In this paper, we present an analytical solution for the system of two-level semiconductor quantum dot. In addition, we discuss the rates of the photon radiative and phonon radiationless transitions from the excited state $$ (\alpha _{12}, \alpha _{21}),$$ ( α 12 , α 21 ) , the rate of processes of pure dephasing $$ (\gamma )$$ ( γ ) , the detuning parameter ( $$\Delta $$ Δ ) and the Rabi frequency ( $$\Omega $$ Ω ), on the atomic occupation probabilities ( $$\rho _{11}(t)$$ ρ 11 ( t ) and $$\rho _{22}(t)),$$ ρ 22 ( t ) ) , the atomic population inversion ( $$\rho _{z}(t)),$$ ρ z ( t ) ) , the purity ( $$P_{A}(t)),$$ P A ( t ) ) , the von Neumann entropy ( S ( t )) and the information entropies ( $$H(\sigma _{x}),$$ H ( σ x ) , $$H(\sigma _{y})$$ H ( σ y ) and $$H(\sigma _{z}))$$ H ( σ z ) ) . We clearly observe the emergence of long-lived quantum coherence phenomenon in all the curves for some special cases of $$\alpha _{12},$$ α 12 , $$\alpha _{21}$$ α 21 , $$\gamma $$ γ , $$\Delta $$ Δ and $$ \Omega .$$ Ω . Besides, the decay phenomenon is quite evident in the purity curves, which can be simply controlled by changing the values of $$\alpha _{12},$$ α 12 , $$ \alpha _{21}$$ α 21 and $$\gamma .$$ γ .

中文翻译：

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两能级半导体量子点中的长寿命量子相干性

在本文中，我们提出了两能级半导体量子点系统的解析解。此外，我们讨论了从激发态 $$ (\alpha _{12}, \alpha _{21}), $$ ( α 12 , α 21 ) 的光子辐射跃迁和声子无辐射跃迁的速率，纯移相过程 $$ (\gamma )$$ ( γ ) ，失谐参数 ( $$\Delta $$ Δ ) 和 Rabi 频率 ( $$\Omega $$ Ω )，对原子占据概率 ( $$ \rho _{11}(t)$$ ρ 11 ( t ) 和 $$\rho _{22}(t)),$$ ρ 22 ( t ) ) ，原子布居反转 ( $$\rho _{ z}(t))、$$ ρ z ( t ) ) 、纯度 ( $$P_{A}(t) )、$$ PA ( t ) ) 、冯诺依曼熵 ( S ( t ) ) 和信息熵 ( $$H(\sigma _{x}), $$ H ( σ x ) , $$H(\sigma _{y})$$ H ( σ y ) 和 $$H(\sigma _{ z}))$$ H (σ z ) ) 。我们清楚地观察到 $$\alpha _{12},$$ α 12 , $$\alpha _{21}$$ α 21 , $$ \gamma $$ γ , $$\Delta $$ Δ 和 $$ \Omega .$$ Ω 。此外，在纯度曲线中衰减现象非常明显，可以通过改变$$\alpha _{12}、$$ α 12 、$$ \alpha _{21}$$ α 21 和$$\gamma .$$ γ .