Shape of the coherent-population-trapping resonances and high-rank polarization moments

Abstract

The shape of the coherent-population-trapping ͑CPT͒ resonances was investigated theoretically and experimentally at different laser powers. The CPT resonances were observed in fluorescence on the degenerate two-level system of the ͑F =2→ F f =1͒ transition of the 87 Rb D 1 line by means of a Hanle effect configuration in an uncoated vacuum cell. Numerical simulations based on the density matrix formalism, which take into account the high-rank polarization moment ͑HRPMs͒ influence and the velocity distribution of the atoms, were used to calculate the shape of the nonlinear magnetic resonances. The comparison of the theoretical and experimental shapes of the CPT resonances demonstrated that the HRPMs influence the shape at all laser excitation powers, and this influence can be used to explain some peculiarities at the center of the CPT resonance shape.There has been increasing interest in the investigation of the coherent-population-trapping ͑CPT͒ resonances, prepared and registered in different ways, because of many applications in high-resolution spectroscopy, magnetometry, lasing without inversion, laser cooling, ultraslow group velocity propagation of light, etc. ͓1-3͔. In many applications to ensure a reliable operation, a good knowledge of the internal and external factors influencing the resonance shape is required ͓4͔.The CPT resonance shape has been studied experimentally and theoretically in many works ͑see ͓1-6͔, and references therein͒. Most of the experimental investigations ͓1,2,7-11͔ were performed at low laser power, the shape of the resonances was practically Lorentzian, and the dependence of the resonance width on the laser power density was linear up to a few mW/ cm 2 . However, more precise investigations of the shape of the resonances showed that the theoretical shape could not reproduce the measured one ͓4,12-16͔, and in some works ͓4,12,14,16͔ theoretical dependences were proposed describing better the shape of the resonances for the particular experimental conditions. At a high laser power, the influence of the multiphoton interactions increases. The coherences obtained, described in density matrix representation by the components MM Ј , are related in irreducible representation to the polarization moments q k of rank k ͓k =0,1, ... ,2F , q = M − MЈ, where F is the total angular momentum of the lower level͔. For the case of F = 2, the maximum rank of the polarization moment is k = 4, the so-called hexadecapole moment.The manifestation of the hexadecapole moments in laserstimulated polarized fluorescence intensity was observed and described in terms of the iteration approach more than three decades ago ͓17͔. Recently, the influence of the transverse components ͑k =4, q = ±4͒ of the Rb lower-level hexadecapole moments on the transverse ͑k =2, q = ±2͒ upper-level quadrupole components was discussed ͓18͔. The influence of the high-rank polarization moments ͑HRPMs͒ on the nonlinear magneto-optical rotation resonances and their potential applications in nonlinear optics and in magnetometry were st...

An atomic magnetometer with autonomous frequency stabilization and large dynamic range

“…The polarization rotation signal with this autonomous frequency stabilized laser is shown as the magnetic field is scanned across the zero field. The illustrated magnetic field resonance is originated from the Zeeman coherence in degenerate two level systems [6,8,[13][14][15]. The linearly polarized light in sigma configuration can be viewed as a combination of σ + and σ -component, when its interaction with an atomic system is envisaged.…”

Manifestation of high-rank polarization moments in the fluorescence CPT resonance

“…Theoretical and experimental investigation of the shape of the CPT resonance was performed taking into account the influence of the high-rank polarization moments 8 . Theoretical calculations are based on the system of equations for density matrix tensor components κ ρ q , describing the interaction of the atom system with resonance laser field, scanned magnetic field B 0 and an additional transverse MF.…”

“…Our task is to resolve resonance due to hexadecapole moment in fluorescence in order to estimate its potential for application. The experimental set-up was the same as the one used in our previous investigations 8,9 and is shown in Fig. 1.…”

Shape of the Coherent Population Trapping Resonances Registered in Fluorescence

“…Our theoretical evaluations of the influence of the HRPM on the shape of the CPT resonances (Gateva et al, 2007(Gateva et al, , 2008a proved that HRPM conversion (Okunevich, 2001) cause the CPT resonance shape peculiarities at the center of the resonance.…”