arXiv:1011.0503 · Physical Review A

Measurements of the magnetic field vector using multiple electromagnetically induced transparency resonances in Rb vapor

Kevin C. Cox, Valeriy I. Yudin, А. В. Тайченачев, Irina V. Novikova, Eugeniy E. Mikhailov

Published Jan 14, 2011• 94 citations

Abstract

We study the dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a linearly polarized bichromatic light ($\mathit{lin}||\mathit{lin}$) configuration in $^{87}\mathrm{Rb}$ vapor. We demonstrate that all seven resolvable EIT resonances exhibit maxima or minima at certain orientations of the laser polarization relative to the wave vector and magnetic field. This effect can be used for the development of a high-precision EIT vector magnetometer.

DOI: 10.1103/physreva.83.015801

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arXiv:1011.0503 · Physical Review A

Measurements of the magnetic field vector using multiple electromagnetically induced transparency resonances in Rb vapor

Kevin C. Cox, Valeriy I. Yudin, А. В. Тайченачев, Irina V. Novikova, Eugeniy E. Mikhailov

Published Jan 14, 2011• 94 citations

arXiv HTML PDF

Abstract

We study the dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a linearly polarized bichromatic light (

\mathit{lin}||\mathit{lin}

) configuration in

^{87}\mathrm{Rb}

vapor. We demonstrate that all seven resolvable EIT resonances exhibit maxima or minima at certain orientations of the laser polarization relative to the wave vector and magnetic field. This effect can be used for the development of a high-precision EIT vector magnetometer.

DOI: 10.1103/physreva.83.015801

Related papers

Vector atomic magnetometer based on EIT

Irina V. Novikova, Eugeniy E. Mikhailov, Mario Alberto González Maldonado +6 more

Here, we describe progress toward realization of a vector magnetometer based on all-optical excitation of an atomic ensemble in a vapor cell under the conditions of electromagnetically induced transparency (EIT). The EIT resonance amplitudes depend on relative orientations of the three key vectors: laser wave-vector, polarization, and the direction of the magnetic field. By analyzing possible two-photon transitions and their combinations, we can, in principle, analytically calculate the amplitude of various EIT resonances as functions of the relative angles between the magnetic field, polarization and laser propagation vectors. By locking the polarization to one of these maxima, one can determine the plane formed by the magnetic field and the light wave vector to the accuracy better than 0.001 rad. Analysis of the relative resonance amplitude may be used to extract the full information about the magnetic field direction.Here, we describe progress toward realization of a vector magnetometer based on all-optical excitation of an atomic ensemble in a vapor cell under the conditions of electromagnetically induced transparency (EIT). The EIT resonance amplitudes depend on relative orientations of the three key vectors: laser wave-vector, polarization, and the direction of the magnetic field. By analyzing possible two-photon transitions and their combinations, we can, in principle, analytically calculate the amplitude of various EIT resonances as functions of the relative angles between the magnetic field, polarization and laser propagation vectors. By locking the polarization to one of these maxima, one can determine the plane formed by the magnetic field and the light wave vector to the accuracy better than 0.001 rad. Analysis of the relative resonance amplitude may be used to extract the full information about the magnetic field direction.

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Vector magnetometry based on electromagnetically induced transparency in linearly polarized light

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We develop a generalized principle of electromagnetically induced transparency (EIT) vector magnetometry based on high-contrast EIT resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the ${D}_{1}$ line of $^{87}\mathrm{Rb}$ has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected angular sensitivity to magnetic field orientation is ${10}^{\ensuremath{-}3}$ deg/Hz ${}^{1/2}$ , which is limited by laser intensity fluctuations, light polarization quality, and magnitude of the magnetic field.We develop a generalized principle of electromagnetically induced transparency (EIT) vector magnetometry based on high-contrast EIT resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the ${D}_{1}$ line of $^{87}\mathrm{Rb}$ has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected angular sensitivity to magnetic field orientation is ${10}^{\ensuremath{-}3}$ deg/Hz${}^{1/2}$, which is limited by laser intensity fluctuations, light polarization quality, and magnitude of the magnetic field.

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Vector magnetometry using electromagnetically induced transparency with $lin\perp lin$ polarizationVector magnetometry using electromagnetically induced transparency with $lin\perp lin$ polarization

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Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $\perp$ linear ( $lin \perp lin$ ) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $σ$ and $π$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $σ$ and $π$ EIT peaks, the strengths of the magnetic field can be calculated. We have also demonstrated that the EIT peak amplitudes show oscillatory behaviour depending upon the orientation of the laser polarization relative to the magnetic field direction. Using the positions of the maxima and minima, the direction of the magnetic field can be calculated. To understand the experimental observation, a theoretical study has been done numerically considering all the thirteen Zeeman sub-levels. Apart from the numerical model, a toy model has also been considered to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and the polarization direction of the electric fields have been explicitly derived in the analytical model. Further the direction of the magnetic field is calculated using the analytical solution. This study can be helpful in order to make an EIT based atomic vector magnetometer at room temperature.Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $\perp$ linear ($lin \perp lin$) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $σ$ and $π$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $σ$ and $π$ EIT peaks, the strengths of the magnetic field can be calculated. We have also demonstrated that the EIT peak amplitudes show oscillatory behaviour depending upon the orientation of the laser polarization relative to the magnetic field direction. Using the positions of the maxima and minima, the direction of the magnetic field can be calculated. To understand the experimental observation, a theoretical study has been done numerically considering all the thirteen Zeeman sub-levels. Apart from the numerical model, a toy model has also been considered to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and the polarization direction of the electric fields have been explicitly derived in the analytical model. Further the direction of the magnetic field is calculated using the analytical solution. This study can be helpful in order to make an EIT based atomic vector magnetometer at room temperature.

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Effects of vector magnetic field on electromagnetically induced transparency with lin ⊥ lin polarization

Bankim Chandra Das, Arpita Das, Dipankar Bhattacharyya +1 more

The effect of a vector magnetic field was studied on electromagnetically induced transparency (EIT) with linear ⊥ linear polarization of the probe and pump beams in 87 R b − D 2 transition with a vapor cell at room temperature. The dependence of EIT on the direction of the quantization axis and the relative orientation of the polarizations of the applied electric fields was studied experimentally. We show that from the relative strengths of σ and π EITs, the direction of the magnetic field can be found. Moreover, from the relative separation between σ and π EITs, the strength of the magnetic field can be calculated. We also demonstrate that the EIT peak amplitudes show oscillatory behavior depending upon the orientation of the laser polarization relative to the magnetic field direction. To understand the experimental observations, a theoretical study was done numerically considering all 13 Zeeman sub-levels. Apart from the numerical simulation, a toy model was also constructed to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and polarization direction of the electric field were explicitly derived with the analytical model.The effect of a vector magnetic field was studied on electromagnetically induced transparency (EIT) with linear ⊥ linear polarization of the probe and pump beams in 87 R b − D 2 transition with a vapor cell at room temperature. The dependence of EIT on the direction of the quantization axis and the relative orientation of the polarizations of the applied electric fields was studied experimentally. We show that from the relative strengths of σ and π EITs, the direction of the magnetic field can be found. Moreover, from the relative separation between σ and π EITs, the strength of the magnetic field can be calculated. We also demonstrate that the EIT peak amplitudes show oscillatory behavior depending upon the orientation of the laser polarization relative to the magnetic field direction. To understand the experimental observations, a theoretical study was done numerically considering all 13 Zeeman sub-levels. Apart from the numerical simulation, a toy model was also constructed to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and polarization direction of the electric field were explicitly derived with the analytical model.

Journal of the Optical Society of America BDec 17, 202010 citations

Vector Magnetometer Using Rb Vapor

Kevin C. Cox

This project demonstrates an optical method for measuring the strength and\ndirection of a magnetic field using electromagnetically induced transparency\n(EIT) in rubidium vapor. In rubidium atoms, the Zeeman effect causes atomic\nstates to shift when an external magnetic field is applied. The magnitude of\nthese shifts, and consequently the strength of the magnetic field, can be measured\nby recording electromagnetically induced transparency resonances with\ntuned laser fields. Furthermore, since the atom's interaction with the laser field\nis dependent on the direction of the magnetic field and the laser polarization,\nwe are able to determine the direction as well as the strength of the magnetic\nfield by analyzing relative intensities of EIT resonances. With a feasible precision\ndown to 10 picoTesla and the possibility of complete field mapping, this\nmagnetometer can be useful for medical, geophysical, and materials testing\napplications.This project demonstrates an optical method for measuring the strength and\ndirection of a magnetic field using electromagnetically induced transparency\n(EIT) in rubidium vapor. In rubidium atoms, the Zeeman effect causes atomic\nstates to shift when an external magnetic field is applied. The magnitude of\nthese shifts, and consequently the strength of the magnetic field, can be measured\nby recording electromagnetically induced transparency resonances with\ntuned laser fields. Furthermore, since the atom's interaction with the laser field\nis dependent on the direction of the magnetic field and the laser polarization,\nwe are able to determine the direction as well as the strength of the magnetic\nfield by analyzing relative intensities of EIT resonances. With a feasible precision\ndown to 10 picoTesla and the possibility of complete field mapping, this\nmagnetometer can be useful for medical, geophysical, and materials testing\napplications.

May 4, 20110 citations

Sensitivity of a vector atomic magnetometer based on electromagnetically induced transparency

Mario Alberto González Maldonado, Owen Rollins, Alex Toyryla +8 more

We present a realization of a magnetic sensor based on electromagnetically induced transparency (EIT) resonances observed in hot Rb vapor using lin $\parallel$ lin polarized dichromatic light and evaluate scalar and vector capabilities of the sensor for measuring Earth-like magnetic fields. We demonstrate scalar measurement sensitivity of 2 pT/Hz^1/2 in the 1-100~Hz spectral frequency band using a cm^3 Rb vapor cell, significantly improving the performance for such a configuration if compared with earlier measurements of large magnetic fields. By using a single linearly polarized dichromatic optical field, we are also able to determine the direction of the magnetic field with respect to the light propagation direction and polarization, taking advantage of the symmetries of the interaction scheme. We accomplish that by combining the polarization-sensitive transmission measurements and sparse sensing machine learning techniques. A path for further improvement of the sensitivity and elimination of systematic effects, such as heading error, is discussed.We present a realization of a magnetic sensor based on electromagnetically induced transparency (EIT) resonances observed in hot Rb vapor using lin$\parallel$lin polarized dichromatic light and evaluate scalar and vector capabilities of the sensor for measuring Earth-like magnetic fields. We demonstrate scalar measurement sensitivity of 2 pT/Hz^1/2 in the 1-100~Hz spectral frequency band using a cm^3 Rb vapor cell, significantly improving the performance for such a configuration if compared with earlier measurements of large magnetic fields. By using a single linearly polarized dichromatic optical field, we are also able to determine the direction of the magnetic field with respect to the light propagation direction and polarization, taking advantage of the symmetries of the interaction scheme. We accomplish that by combining the polarization-sensitive transmission measurements and sparse sensing machine learning techniques. A path for further improvement of the sensitivity and elimination of systematic effects, such as heading error, is discussed.

Optics ExpressJun 12, 202414 citations

We study the dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a linearly polarized bichromatic light (

\mathit{lin}||\mathit{lin}

) configuration in

^{87}\mathrm{Rb}

{D}_{1}

line of

^{87}\mathrm{Rb}

has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected angular sensitivity to magnetic field orientation is ${10}^{\ensuremath{-}3}$ deg/Hz

{}^{1/2}

, which is limited by laser intensity fluctuations, light polarization quality, and magnitude of the magnetic field.

Vector magnetometry using electromagnetically induced transparency with

lin\perp lin

polarization

Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear

\perp

linear (

lin \perp lin

) polarization of the probe and the pump beams in

^{87}Rb

D_2

transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the

σ

and

π

EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the

σ

and

π

EIT peaks, the strengths of the magnetic field can be calculated. We have also demonstrated that the EIT peak amplitudes show oscillatory behaviour depending upon the orientation of the laser polarization relative to the magnetic field direction. Using the positions of the maxima and minima, the direction of the magnetic field can be calculated. To understand the experimental observation, a theoretical study has been done numerically considering all the thirteen Zeeman sub-levels. Apart from the numerical model, a toy model has also been considered to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and the polarization direction of the electric fields have been explicitly derived in the analytical model. Further the direction of the magnetic field is calculated using the analytical solution. This study can be helpful in order to make an EIT based atomic vector magnetometer at room temperature.

We present a realization of a magnetic sensor based on electromagnetically induced transparency (EIT) resonances observed in hot Rb vapor using lin

\parallel

lin polarized dichromatic light and evaluate scalar and vector capabilities of the sensor for measuring Earth-like magnetic fields. We demonstrate scalar measurement sensitivity of 2 pT/Hz^1/2 in the 1-100~Hz spectral frequency band using a cm^3 Rb vapor cell, significantly improving the performance for such a configuration if compared with earlier measurements of large magnetic fields. By using a single linearly polarized dichromatic optical field, we are also able to determine the direction of the magnetic field with respect to the light propagation direction and polarization, taking advantage of the symmetries of the interaction scheme. We accomplish that by combining the polarization-sensitive transmission measurements and sparse sensing machine learning techniques. A path for further improvement of the sensitivity and elimination of systematic effects, such as heading error, is discussed.