# Dynamic Response of a Light-Modulated Magnetometer to Time-Dependent Fields

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## Abstract

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## 1. Introduction

## 2. Model

#### Low-Intensity Limit

## 3. Results

## 4. Discussion

#### 4.1. Perturbative Results

#### 4.2. Non-Perturbative Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematics of a Bell-and-Bloom setup. Two laser beams copropagate in an atomic medium along the x direction in the presence of a transverse time-dependent field oriented along z. The pump beam is modulated in (near) resonance with the spin precession and this causes a macroscopic precessing magnetization. An interference filter (IF) blocks the pump radiation while the probe is polarimetrically analyzed. The polarimeter—made of a polarizing beam splitter, two photo detectors, and a transimpedence amplifier (TIA)—outputs a signal that reproduces the magnetization dynamics and is acquired by an analog-to-digital converter (DAQ) for subsequent numerical elaboration.

**Figure 2.**The modulus of the first Fourier coefficients of the phase for ${\mathrm{\Omega}}_{\Vert}=0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

**Figure 3.**The modulus of the first Fourier coefficients of the phase for ${\mathrm{\Omega}}_{\Vert}=0.5\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

**Figure 4.**The modulus of the first Fourier coefficients of the phase for ${\mathrm{\Omega}}_{\Vert}=1.0\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

**Figure 5.**The modulus of the first Fourier coefficients of the phase for ${\mathrm{\Omega}}_{\Vert}=2.0\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

**Figure 6.**Maps of the modulus of the first Fourier coefficients of the phase for $\delta =0.4\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

**Figure 7.**Maps of the modulus of the first Fourier coefficients of the phase for $\delta =10\mathrm{\Gamma}$. From left to right: $|{\phi}_{1}|$, $|{\phi}_{2}|$, and $|{\phi}_{3}|$.

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**MDPI and ACS Style**

Bevilacqua, G.; Biancalana, V.; Dancheva, Y.
Dynamic Response of a Light-Modulated Magnetometer to Time-Dependent Fields. *Atoms* **2023**, *11*, 111.
https://doi.org/10.3390/atoms11080111

**AMA Style**

Bevilacqua G, Biancalana V, Dancheva Y.
Dynamic Response of a Light-Modulated Magnetometer to Time-Dependent Fields. *Atoms*. 2023; 11(8):111.
https://doi.org/10.3390/atoms11080111

**Chicago/Turabian Style**

Bevilacqua, Giuseppe, Valerio Biancalana, and Yordanka Dancheva.
2023. "Dynamic Response of a Light-Modulated Magnetometer to Time-Dependent Fields" *Atoms* 11, no. 8: 111.
https://doi.org/10.3390/atoms11080111