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Modelling of Nonlinear Interaction of Rb 87 Atoms with Polarized Radiation

Vladimir A. Polischuk, V. G. Domelunksen, Emilia A. Alipieva, G. Todorov, E. Djakov

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

The ultra narrow resonances, obtained by means of polarization spectroscopy of alkali atoms, originate from the destruction of the laser-induced coherence in the ground state. In the case of single-frequency, near resonance excitation and suitable geometry the well-known ground state Hanle effect is observed. Coherent population trapping in Hanle configuration is a nonlinear modification of this effect, observed in the fluorescence from the upper level. The ground state coherence is transmitted from the laser field and higher rank polarization moments are created. Using the irreducible tensor operator formal- ism programs for numerical modelling of this effect has been developed and presented here. The velocity distribution of the atoms, the Gaussian distribu- tion of the laser beam, stray magnetic field, and the experimental geometry are taken into account. The scheme of conversion of the octupole (� = 3) and hex- adecapole (� = 4) polarization moments (PM) through the laser and magnetic fields into the upper level quadropoles f 2 q is proposed. The conversion of the high-rank polarization moments (PM) into observable components is also dis- cussed. The results of the modelling are compared with the measured ones at different experimental conditions.

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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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 22, 2008•0 citations
The ultra narrow resonances, obtained by means of polarization spectroscopy of alkali atoms, originate from the destruction of the laser-induced coherence in the ground state. In the case of single-frequency, near resonance excitation and suitable geometry the well-known ground state Hanle effect is observed. Coherent population trapping in Hanle configuration is a nonlinear modification of this effect, observed in the fluorescence from the upper level. The ground state coherence is transmitted from the laser field and higher rank polarization moments are created. Using the irreducible tensor operator formal- ism programs for numerical modelling of this effect has been developed and presented here. The velocity distribution of the atoms, the Gaussian distribu- tion of the laser beam, stray magnetic field, and the experimental geometry are taken into account. The scheme of conversion of the octupole (� = 3) and hex- adecapole (� = 4) polarization moments (PM) through the laser and magnetic fields into the upper level quadropoles f 2 q is proposed. The conversion of the high-rank polarization moments (PM) into observable components is also dis- cussed. The results of the modelling are compared with the measured ones at different experimental conditions.
The ultra-narrow resonances, obtained in the coherent spectroscopy of alkali atoms, originate from the destruction of the laser-induced coherence in the ground state. In the case of a single frequency, near-resonant excitation and a suitable geometry of irradiation and observation by scanning a weak magnetic field, one observes coherent population trapping in a Hanle - configuration. The laser field transfers the nonlinear interference resonances created in the degenerate Zeeman sublevels of the ground states to the upper level. As a result, the well-known ground state Hanle - effect is observed in the fluorescence. We investigated theoretically and experimentally the shape, amplitude and sign of these resonances and their dependence on the excitation and registration conditions. The experiment was performed on the D1 87Rb line. Results of the computations were compared with the measurements for corresponding experimental conditions.
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.
AbstractThe 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.
The shape of the coherent-population-trapping (CPT) 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 $({F}_{\ensuremath{\varphi}}=2\ensuremath{\rightarrow}{F}_{f}=1)$ transition of the 87Rb^{87}\mathrm{Rb}87Rb D1{D}_{1}D1​ 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 (HRPMs) 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.
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.
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.