# Decoherence Effects in a Three-Level System under Gaussian Process

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## Abstract

**:**

## 1. Introduction

## 2. Model and Dynamics

#### 2.1. Impact of Local Gaussian Noises

#### 2.2. Coherence Measures

## 3. Main Results

#### 3.1. The Noiseless Classical Field

#### 3.2. A Classical Field with Gaussian Noises

#### 3.2.1. A Classical Field with ${\mathcal{FG}}_{n}$

#### 3.2.2. A Classical Field with ${\mathcal{G}}_{n}$

#### 3.2.3. A Classical Field with ${\mathcal{OU}}_{n}$

#### 3.2.4. A Classical Field with ${\mathcal{PL}}_{n}$

#### 3.3. Relative Dynamics

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The current configuration model depicts the coupling of a three-level system $qt$ exposed to a classical fluctuation field $\mathcal{EL}\left(t\right)$. The system–environment coupling strength $\omega $ is shown by the blue-reddish wavy lines, while the noise’s influence is represented by the yellowish light in the qutrit. The brownish-wavy lines depict system dynamics as defined by the associated environment’s stochastic parameter $\eta \left(t\right)$, with diminishing amplitude showing Gaussian noise-induced dephasing.

**Figure 2.**Time evolution of coherence in a single qutrit system prepared in the time-evolved state ${\rho}_{qt}\left(t\right)$ given in Equation (19) subjected to a noiseless classical channel when (

**a**) $\eta =1$, $0\le \omega \le 1$ and (

**b**) $0\le \eta \le 1$, $\omega =0.5$ against the time evolution parameter t.

**Figure 3.**Time evolution of coherence in a single qutrit system prepared in the time-evolved state ${\rho}_{qt}\left(\tau \right)$ given in Equation (19) when subjected to the classical field generating (

**a**) fractional Gaussian noise when $0\le H\le 1$ and (

**b**) Gaussian noise when $0\le g\le 1$, (

**c**) Ornstein–Uhlenbeck noise when $0\le g\le 1$ and (

**d**) power law noise when $2\le \alpha \le 4$ with $g=1$ against evolution parameter $\tau =3$.

**Figure 4.**Time evolution of (

**a**) purity and (

**b**) von Neumann entropy as functions of H versus $\tau $ in a single qutrit system when subjected to the classical field generating fractional Gaussian noise.

**Figure 5.**Time evolution of (

**a**) purity and (

**b**) von Neumann entropy as functions of H versus $\tau $ in a single qutrit system when subjected to the classical field generating Gaussian noise.

**Figure 6.**Time evolution of (

**a**) purity and (

**b**) von Neumann entropy as functions of H versus $\tau $ in a single qutrit system when subjected to the classical field generating Ornstein–Uhlenbeck noise.

**Figure 7.**Upper Panel: Time evolution of (

**a**) purity and (

**b**) von Neumann entropy as functions of g versus $\tau $ in a single qutrit system when subjected to the classical field generating power law noise when $\alpha =3$. Bottom panel: Time evolution of (

**c**) purity and (

**d**) von Neumann entropy as functions of $\alpha $ versus $\tau $ in a single qutrit system when subjected to the classical field generating power law noise when $g=0.5$.

**Figure 8.**Prolonged preservation of (

**a**) purity and (

**b**) von Neumann entropy as functions of g versus $\tau $ in a single qutrit system under Gaussian (green), Ornstein–Uhlenbeck (blue), and power law noise (red) stemming from the classical field when $g={10}^{-3}$ (non-dashed) and $g={10}^{-2}$ (dashed).

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**MDPI and ACS Style**

Zangi, S.M.; ur Rahman, A.; Ji, Z.-X.; Ali, H.; Zhang, H.-G.
Decoherence Effects in a Three-Level System under Gaussian Process. *Symmetry* **2022**, *14*, 2480.
https://doi.org/10.3390/sym14122480

**AMA Style**

Zangi SM, ur Rahman A, Ji Z-X, Ali H, Zhang H-G.
Decoherence Effects in a Three-Level System under Gaussian Process. *Symmetry*. 2022; 14(12):2480.
https://doi.org/10.3390/sym14122480

**Chicago/Turabian Style**

Zangi, Sultan M., Atta ur Rahman, Zhao-Xo Ji, Hazrat Ali, and Huan-Guo Zhang.
2022. "Decoherence Effects in a Three-Level System under Gaussian Process" *Symmetry* 14, no. 12: 2480.
https://doi.org/10.3390/sym14122480