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Physical Review A

Absorption and quantum coherence of a degenerate two-level system in the presence of a transverse magnetic field in different directions

Hebin Zhang, Guoqing Yang, Guangming Huang, Gao‐xiang Li

Published Mar 1, 2019• 5 citations
Publisher

Abstract

We investigate the absorption spectra for the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=0$ transition of the ${D}_{2}$ line of $^{87}\mathrm{Rb}$ excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.

DOI
10.1103/physreva.99.033803

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We investigate the absorption spectra for the Fg=1\ensuremath→Fe=0{F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=0Fg​=1\ensuremath→Fe​=0 transition of the D2{D}_{2}D2​ line of 87Rb^{87}\mathrm{Rb}87Rb excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.
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.
We discuss the effect of static and time-dependent longitudinal and transverse magnetic fields on degenerate two-level and three-level systems in Rb atomic vapor. The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2 line of 87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a σ polarized pump in the Hanle configuration with that of a σ− probe in the presence of a σ+ pump in the pump-probe configuration, and show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to the magnitude of the TMF. Coherent population trapping (CPT) transients induced by a modulated longitudinal magnetic field (LMF) are investigated theoretically for a realistic three-level Λ system in the D1 line of 87Rb. The contributions to the transient probe absorption from the various subsystems that comprise the realistic atomic system are examined and the absorption of each Λ subsystem is compared to that of a simple Λ system. We also present theoretical results for CPT transients induced by a modulated TMF. The application of a TMF leads to the appearance of new Λ subsystems, the creation of new dark states and the rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between various steady-state situations and we identify the various components of the total probe absorption.
Coherent population trapping (CPT) resonances on the degenerate two-level system of the (Fg=2→Fe=1) transition of the 87Rb D1 line were investigated in an uncoated vacuum cell by means of level-crossing type experiments-sweeping a magnetic field around zero value and using a single laser beam. The two-photon resonance manifests itself as fluorescence canceling when the system of levels is degenerate (at zero point of magnetic field). The influence of weak transverse magnetic fields on the amplitude and width of the resonance was investigated. The CPT resonances were observed with linear, circular and elliptical polarized laser light. Transverse magnetic field widens the resonances obtained by linear and circular polarization but splits the resonance created by slightly elliptically polarized laser light. The dependence of this splitting on the elliptical ratio and experimental geometry were investigated. Due to its narrow width and sensitivity to low magnetic fields (< 1 G) this resonance is very promising for small magnetic field measurement.
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.
Abstract We present experimental and theoretical investigations of the dependence of double Hanle resonance spectrum on the light polarization angle and the direction of the applied transverse magnetic field (TMF). The experiments are done for F g = 2 → F e = 1 transition of 87Rb D1 line using a rubidium vapor cell containing buffer gas. We show that a small light polarization component along the direction of TMF introduces asymmetry in the double Hanle resonance signal. Both the magnitude and sign of asymmetry in the signal are sensitive to the TMF orientation, suggesting a possible method for in-situ measurement of the direction of the magnetic fields generated by the coils. The physical origin of this asymmetry is explained by considering the redistribution of population among the ground-state Zeeman sublevels in the presence of TMF. In addition, we systematically vary both the polarization angle and TMF direction to study their effect on the line profile of Hanle resonances. We demonstrate that a double Hanle resonance changes to a dark Hanle resonance by rotating the light polarization vector irrespective of the TMF direction. We have developed a simple theoretical model based on a degenerate two-level system to explain our experimental observations.
We computationally compare Hanle-type resonances for a transition of the line for magnetic field scans parallel (longitudinal scan) and perpendicular (transverse scan) to the direction of propagation of the optical field in the presence of an additional transverse magnetic field (TMF). For a linearly polarized light, the coherent population trapping (CPT) resonances split at line centre and are identical for both longitudinal and transverse scans. When the probe beam ellipticity is varied, the effect of the TMF is found to be opposite for longitudinal and transverse scans. For a longitudinal scan, the splitting observed in the CPT resonance evolves into an enhanced absorption resonance with an increase in ellipticity. For a transverse scan, the splitting vanishes at higher ellipticities. This can be understood in terms of population redistribution in the ground state sublevels and near-neighbor ground state coherences created by the TMF. We also show that the enhanced absorption signal that splits the CPT resonance strongly depends on transit time, and the CPT resonance strength depends on the excited state dephasing rate.