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Physical Review A

Influence of laser beam profile on electromagnetically induced absorption

Senka Ćuk, Milan Radonjić, Aleksandar J. Krmpot, Stanko N. Nikolić, Z. D. Grujić, B. M. Jelenković

Published Dec 1, 2010• 4 citations
Publisher

Abstract

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 ${D}_{2}$ line of $^{87}\mathrm{Rb}$ in a vacuum cell. EIA linewidths obtained for the two laser profiles were significantly different in the range of laser intensities $1$--$4$ mW/cm${}^{2}$. 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.

DOI
10.1103/physreva.82.063802

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Physica Scripta•Nov 1, 2013•5 citations
We compared, experimentally and theoretically, Hanle electromagnetically induced absorption (EIA) obtained using Gaussian and \ensuremathΠ\ensuremath{\Pi}\ensuremathΠ-shaped laser beams 3 mm in diameter. The study was done by measuring the transmission of a laser locked to the Fg=2\ensuremath→Fe=3{F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3Fg​=2\ensuremath→Fe​=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 \ensuremathΠ\ensuremath{\Pi}\ensuremathΠ-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 \ensuremathΠ\ensuremath{\Pi}\ensuremathΠ-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.
Experimental and theoretical analyses show the effect of laser beam radial intensity distribution on line-shapes and line-widths of the electromagnetically induced transparency (EIT). We used Gaussian and Π (flat top) laser beam profiles, coupling the D1 transition of 87Rb atoms in the vacuum cell in the Hanle experimental configuration. We obtained non-Lorentzian EIT line-shapes for a Gaussian laser beam, while line-shapes for a Π laser beam profile are very well approximated with Lorentzian. EIT line-widths, lower for Gaussian than for Π, show nonlinear dependence on laser intensity for both laser beam profiles. EIT amplitudes have similar values and dependence on laser intensity for both laser beams, showing the maximum at around 0.8 mW cm−2. Differences between the EIT line-shapes for the two profiles are mainly due to distinct physical processes governing atomic evolution in the rim of the laser beam, as suggested from the EIT obtained from the various segments of the laser beam cross-section.
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.
Electromagnetically induced transparency (EIT) due to Zeeman coherences in the Rb buffer gas cell is studied for different laser beam profiles, laser beam radii and intensities from 0.1 to 10 mW cm −2 . EIT line shapes can be approximated by the Lorentzian for wide Gaussian laser beam (6.5 mm in diameter) if laser intensity is weak and for a Π laser beam profile of the same diameter. Line shapes of EIT become non-Lorentzian for the Gaussian laser beam if it is narrow (1.3 mm in diameter) or if it has a higher intensity. EIT amplitudes and linewidths, for both laser beam profiles of the same diameter, have very similar behaviour regarding laser intensity and Rb cell temperature. EIT amplitudes are maximal at a certain laser beam intensity and this intensity is higher for narrower laser beams. The EIT linewidth estimated at zero laser intensity is about 50 nT or 0.7 kHz, which refers to 1.5 ms relaxation times of Zeeman coherences in 87 Rb atoms in our buffer gas cell. Blocking of the centre of the wide Gaussian laser beam in front of the photo detector yields Lorentzian profiles with a much better contrast to the linewidth ratio for EIT at higher intensities, above ∼2 mW cm −2 .
Influence of two different laser beam profiles, the Gaussian and the Π (top hat) profile on the resonance line widths and amplitudes in the Hanle electromagnetically induced transparency was studied.The laser beam propagates through the vacuum Rb glass cell.Studies were done at D 1 line for the open 87 Rb: F g = 2 → F e = 1 transition.Hanle electromagnetically induced transparency was measured for the two beam profiles with the same total power and beam diameter and experimental results showed that Gaussian and the top hat profiles give different amplitudes and widths of the Hanle resonances.Resonances obtained from the top hat laser beam profile have lower amplitudes and higher line widths.
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.
We experimentally studied the effects of laser beam diameter on electromagnetically induced transparency (EIT) due to Zeeman coherences induced by a laser resonant with the hyperfine transition Fg = 2 → Fe = 1 of 87Rb in a rubidium buffer gas cell. We use two laser beams of Gaussian intensity radial profile for laser beam diameters of 6.5 and 1.3 mm, laser intensities in the range of 0.1–35 mW cm−2 and cell temperatures between 60 and 82 °C. The results show that the amplitude of the normalized EIT resonance has a maximum at a laser intensity which depends on laser beam diameter and cell temperature. The laser intensity corresponding to the maximum EIT amplitude is higher for a smaller laser beam and higher cell temperature. The linewidth of Zeeman EIT resonance varies nearly linearly with laser intensity, almost independent of cell temperature and laser beam diameter.