# Dynamics of Entanglement in Jaynes–Cummings Nodes with Nonidentical Qubit-Field Coupling Strengths

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Separate Jaynes–Cummings Nodes

#### 2.1. Vacuum-State Field

#### 2.2. Coherent-State Field

## 3. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Sketch illustrating two separate Jaynes–Cummings nodes. Qubits A and B are independently placed in Nodes 1 and 2, resonantly coupling to the fields a and b, respectively. There is not any interaction between A and B or between a and b.

**Figure 2.**Time-dependent evolution of C for: (

**a**) ${G}_{A}=0.9{G}_{B}$; (

**b**) ${G}_{A}={G}_{B}$; and (

**c**) ${G}_{A}=1.1{G}_{B}$. The corresponding periods are $10\pi /{G}_{B}$, $\pi /{G}_{B}$, and $10\pi /{G}_{B}$, respectively.

**Figure 3.**Two-qubit concurrence as a function of the evolution time under different ratios $\delta ={G}_{A}/{G}_{B}$ with $\overline{n}=100$: (

**a**) analytical results and (

**b**) numerical results, where analytical results are based on the X-form $\rho $ in Equation (15) and numerical results are based on the original $\rho =T{r}_{a,b}\left(\right|\mathsf{\Psi}\left(t\right)\rangle \langle \mathsf{\Psi}\left(t\right)\left|\right)$.

**Figure 4.**Two-qubit concurrence evolves with time under different ratios $\delta ={G}_{A}/{G}_{B}$ for analytical results ((

**a**) $\overline{n}=25$ and (

**b**) $\overline{n}=36$) and numerical results ((

**c**) $\overline{n}=25$ and (

**d**) $\overline{n}=36$).

**Figure 5.**Characteristics of the first revival envelope versus the ratio $\delta $ for different $\alpha $: (

**a**) peek ${P}_{C}$ and (

**b**) period ${T}_{{P}_{C}}$.

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**MDPI and ACS Style**

Shen, L.-T.; Shi, Z.-C.; Wu, H.-Z.; Yang, Z.-B.
Dynamics of Entanglement in Jaynes–Cummings Nodes with Nonidentical Qubit-Field Coupling Strengths. *Entropy* **2017**, *19*, 331.
https://doi.org/10.3390/e19070331

**AMA Style**

Shen L-T, Shi Z-C, Wu H-Z, Yang Z-B.
Dynamics of Entanglement in Jaynes–Cummings Nodes with Nonidentical Qubit-Field Coupling Strengths. *Entropy*. 2017; 19(7):331.
https://doi.org/10.3390/e19070331

**Chicago/Turabian Style**

Shen, Li-Tuo, Zhi-Cheng Shi, Huai-Zhi Wu, and Zhen-Biao Yang.
2017. "Dynamics of Entanglement in Jaynes–Cummings Nodes with Nonidentical Qubit-Field Coupling Strengths" *Entropy* 19, no. 7: 331.
https://doi.org/10.3390/e19070331