In this paper, we present an analysis of the amplitude variations of the opto-magnetic resonance absorption signals obtained in a single-beam magnetometer driven by radially or azimuthally polarized light (RPL/APL). It is shown that optically polarized atoms driven by cylindrical vector beams obtained only the alignment of atomic multipole moments but not the orientation, which is in good agreement with our simulation and experimental results. In comparison with the plane polarized pump light fields, cylindrical vector beams with much more complete electric vector polarization distribution in the transverse plane, make it unlikely to create the "emptying state " (no-atom populated) among the ground-state Zeeman sublevels for any possible orientation of the applied static magnetic field. These characteristics of the RPL/APL lead to generally smaller atomic population difference and lower response intensity of the transmitted signal. The tensor decomposition of atomic polarized states and the evolution of atomic multipole moments with the sweeping radio frequency (RF) field offer the way to show the magnetic orientation sensitivity of the radially or azimuthally polarized probe light, which possess similar profiles as that of the linearly polarized light, only with a constant phase lag of about π/2 and obvious amplitude differences.
In this paper, we present an analysis of the amplitude variations of the opto-magnetic resonance absorption signals obtained in a single-beam magnetometer driven by radially or azimuthally polarized light (RPL/APL). It is shown that optically polarized atoms driven by cylindrical vector beams obtained only the alignment of atomic multipole moments but not the orientation, which is in good agreement with our simulation and experimental results. In comparison with the plane polarized pump light fields, cylindrical vector beams with much more complete electric vector polarization distribution in the transverse plane, make it unlikely to create the "emptying state " (no-atom populated) among the ground-state Zeeman sublevels for any possible orientation of the applied static magnetic field. These characteristics of the RPL/APL lead to generally smaller atomic population difference and lower response intensity of the transmitted signal. The tensor decomposition of atomic polarized states and the evolution of atomic multipole moments with the sweeping radio frequency (RF) field offer the way to show the magnetic orientation sensitivity of the radially or azimuthally polarized probe light, which possess similar profiles as that of the linearly polarized light, only with a constant phase lag of about π/2 and obvious amplitude differences.
In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency or the amplitude of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency-, or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic m of the Larmor frequency ${\ensuremath{\omega}}_{L}$ (either by DC or phase sensitive detection at harmonics q of the modulation frequency ${\ensuremath{\omega}}_{\mathrm{mod}}$) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum F in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated light.
As is well known a linearly polarized resonant laser will cause atoms to generate a magnetic tensor moment (MTM) by polarizing them. When there exists an external magnetic field, it is possible that the moment will precess around the field. In the presence of a radio frequency (RF) exciting source, we investigate theoretically the dependence of time-independent (direct current, DC), the first and second harmonic signal of the MTM precession on magnetic vector field, and obtain its analytical solution by solving the Liouville equation. The results show that the interference of both harmonic components will result in the precession spectrum evidently varying. A detailed explanation is described in the following. For the DC signal, Rabi frequency Ω of 1/(2√2) is a spectral splitting threshold. When it is greater than the threshold, the interference will cause single resonant absorption dip characterized usually to split into two dips, which has not been reported before to the best of our knowledge, and the separation between both the dips may be expressed as √3√Ω2+Ω4 -Ω2-1. For the first harmonic signal including symmetric and antisymmetric component, an interference fringe will appear near the center of antisymmetric part when Ω >1/(2√2), simultaneously its symmetric part behaves like the above dc component, such as splitting threshold and separation between both dips. With regard to the second harmonic signal, it is found that the interference can also lead to the width of the second harmonic decreasing to 38% compared with the case of the first harmonic signal. At the optimum RF Rabi frequency, on the assumption that noise spectral density is constant, it is theoretically shown that the most sensitive magnetometer, realized by the DC component or the first or second harmonic signal of the precession, depends only on the angle between the light polarization and the measured magnetic field.In fact, we are able to obtain the modules of the measured magnetic vector by RF resonant frequency. The angle between the magnetic field and the laser polarization is determined just by the ratio of the intensity of the DC component to the intensity of the second harmonic signal and the ratio between the intensities of the symmetric parts of two harmonic signals in resonance, and another orientation angle between the measured field projection at the plane perpendicular to the light polarization and the direction of RF source depends on the phase difference between the antisymmetric components of both harmonic signals. Consequently, we demonstrate a vectorial atomic magnetometer that is realized by using the RF source and the linearly polarized resonant laser without rotating laser polarization. This kind of atomic magnetometer with simple sensor structure is easy to integrate vector magnetometer array which will be suitable for solving the inverse problem and geomagnetic navigation.
Double-resonance optically pumped magnetometry can be used to measure static magnetic fields with high sensitivity by detecting a resonant atomic spin response to a small oscillating field perturbation. Determination of the resonant frequency yields a scalar measurement of static field (B0) magnitude. We present calculations and experimental data showing that the on-resonance polarimeter signal of light transmitted through an atomic vapor in arbitrarily oriented B0 may be modeled by considering the evolution of alignment terms in atomic polarization. We observe that the amplitude and phase of the magnetometer signal are highly dependent upon B0 orientation and present precise measurements of the distribution of these parameters over the full $4\ensuremath{\pi}$ solid angle.
Optically pumped magnetometers usually rely on optical pumping using circularly or linearly polarized light. We study here zero-field magnetometers pumped with elliptically polarized light, preparing both atomic orientation and alignment with complementary geometries. We start by extending the three-step approach for elliptically polarized pumping. This allows us to study the Hanle effect in elliptical polarization by comparing the analytical absorption signals with experiments made on 4He metastable state. We then study parametric resonance magnetometers based on elliptical polarization by using the dressed-atom formalism with one and two radio-frequency fields. The results show good agreement with the experimental measurements and interesting perspectives for magnetometry where symmetry breaking by pumping light is mitigated.
We explore the role of the linearly polarized probe beam in the radio-frequency atomic magnetometer. Two regimes of coupling of the linearly polarized light to the atomic ensemble, near and off-resonant, are demonstrated and discussed. Our studies cover three types of interaction between the atomic spin system and the linearly polarized beam, i.e., absorptive production of spin polarization, dispersive spin state readout, and nonlinear spin couplings. The work is performed with the outlook of optimization and simplification of magnetometer operation. Operation of a magnetometer with a single beam, generating and probing the atomic orientation, is presented. This single-beam configuration, which combines optical pumping, nonlinear spin couplings, and spin-exchange collisions, creates the option for a portable device with simple instrumentation.
We report a rubidium atomic magnetometer based on pump-probe nonlinear magneto-optical rotation. The rubidium vapor cell is placed in a five-layer magnetic shield with inner coils that can generate uniform magnetic fields along the direction of pump beam, and the cell is also placed in the center of a Helmholtz coil that can generate an oscillating magnetic field perpendicular to the direction of pump beam. The atoms are optically pumped by circularly polarized pump beam along a constant magnetic field in a period of time, then the pump beam is turned off and a /2 pulse of oscillating magnetic field for 87Rb atoms is applied. After the above process, the individual atomic magnetic moments become phase coherent, resulting in a transverse magnetization vector precessing at the Larmor frequency in the magnetic field. The linearly polarized probing beam is perpendicular to the direction of magnetic field, and can be seen as a superposition of the left and right circularly polarized light. Because of the different absorptions and dispersions of the left and right circularly polarized light by rubidium atoms, the polarization direction of probing beam rotates when probing beam passes through rubidium vapor cell. The rotation of the polarization is subsequently converted into an electric signal through a polarizing beam splitter. Finally, the decay signal related to the transverse magnetization vector is measured. The Larmor frequency proportional to magnetic field is obtained by the Fourier transform of the decay signal. The value of magnetic field is calculated from the formula:B=(2/) f, where and f are the gyromagnetic ratio and Larmor frequency, respectively. In order to measure the magnetic field in a wide range, the tracking lock mode is proposed and tested. The atomic magnetometer can track the magnetic field jump of 1000 nT or 10000 nT, indicating that the atomic magnetometer has strong locking ability and can be easily locked after start-up. The main performances in different magnetic fields are tested. The results show that the measurement range of the atomic magnetometer is from 100 nT to 100000 nT, the extreme sensitivity is 0.2 pT/Hz1/2, and the magnetic field resolution is 0.1 pT. The transverse relaxation times of the transverse magnetization vector in different magnetic fields are obtained, and the relaxation time decreases with the increase of the magnetic field. When the measurement range is from 5000 nT to 100000 nT, the magnetic field sampling rate of the atomic magnetometer can be adjusted in a range from 1 Hz to 1000 Hz. The atomic magnetometer in high sampling rate can measure weak alternating magnetic field at low frequency. This paper provides an important reference for developing the atomic magnetometer with large measurement range, high sensitivity and high sampling rate.