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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Frequency-modulation spectroscopy of coherent dark resonances of multilevel atoms in magnetic field

Yu. V. Vladimirova, Victor N. Zadkov

Published Sep 10, 2010• 0 citations
Publisher

Abstract

Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.

DOI
10.1117/12.883103

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Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
The results of frequency-modulation (FM) spectroscopy of coherent dark resonances from the Zeeman sublevels of the transition F=2 ↔ F=1 of D1 line in absorption of 87Rb atoms are presented and discussed in detail. By contrast with the conventional spectroscopy of coherent dark resonances employing two laser beams, relative frequency of which can be varied, these data has been obtained with the help of a single frequency-modulated laser field. Variation of the modulation frequency plays then similar role with variation the relative frequency in conventional spectroscopy. Experimental data are fit to the theoretical calculations, which are based on the theory of FM spectroscopy of coherent dark resonances recently developed by us. Feasibility of using such experimental technique for accurate measurements of magnetic fields is also discussed.
In this communication we present our results related to examination of Coherent Population Trapping resonance profile on the D1 line of 87Rb when coupling two ground-state Zeeman sublevels belonging to different hyperfine ground-state levels to a common excited-state one. For this, two coherent laser fields with frequency difference of about 6.8 GHz are used. The resonance is observed as a narrow dip in the fluorescence in dependence on the modulation frequency (fm) of the laser light, centered at 2fm = &Dgr;vhf , where &Dgr;vhf is the frequency difference between the ground-state hyperfine levels of Rb. The resonance observation and its splitting in 7 components have been demonstrated under influence of nonshielded laboratory magnetic field (MF). It has been shown that different components are with different sensitivity to the MF gradients that is in agreement with the performed estimations.
Subnatural-width resonances due to coherent effects in optical pumping at hyperfine (hf) transitions of Rb are investigated using a linearly or circularly polarized single-frequency diode laser beam. The sign and amplitude of the resonances in the fluorescence are measured by scanning the laser frequency over the hf transitions of the Rb D 1 and D 2 lines. The fluorescence perpendicular to the laser beam is detected as a function of magnetic field parallel to the beam propagation and scanned around zero value. In the case of linear polarization of the field, dark resonances are observed for hf transitions with F g → F e = F g -1 and F g → F e = F g , and bright resonances are observed for transitions with F g → F e = F g + 1. This is in agreement with the recently developed theories. For all (except F g = 2→ F e = 3, 85 Rb, D 1 line) hf transitions the sign of the resonances reverses when the polarization of the field changes to circular. The amplitudes of the resonances correspond to the probability of the hf transitions and to the calculated loss rate of the population to the ground hf level not excited by the laser field. The observed narrow resonances (FWHM: few tens of kHz) and their sensitivity to weak magnetic fields are interesting for high-resolution spectroscopy and for development of simple and precise magnetometers.
A universal theory for calculating coherent population trapping resonances in multilevel atoms is suggested. The theory allows arbitrary schemes of multilevel atoms and their excitations to be calculated taking into account the influence of relaxation effects in atoms, applied magnetic field, and the Doppler effect. The experimental data obtained by high-precision diode spectroscopy of coherent dark resonances in samarium vapor are systematically analyzed using the suggested theory. In the absence of a magnetic field, the model of samarium is based on consideration of a degenerate Λ system of the 4f 66s 2(7 F 0) ↔ 4f 6(7 F)6s6p(3 P 0)9 F 1 0 ↔4f 66s 2(7 F 1) active transitions. If the fourth 4f 66s 2(7 F 2) level is taken into account, this Λ system becomes open. Numerical simulation of coherent population trapping resonances shows that the open character of the system decreases the contrast of resonance curves in absorption spectra without changing resonance widths. The system under applied external longitudinal and transverse magnetic fields is correctly described by 7-and 12-level models of atomic transitions, respectively.
Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of 85Rb^{85}\mathrm{Rb}85Rb atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85Rb^{85}\mathrm{Rb}85Rb atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.