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Physical Review A

Calculated Hanle transmission and absorption spectra of the Rb87 D1 line with residual magnetic field for arbitrarily polarized light

Heung‐Ryoul Noh, Han Seb Moon

Published Sep 9, 2010• 22 citations
Publisher

Abstract

This paper reports a theoretical study on the transmission spectra of an arbitrarily polarized laser beam through a rubidium cell with or without a buffer gas in Hanle-type coherent population trapping (CPT). This study examined how laser polarization, transverse magnetic field, and collisions with buffer gas affects the spectrum. The transmission spectrum due to CPT and the absorption spectrum due to the level crossing absorption (LCA) were calculated according to the laser polarization. The results show that the LCA is strongly dependent on the transverse magnetic field and interaction time of the atoms with a laser light via collisions with the buffer gas. In addition, the spectral shape of the calculated Hanle spectrum is closely related to the direction between the (stray) transverse magnetic field and polarization of the laser.

DOI
10.1103/physreva.82.033407

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This paper reports a theoretical study on the transmission spectra of an arbitrarily polarized laser beam through a rubidium cell with or without a buffer gas in Hanle-type coherent population trapping (CPT). This study examined how laser polarization, transverse magnetic field, and collisions with buffer gas affects the spectrum. The transmission spectrum due to CPT and the absorption spectrum due to the level crossing absorption (LCA) were calculated according to the laser polarization. The results show that the LCA is strongly dependent on the transverse magnetic field and interaction time of the atoms with a laser light via collisions with the buffer gas. In addition, the spectral shape of the calculated Hanle spectrum is closely related to the direction between the (stray) transverse magnetic field and polarization of the laser.
We present the transformation in the Hanle configuration of the transmission that results from coherent population trapping (CPT) into the level-crossing absorption (LCA) that results from the single-photon optical pumping in the 87Rb^{87}\mathrm{Rb}87Rb D1{D}_{1}D1​ line of a Rb vapor cell with a Ne buffer gas when the polarization of the laser field is changed from linear to circular. The LCA spectrum, with a narrow spectral width of 2.42.42.4 mG (1.71.71.7 kHz), was observed in the ${F}_{g}\ensuremath{\rightarrow}{F}_{e}\ensuremath{\leqslant}{F}_{g}$ transition with the circularly polarized laser. This may be because the LCA is both related to the transverse magnetic field and the atom-laser interaction time resulting from diffusive atomic motion in the cell with the buffer gas. The CPT and LCA spectra were calculated numerically using the full density matrix equations for the relevant magnetic sublevels of the hyperfine levels, considering the residual magnetic fields perpendicular to laser propagation and the collision effects resulting from the buffer gas. There was good qualitative agreement between theoretical and experimental results.
We investigated the switching between the transmittance and absorption of the 5S1/2(F=2)→5P1/2(F′=1) transition of Rb87 in a paraffin-coated Rb vapor cell in the Hanle configuration. When the laser polarization was changed from linear to circular, the coherent population trapping (CPT) spectrum, with a spectral width of 0.12 mG due to the Ramsey effect, transformed into a narrow absorption spectrum with a sub-milligauss spectral width of 0.2 mG. The CPT and narrow absorption spectra were numerically calculated for both polarizations by considering the degenerate magnetic sublevels of the 5S1/2–5P1/2 transition in the antirelaxation-coated atomic vapor cell. This narrow absorption spectrum was revealed to be magnetic-field-induced absorption due to the residual transverse magnetic field and preservation time of the ground-state coherent spin states.
Coherent-population-trapping resonances within the degenerate two-level system of the F=2-->F′=1 transition of the 87Rb D1 line were investigated in an uncoated Rb vapor cell by means of level-crossing-type experiments. Tuning over the two-photon resonance is achieved sweeping a magnetic field around zero value. The influence of transverse magnetic fields on the amplitude and the width of the resonances, recorded in fluorescence and absorption, were investigated in the cases of excitation with linear, circular, and elliptical laser light polarization. A theoretical analysis was performed for the case of linearly polarized excitation, the results of which are in good agreement with the experiment.
We computationally compare Hanle-type resonances for a transition of the line for magnetic field scans parallel (longitudinal scan) and perpendicular (transverse scan) to the direction of propagation of the optical field in the presence of an additional transverse magnetic field (TMF). For a linearly polarized light, the coherent population trapping (CPT) resonances split at line centre and are identical for both longitudinal and transverse scans. When the probe beam ellipticity is varied, the effect of the TMF is found to be opposite for longitudinal and transverse scans. For a longitudinal scan, the splitting observed in the CPT resonance evolves into an enhanced absorption resonance with an increase in ellipticity. For a transverse scan, the splitting vanishes at higher ellipticities. This can be understood in terms of population redistribution in the ground state sublevels and near-neighbor ground state coherences created by the TMF. We also show that the enhanced absorption signal that splits the CPT resonance strongly depends on transit time, and the CPT resonance strength depends on the excited state dephasing rate.
We have studied experimentally and theoretically Hanle EIA on the closed Fg = 3 goes to Fe = 4 D2 transition of 85Rb. Atoms were excited by the laser light with different polarization, from linear to circular. Results of the theoretical calculations of the laser transmission, based on optical Bloch equations for density matrix elements for the same atomic system, show important effects of magnetic field transverse to the laser light. We were not able to control transverse magnetic field in the experiment but the theoretical results are still applicable to our experimental data due the presence of laboratory stray magnetic field in the vicinity of the Rb cell, occurring because of imperfect magnetic shielding.
Using the closed ${F}_{g}\ensuremath{\rightarrow}{F}_{e}={F}_{g}+1$ D2D2D2 line transition of Rb atoms, we report experimental and numerical evidence of influence of additional transverse magnetic field when examining electromagnetically induced absorption (EIA) in the Hanle configuration. The effect was analyzed with two directions of additional magnetic field and in the cases of excitation with linear, elliptical, and circular laser light polarization. The transverse magnetic field brings substantial differences in the resonance line shape, amplitude, and width. Our theoretical model includes Doppler broadening. Numerical solutions of our theoretical model are in good agreement with experimental results. This analysis points out the importance of the presence of stray magnetic fields when studying EIA.