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

Contribution of the polarization moments of different rank to the integral CPT signal

Elena T. Taskova, Emilia A. Alipieva, G. Todorov

Published Jan 4, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2261673

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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.
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.
Abstract We present an experimental and theoretical investigation of the influence of the transverse magnetic field (TMF) on the coherent population trapping resonances obtained on the Zeeman sublevels of the D 1 line of 87 Rb in a paraffin-coated vacuum cell. It is shown that a TMF changes the shape and sign of the resonance or destroys it completely. The role of the different rank polarization moments in the integral registered fluorescent signal in the presence of stray magnetic fields is clarified using numerical simulations.
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.
A model for description of the shapes of the coherent population trapping (CPT) resonances at different geometries of excitation and observation is developed. The numerical calculations, based on the irreducible tensor operator formalism, take into account the experimental geometry, the velocity distribution of the atoms, the Gaussian distribution of the laser beam intensity and the high rank polarization moments (HRPM). The results for different laser beam diameters, aperture of the detection, position of the photodetector etc. are compared with the experimental data. A method for description of the experimental shapes is proposed.
Coherent Population Trapping (CPT) resonance obtained with linearly polarized laser beam through magnetic field sweep (Hanle configuration) was investigated in 87Rb D1 line. Influence of the coherence due to high-rank polarization moment (hexadecapole moment), created in the medium, on the CPT resonance shape was calculated and experimentally detected in fluorescence. It was observed as an inverted structure at a high power of excitation. To distinguish resonances due to coherence between Zeeman sub-levels with ΔmF=2 from that with ΔmF=4, the Larmour frequency ωLmodulated by applying an a.c. magnetic field (a.c. MF). Resonance signal at frequency corresponding to 4ωL observed in a fluorescence, and after lock-in on the frequency corresponding to frequency difference between sub-levels ΔmF=4.
In this work we investigate the magneto-optical resonance on 87Rb D1 line. In two-level degenerated system this resonance is due to the interference between the Zeeman sub-levels, created by interaction of resonance linear polarized laser beam with the atoms. The observed signal is detected by sweeping magnetic field B around its zero value. This phenomenon is also known as a Coherent Population Trapping (CPT) in Hanle-configuration. In a coated vacuum cell the fluorescence signal has a complex form, because the anti-relaxation coating preserves the created coherence, having different relaxation rates. The ground state coherence is transmitted by the laser field to the upper level; thereby polarization moments with different rank contribute to the fluorescence. The manifestation of the different polarization moments in the observed signal depends on the geometry of the experiment – direction of observation, plane of the laser polarization, polarization of the registered light. The resonances obtained in the fluorescence having different polarization are compared in order to clear up what are the contributions to the fluorescent signal from the polarization moments with different rank. The experiment is performed on the D1 87Rb line, F=2→ F=1 transition in a paraffin-coated cell. The magneto-optical resonances, detected in two orthogonal polarizations are measured. Numerical calculations with parameters, close to the experimental ones are performed by using a program, which is based on the irreducible tensor operator formalism. The results of the modelling are compared with the measured ones at different experimental conditions.