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Moscow University Physics Bulletin

Frequency modulation spectroscopy of coherent dark resonances of multi-level atoms in a magnetic field

Yu. V. Vladimirova, Victor N. Zadkov

Published Dec 1, 2010• 4 citations
Publisher

Abstract

The resonances of coherent population trapping (CPT) excited by a frequency-modulated (FM) field at the Zeeman sublevels during the transition F g = 2 → F e = 1 of the 87Rb D 1-absorption line were studied theoretically. The influence of the nonlinear Zeeman effect on the structure of the observed resonances was considered. The spectra of CPT resonances were calculated for different values of magnetic field induction and compared with the experimental data.

DOI
10.3103/s0027134910060123

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 9, 2001•0 citations
The resonances of coherent population trapping (CPT) excited by a frequency-modulated (FM) field at the Zeeman sublevels during the transition F g = 2 → F e = 1 of the 87Rb D 1-absorption line were studied theoretically. The influence of the nonlinear Zeeman effect on the structure of the observed resonances was considered. The spectra of CPT resonances were calculated for different values of magnetic field induction and compared with the experimental data.
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.
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.
We consider the coherent-population-trapping (CPT) phenomenon in a sodium atomic vapor. The experiment leading to the first observation of CPT is revisited with an improved experimental setup and a larger range of magnetic-field strengths. From the analysis of the ground-state hyperfine splitting as a function of the applied magnetic field, we conclude that we have observed the whole spectrum of dark resonances within the D1 line corresponding to the nonabsorbing coherent superposition of two Zeeman sublevels of two different components of the 32S1/2 level. This was not obvious a priori because the transition probabilities at high magnetic-field strengths, as applied in the experiment, have to be taken into account. The differences in the contrast of the various black lines are explained in terms of pumpings outside the interaction scheme preparing the nonabsorbing state. Possible applications of CPT in high magnetic fields are discussed.
In this communication we present experimental investigation of coherent effects at Zeeman sublevels of hyperfine levels of Rb in dependence on the polarization of the pumping laser field in order to obtain more complete information about the dark and bright CPT resonances. The coherent effects are examined in Hanle effect configuration, exciting Rb vapor cell with a single-frequency diode laser. By means of phase-sensitive detection (PSD) the amplitude and sign of the CPT resonances are registered in the vicinity of the Rb D1 and D2 lines. It is shown that the sign of the CPT resonances changes when the polarization of the exciting beam changes. Theoretical calculations are performed for the population losses of the given transition in order to clarify the observed experimental results.