# Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup

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## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Monitoring the Atom–Cavity System by Driven the Cavity Mode

## 4. Monitoring the Atom–Cavity System by Driven the Single Atom

## 5. Transfer of Entanglement between Two Atoms and Two Modes

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental scheme of the atom–cavity system. The cavity consists of two WGMs coupled simultaneously to a pair of two-level atoms interacting via dipole–dipole interaction $\mathsf{\Omega}$. In this case, both the cavity and the atom are coupled to a tapered optical fiber in an overcoupled regime [21]. The modes of fiber are described by $\{{\widehat{a}}_{in},{\widehat{a}}_{out},{\widehat{b}}_{in},{\widehat{b}}_{out}\}$ coupled to the cavity and $\{{\widehat{\sigma}}_{1,in},{\widehat{\sigma}}_{1,out},{\widehat{\sigma}}_{2,in},{\widehat{\sigma}}_{2,out}\}$ coupled to the atom, in terms of the input–output fields to a detectors.

**Figure 2.**Energy levels diagram of the atom-cavity system with collective decay rates and probe fields where (blue) driving the cavity mode with strength $\u03f5$ and frequency ${\omega}_{L}$ and (red) driving the single atom with strength $\eta $ and frequency ${\omega}_{P}$.

**Figure 3.**Transmission (blue) and reflection (red) of the cavity modes as a function of the detuning between the frequencies of the probe field and the atom–cavity system in overcoupled regime ${\kappa}_{ex}\gg \{{\kappa}_{in},J\}$ and ${\omega}_{c}={\omega}_{a}$. The chosen parameters were $\{\u03f5,{\kappa}_{ex},{\kappa}_{in},\mathsf{\Omega},J,{\mathsf{\Gamma}}_{c},g\}/2\pi =\{10,20,0.2,0,0,5.2,45\}$ MHz. The dashed line corresponds to ${\rho}_{ss}^{at}\to |{\psi}^{-}\rangle \langle {\psi}^{-}|$ and the solid line for ${\rho}_{ss}^{at}\to |G\rangle \langle G|$.

**Figure 4.**Transmission (blue) and reflection (red) of the atoms as a function of the detuning between the frequencies of the probe field and the atom–cavity system in an overcoupled regime ${\gamma}_{ex}\gg \{{\gamma}_{in},\mathsf{\Omega}\}$ and ${\omega}_{c}={\omega}_{a}$. The chosen parameters were $\{{\gamma}_{ex},{\gamma}_{in},\mathsf{\Omega},J,{\mathsf{\Gamma}}_{c}\}/2\pi =\{40,0.2,0,0,5.2\}$ MHz. The dashed line corresponds to ${\rho}_{ss}^{c}\to |{\varphi}^{-}\rangle \langle {\varphi}^{-}|$ and the solid line for ${\rho}_{ss}^{c}\to |V\rangle \langle V|$.

**Figure 5.**Time evolution of the negativity between the atoms (blue) and fields (red) as a function of time scaled $gt$ for the initial states: (

**left**) ${|\varphi \left(0\right)\rangle}_{1}=\frac{1}{\sqrt{2}}(|eg00\rangle +|ge00\rangle )$; and (

**right**) ${|\varphi \left(0\right)\rangle}_{2}=\frac{1}{\sqrt{2}}(|gg10\rangle +|gg01\rangle )$. The chosen parameters were $\gamma =0.01g$ and $\mathsf{\Omega}=J=0$ for $\kappa =0.01g$ (solid line), $\kappa =0.5g$ (dot-dashed line) and $\kappa =1.0g$ (dashed line).

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**MDPI and ACS Style**

Sousa, E.H.S.; Roversi, J.A.
Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup. *Quantum Rep.* **2019**, *1*, 63-70.
https://doi.org/10.3390/quantum1010007

**AMA Style**

Sousa EHS, Roversi JA.
Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup. *Quantum Reports*. 2019; 1(1):63-70.
https://doi.org/10.3390/quantum1010007

**Chicago/Turabian Style**

Sousa, Emilio H. S., and J. A. Roversi.
2019. "Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup" *Quantum Reports* 1, no. 1: 63-70.
https://doi.org/10.3390/quantum1010007