87)Rb, have maximum values at few mW/cm2. Amplitude of the EIA reaches steady value different from zero for higher laser intensities, even for laser intensities of 40 mW/cm(2). Theoretical model of EIA, for the same atomic system as in the experiment, show that the laser intensity, at which maximum of amplitudes and widths occur, depends on the laser detuning. For smaller laser detuning of a few tens of MHz, EIA has a maximum and then vanishes at higher laser intensities. For larger laser detuning of the order of hundreds MHz (but still in the range of Doppler broadening) amplitude of the EIA has very broad maximum and remains above zero for intensities above 40 mW/cm(2). Such theoretical results indicate that Hanle absorption peak remains in the experimental results, regardless of the laser intensities, due to Doppler effect.

DOI
10.1364/oe.15.001328

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Physical Review A•Oct 25, 2011•6 citations
Amplitude and linewidts of the Hanle EIA, obtained from transmission of the laser locked to closed F(g) ? F(e) = F(g) +1 transitions in (85)Rb and(87)Rb, have maximum values at few mW/cm2. Amplitude of the EIA reaches steady value different from zero for higher laser intensities, even for laser intensities of 40 mW/cm(2). Theoretical model of EIA, for the same atomic system as in the experiment, show that the laser intensity, at which maximum of amplitudes and widths occur, depends on the laser detuning. For smaller laser detuning of a few tens of MHz, EIA has a maximum and then vanishes at higher laser intensities. For larger laser detuning of the order of hundreds MHz (but still in the range of Doppler broadening) amplitude of the EIA has very broad maximum and remains above zero for intensities above 40 mW/cm(2). Such theoretical results indicate that Hanle absorption peak remains in the experimental results, regardless of the laser intensities, due to Doppler effect.
In this paper, we present a theoretical model for studying the interaction between linearly polarized laser light and near-degenerated Zeeman sublevels for a multiple V-type atomic system of $^{2}S_{1∕2}{F}_{g}=2\ensuremath{\rightarrow}^{2}P_{3∕2}{F}_{e}=3$ transition in 87Rb^{87}\mathrm{Rb}87Rb. We have calculated the laser absorption in a Hanle configuration, as well as the amplitudes and the widths of electromagnetically induced absorption (EIA) in the range of laser intensities from 0.01to40mW∕cm20.01\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}40\phantom{\rule{0.3em}{0ex}}\mathrm{mW}∕{\mathrm{cm}}^{2}0.01to40mW∕cm2. Our results, showing nonvanishing EIA amplitude, a nonmonotonic increase of the EIA width for the increase of laser intensity, and pronounced shape differences of the Hanle EIA curves at different laser intensities, are in good agreement with recent experimental results. We have found that the EIA behaves differently than the electromagnetically induced transparency (EIT) as a function of the laser intensity. Both the amplitude and width of the EIA have narrow maximums at 1to2mW∕cm21\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2\phantom{\rule{0.3em}{0ex}}\mathrm{mW}∕{\mathrm{cm}}^{2}1to2mW∕cm2. We have shown the strong influence of Doppler broadening of atomic transition on Hanle resonances and have suggested the explanation of it.
We compared, experimentally and theoretically, Hanle electromagnetically induced absorption (EIA) obtained using Gaussian and $\ensuremath{\Pi}$-shaped laser beams 3 mm in diameter. The study was done by measuring the transmission of a laser locked to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition at the D2{D}_{2}D2​ line of 87Rb^{87}\mathrm{Rb}87Rb in a vacuum cell. EIA linewidths obtained for the two laser profiles were significantly different in the range of laser intensities 111--444 mW/cm2{}^{2}2. EIA with the $\ensuremath{\Pi}$-shaped laser beam has a broad intensity maximum and linewidths larger than those obtained with the Gaussian beam profile. We also studied Hanle EIA by measuring the transmission of selected segments of the entire laser beam by placing a small movable aperture in front of the detector. Waveforms so obtained in Hanle EIA resonances were strongly influenced both by the radial distance of the transmitted segment from the beam center and by the radial profile of the laser beam. We show that outer regions of Gaussian beam, and central regions of the $\ensuremath{\Pi}$-shaped beam generate the narrowest lines. The different behaviors of EIA owing to different beam profiles revealed by both theory and experiment indicate the importance of the radial profile of the laser beam for proper modeling of coherent effects in alkali metal vapors.
Using the 2 S 1/2 Fg = 2 -→ 2 P 3/2 Fe = 3 transition in 87 Rb, we analyzed the interaction between the arbitrarily polarized laser light and Zeeman sublevels in the Hanle configuration.We studied theoretically and confirmed experimentally that the effect of the laser light polarization on the electromagnetically induced absorption strongly depends on the laser light power.For the same atomic transition, and for single laser light power (3 mW), it was recently shown that electromagnetically induced absorption line widths increase with polarization ellipticity and that electromagnetically induced absorption amplitude has maximum for certain laser light polarization different than linear.Here, we present results for amplitudes and widths of electromagnetically induced absorption for different laser light polarizations and for the laser light power ≤ 200 µW.It is verified that for small laser light power maximal electromagnetically induced absorption amplitude is for the linear polarization, whereas for larger power maximum of the electromagnetically induced absorption is at higher polarization ellipticity.
Abstract The influence of the closed transition on the neighboring and open transitions of the 87 Rb D 2 line, partially resolved under Doppler broadening, is studied at different ellipticities in the Hanle configuration with longitudinal and transverse magnetic field scans. We show that a sign reversal from an electromagnetically induced transparency (EIT) resonance to an electromagnetically induced absorption (EIA) resonance occurs with an increase in ellipticity for the transition in a transverse field scan. This transformation is not observed for a longitudinal field scan. These observations are attributed to the higher amplitude of the EIA resonance for the transition in transverse field scans for elliptical polarized light. The EIA character in the Hanle transmission profile of and transitions is enhanced (weakened) when the laser beam frequency is detuned towards (away from) the transition. We show by computation that at higher ellipticities, a transformation from an EIT to an EIA resonance for the transition occurs at low frequency shifts (towards the transition) in a transverse field scan.
Using the (2)S(1/2)F(g) = 2 --> (2)P(3/2)F(e) = 3 transition in (87)Rb vapor at room temperature, we study effect of the laser light polarization on the electromagnetically induced absorption (EIA). This work extends the recent study of the behavior of the EIA as a function of the laser ellipticity (Brazhnikov et. al., JETP Lett. 83, 64, 2006). We have shown that such behavior strongly depends on the laser power. For the low laser power EIA amplitude has maximum for linearly polarized light, while for high laser power elliptically polarized light of ellipticity 15-20 degrees generates maximum of the EIA amplitude. EIA width varies slowly with the laser ellipticity at lower laser power, and much stronger at higher laser power. Through our theoretical model we attributed observed results to combined effect of the laser ellipticity and power on the population of ground state Zeeman sublevels.
We studied experimentally and theoretically the evolution of open atomic systems in the constant intensity laser field. The study is performed by analyzing the line shapes of Hanle electromagnetically induced transparency (EIT) obtained in different segments of a laser beam cross section of constant intensity, i.e., a $\ensuremath{\Pi}$-shaped laser beam. Such Hanle EIT resonances were measured using a small movable aperture placed just in front of the photodetector, i.e., after the entire laser beam had passed through the vacuum Rb cell. The laser was locked to the open transition ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1$ at the D1{D}_{1}D1​ line of 87{}^{87}87Rb with laser intensities between 0.5 and 4 mW/cm2{}^{2}2. This study shows that the profile of the laser beam determines the processes governing the development of atomic states during the interaction. The resonances obtained near the beam center are narrower than those obtained near the beam edge, but the significant changes of the linewidths occur only near the beam edge, i.e., right after the atom enters the beam. The Hanle EIT resonances obtained near the beam center exhibit two pronounced minima next to the central maximum. The theoretical model reveals that the occurrence of these transmission minima is a joint effect of the preparation of atoms into the dark state and the optical pumping into the uncoupled ground level Fg=1{F}_{g}=1Fg​=1. The appearance of the transmission minima, although similar to that observed in the wings of a Gaussian beam [A. J. Krmpot et al., Opt. Express 17, 22491 (2009)], is of an entirely different nature for the $\ensuremath{\Pi}$-shaped laser beam.