# Dephasing Process of a Single Atom Interacting with a Two-Mode Field

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## Abstract

**:**

## 1. Introduction

## 2. Model and Solution

## 3. Numerical Results

#### 3.1. Population Inversion

#### 3.2. Linear Entropy

#### 3.3. Quantum Fisher Information

#### 3.4. Squeezing Phenomena

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The evolution of the atomic inversion $W(T)$ as a function of the dimensionless time $T=\epsilon t$. The radiation field (RF) is initially in a finite-dimensional pair coherent state (FDPCS) for $\xi =30$ and the single qubit is in its upper state. Plots (

**a**,

**c**) are for one-photon processes with $k=1$ and the two-photon processes with $k=2$ are shown in (

**b**,

**d**). The parameter $q=50$ is used in (

**a**,

**b**) and $q=100$ in (

**c**,

**d**). The red curve indicates the absence of the phase damping (PD) effect ($\gamma /\epsilon =0$) and the blue curve indicates the presence of the PD effect ($\gamma /\epsilon =0.5$).

**Figure 2.**The evolution of the linear entropy $L(T)$ as a function of the dimensionless time $T=\epsilon t$ for the same conditions and parameters of Figure 1.

**Figure 3.**The evolution of the quantum Fisher information ${F}_{q}(T)$ as a function of the dimensionless time $T=\epsilon t$ for the same conditions and parameters of Figure 1.

**Figure 4.**The evolution of the entropy squeezing components $E({\widehat{S}}_{X})$ (red curve) and $E({\widehat{S}}_{Y})$ (blue curve) as a function of the dimensionless time $T=\epsilon t$ in absence of the PD effect $\gamma /\epsilon =0$. The RF is initially in a FDPCS for $\xi =30$ and the single qubit is in its upper state. (

**a**,

**c**) for one-photon processes $k=1$ and for the two-photon processes $k=2$ in (

**b**,

**d**). The parameter $q=50$ is used in (

**a**,

**b**) and $q=100$ in (

**c**,

**d**).

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**MDPI and ACS Style**

Khalil, E.M.; Berrada, K.; Abdel-Khalek, S.; Alsubei, B.; Eleuch, H. Dephasing Process of a Single Atom Interacting with a Two-Mode Field. *Entropy* **2021**, *23*, 252.
https://doi.org/10.3390/e23020252

**AMA Style**

Khalil EM, Berrada K, Abdel-Khalek S, Alsubei B, Eleuch H. Dephasing Process of a Single Atom Interacting with a Two-Mode Field. *Entropy*. 2021; 23(2):252.
https://doi.org/10.3390/e23020252

**Chicago/Turabian Style**

Khalil, Eied M., Kamal Berrada, Sayed Abdel-Khalek, Beida Alsubei, and Hichem Eleuch. 2021. "Dephasing Process of a Single Atom Interacting with a Two-Mode Field" *Entropy* 23, no. 2: 252.
https://doi.org/10.3390/e23020252