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Journal of Physics B Atomic Molecular and Optical Physics

Peculiarities of the coherent population trapping resonance in the fluorescence obtained in a coated 87 Rb cell in the presence of transverse magnetic field: theory and experiment

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

Published Nov 21, 2017• 11 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/aa9c36

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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.

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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.

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Degenerate two-level system in the presence of a transverse magnetic field

L. Margalit, M. Rosenbluh, A. D. Wilson‐Gordon

The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the ${D}_{2}$ line of ${}^{87}$Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a $\ensuremath{\sigma}$ polarized pump in the Hanle configuration with that of a ${\ensuremath{\sigma}}^{\ensuremath{-}}$ probe in the presence of a ${\ensuremath{\sigma}}^{+}$ pump in the pump-probe configuration, and we show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to its magnitude. The population redistribution in the ground state due to the TMF is reinforced by collisional effects, leading to increased splitting of the coherent population trapping (CPT) dip in the absorption spectrum. We explain the appearance of the splitting by setting the quantization axis along the total magnetic field. Then, in the Hanle configuration, the direction of the quantization axis changes as the longitudinal magnetic field is scanned, so that the laser polarization also changes. This leads to the creation of new two-photon detuned $\ensuremath{\Lambda}$ subsystems. The evolution of the populations and coherences of the ground-state Zeeman sublevels is illustrated using the angular momentum probability surface. In addition to being split, the CPT dip in the pump-probe configuration is also shifted by the longitudinal magnetic field, so that the effects of the longitudinal and transverse magnetic fields can be distinguished from each other.

Physical Review A•Mar 12, 2013•44 citations
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.
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 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.
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.
Coherent-population-trapping resonances within the degenerate two-level system of the F=2-->F′=1 transition of the 87Rb D1 line were investigated in an uncoated Rb vapor cell by means of level-crossing-type experiments. Tuning over the two-photon resonance is achieved sweeping a magnetic field around zero value. The influence of transverse magnetic fields on the amplitude and the width of the resonances, recorded in fluorescence and absorption, were investigated in the cases of excitation with linear, circular, and elliptical laser light polarization. A theoretical analysis was performed for the case of linearly polarized excitation, the results of which are in good agreement with the experiment.
The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2{D}_{2}D2​ line of 87{}^{87}87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a $\ensuremath{\sigma}$ polarized pump in the Hanle configuration with that of a ${\ensuremath{\sigma}}^{\ensuremath{-}}$ probe in the presence of a ${\ensuremath{\sigma}}^{+}$ pump in the pump-probe configuration, and we show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to its magnitude. The population redistribution in the ground state due to the TMF is reinforced by collisional effects, leading to increased splitting of the coherent population trapping (CPT) dip in the absorption spectrum. We explain the appearance of the splitting by setting the quantization axis along the total magnetic field. Then, in the Hanle configuration, the direction of the quantization axis changes as the longitudinal magnetic field is scanned, so that the laser polarization also changes. This leads to the creation of new two-photon detuned $\ensuremath{\Lambda}$ subsystems. The evolution of the populations and coherences of the ground-state Zeeman sublevels is illustrated using the angular momentum probability surface. In addition to being split, the CPT dip in the pump-probe configuration is also shifted by the longitudinal magnetic field, so that the effects of the longitudinal and transverse magnetic fields can be distinguished from each other.