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

Stray magnetic field influence on coherent population trapping resonances

Vladimir A. Polischuk, L. Petrov, Dimitar G. Slavov, V. G. Domelunksen, G. Todorov

Published Mar 2, 2006• 3 citations
Publisher

Abstract

In the present work we consider theoretically the influence of an arbitrary oriented additional magnetic field on the main properties of the Coherent Population Trapping (CPT) resonances in fluorescence and/or in absorption. The exact numerical solutions are obtained for the tensor components Ρk0 (ρ = f, φ) which describe the population and the longitudinal alignment of the resonant (f) levels with quantum numbers Ff 0 and Ff =1, exited with a single frequency laser field from the ground (φ) state with Fφ=l and Fφ=2. Numerical simulations was used to obtain the width and the amplitude dependences of the resonances under different parameters and parasitic fields. The results are in qualitative agreement with resent experimental investigations.

DOI
10.1117/12.677961

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In the present work we consider theoretically the influence of an arbitrary oriented additional magnetic field on the main properties of the Coherent Population Trapping (CPT) resonances in fluorescence and/or in absorption. The exact numerical solutions are obtained for the tensor components Ρk0 (ρ = f, φ) which describe the population and the longitudinal alignment of the resonant (f) levels with quantum numbers Ff 0 and Ff =1, exited with a single frequency laser field from the ground (φ) state with Fφ=l and Fφ=2. Numerical simulations was used to obtain the width and the amplitude dependences of the resonances under different parameters and parasitic fields. The results are in qualitative agreement with resent experimental investigations.
Theoretical model describing the influence of a parasitic magnetic field on CPT-resonance in Hanle configuration in a strong laser field was proposed. The exact solution of the system of equations has been obtained for the transition between a ground state with Jφ=1 and an excited state with Jf=0 and/or 1. The solutions for the tensor components f k0, describing the population and longitudinal alignment of the upper level f, are obtained, and the dependences of the resonances on the different parameters and parasitic fields were analyzed. The results are in qualitative agreement with resent experimental investigations.
Interaction of a resonant laser beam with an atomic absorption medium creates population redistribution and interference between atomic levels. This anisotropy of the medium is experimentally observed as coherent population trapping (CPT) or electromagnetically induced transparency (EIT). Due to the small sub-natural width of the CPT and EIT resonances, they find wide applications in metrology, quantum optics, atom cooling. A non-compensated stray magnetic field (SMF) can change the shape and sign of the resonance or destroy it completely. In this work, we present an experimental and theoretical investigation of the influence of a stray magnetic field on the CPT resonances obtained on Zeeman sublevels of the D 1 line of 87 Rb in a paraffin-coated vacuum cell. The role is clarified of the polarization moments with different rank in creating the integral registered fluorescent signal in the presence of a stray magnetic field. It is shown that a transverse magnetic field plays an important role in changing the shape of the signal.
In the present work we investigate the relation of the polarization moments having different ranks with the tensor components which form the observable integral CPT signal, in the presence of a stray magnetic field. A numerical experiment with parameters close to the real ones is performed, using a program based on the irreducible tensor operator formalism1. The integral fluorescent signal is calculated for the non-polarized fluorescence at different laser power excitation. Detailed analysis of the numerical solutions for all tensor components which describe population and alignment allows visualizing the dynamics of their behavior in dependence on the experimental geometry and laboratory magnetic field B′. The dependence of population f00, longitudinal f02 and transverse f22 alignment in the presence of transverse magnetic field is investigated. The shape and sign of the resonance change with laser power.
Experimental investigation of the width, amplitude and shape of the Coherent Population Trapping (CPT) resonances for magnetic field measurements by means of a Hanle effect configuration (the single frequency CPT resonances) is presented. Different resonance width narrowing effects for increasing the sensitivity of the magnetometers are discussed. Numerical simulations based on density matrix formalism, which take into account the influence of the high rank polarization moments and the velocity distribution of the atoms have been performed for analysis of the shapes of the resonances.
In this communication we present an investigation of the influence of an alternative magnetic field (a.c.MF) on the Coherent Population Trapping (CPT) resonances obtained in Hanle configuration. A.c.MF applied parallel to the sweeping magnetic field creates side-bands of the CPT resonance 1. Their position in dependence on the a.c.MF frequency and amplitude were investigated. This phenomenon was studied for the cases of linear and circular polarized laser excitation. Coherent signal due to the hexadecapole momentum created was detected. At high amplitudes of the a.c.MF alignment to orientation conversion was recorded.
The nonlinear Hanle effect is generally considered in the modern literature as a particular case of coherent population trapping (CPT) at degenerate Zeeman sublevels of the ground atomic state. The shape, amplitude, and sign of observed resonances and their dependence on the excitation parameters and observation geometry were investigated theoretically and experimentally in many studies because of the wide range of application of this effect. The sensitivity of Hanle resonances to the experimental conditions increases significantly in cells with antirelaxation coating, because the atomic ensemble retains its coherence after a large number of collisions with the cell walls. In this paper, the main attention is paid to the joint influence of the excitation radiation intensity and spurious magnetic fields on CPT resonances observed in fluorescence. The theoretical description is based on the numerical solution of an algebraic system of equations for density matrix ρ^\hat {\rho }ρ^​ in the formalism of irreducible tensor operators. The parameters relating different polarization moments in each equation are visualized using the modified sparse matrix of the system. It is established by numerical simulation that the shape, width, amplitude, and sign of nonlinear magnetooptical resonances change nonmonotonically with a change in the parameters of the excitation radiation and atomic system. The presented theoretical results are in good agreement with the experimental data obtained under various conditions.