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利用概率幅变分近似结合多重尺度法, 研究了探测光在两边产生点间隧道耦合的非对称阵列型三量子点电磁诱导透明介质的传播性质. 结果表明, 由于系统的色散效应和点间隧穿耦合产生的非线性效应相平衡, 系统能形成稳定传播的超低速时间光孤子. 有趣的是, 仅开启一边的点间隧穿耦合(即另一边关闭), 随着点间隧穿耦合强度的增加, 光孤子的速度呈现出先增大后减小的变化趋势, 但光孤子的幅度却一直增大. 两边两个点间隧穿耦合强度均开启后, 随着点间隧穿强度逐渐的增大, 光孤子的幅度随着点间隧穿强度的增大会出现逐渐减小, 直到出现一个拐点后才迅速增大; 而光孤子的速度相比较于单个隧穿强度的影响会明显降低, 且出现停滞的现象. 这些结果不但揭示出点间隧道耦合对三量子点电磁感应透明介质光孤子的动力学有着重要影响, 而且还预言在半导体量子点器件中可利用点间隧道耦合调节其光孤子传输的幅度.
Soliton, which can travel over long distance without attenuation or shape change due to the balance of the interplay between dispersion (or diffraction) and nonlinearity in nonlinear medium, becomes a good information carrier in quantum information processing and transmission. Up to now, the study on the optical solitons mainly focuses on ultra-cold atomic electromagnetic induction transparency (EIT) medium. This is mainly because ultra-cold atomic system can generate strong nonlinear effect under low light excitation. However, for the practical application, it is a big challenge to control accurately the optical soliton dynamics in the atomic EIT medium due to its low temperature (which approaches to absolute zero) and rarefaction. Fortunately, with the maturity of semiconductor quantum production technology, quantum dots have extensive application prospect in quantum information processing and transmission. So, in the paper, we study the optical soliton dynamics in a four-level asymmetric array-type three-quantum-dot EIT medium. Based on the current experimental results, we first propose a four-level asymmetric array-type three-quantum-dot EIT model. Subsequently, by using amplitude variable approach combined with multi-scale method, we study analytically the propagation of a probe pulse in this system. It is shown that when one (the another) inter-dot tunneling coupling is turned on (off), only a single transparency window appears in the center range of the probe field detuning. Only if two inter-dot tunneling couplings are turned on will two transparent windows be distributed on both sides of the central region of the probe field detuning. And the width of the single transparent window or the widths of two transparent windows become wider with the strength of the inter-dot tunneling coupling increasing. For the nonlinear case, by choosing appropriate parameters in the area of the transparency window, the stable propagation of soliton can be realized. Interestingly, we find that the strength of the inter-dot tunneling coupling has an important effect on the soliton dynamic behaviors. In the case that one (the another) inter-dot tunneling coupling is turned on (off), with the increase of strength of the inter-dot tunneling coupling, the velocity of the soliton exhibits a trend of first increasing and then decreasing, and the amplitude of the soliton presents a increasing trend for ever. For the case that two inter-dot tunneling couplings are turned on, with the strength of the two inter-dot tunneling coupling increasing, the velocity of the soliton presents a decreasing trend for ever, while the amplitude of the soliton exhibits a trend of first decreasing and then increasing. Thus, the amplitude modulation effect of optical soliton can be realized in semiconductor quantum dot devices. -
Keywords:
- electromagnetically induced transparency medium /
- inter-dot tunneling coupling /
- optical soliton dynamical behaviors
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图 1 四能级非对称阵列型三量子点电磁感应透明介质能级结构示意图
Fig. 1. Energy level structure diagram of a four-level asymmetric array-type three quantum dots electromagnetically induced transparent medium.
图 2 关闭左点间隧穿耦合 ($ {\text{T}}{{\text{e}}_1} = 0 $) 仅开启右点间隧穿耦合情况下, 线性吸收系数$ {K}_{0{\mathrm{i}}} $随失谐$ {{{\varDelta }}}_{{\mathrm{p}}} $的变化情况. 其他参数: $ {\gamma }_{10}=3.3\;\text{μeV}$, $ {\gamma }_{20}={\gamma }_{30}={10}^{-4}{\gamma }_{10} $, $ -\hslash {\omega }_{12}= $$ \hslash {\omega }_{13}=10\;\;\text{μeV} $, $ {\kappa }_{01}=1976\;{{\mathrm{cm}}}^{-1}{\cdot}\text{μeV} $
Fig. 2. In the case that the left (right) inter-dot tunneling coupling is turned off (on), the linear absorption coefficient $ {K}_{0{\mathrm{i}}} $ as a function of the detuning $ {{{\varDelta }}}_{{\mathrm{p}}} $. Other parameters: $ {\gamma }_{10}=3.3\;\;\text{μeV}$, $ {\gamma }_{20}={\gamma }_{30}={10}^{-4}{\gamma }_{10} $, $ -\hslash {\omega }_{12}= \hslash {\omega }_{13}= $$ 10\;\;\text{μeV} $, and $ {\kappa }_{01}=1976\;{{\mathrm{cm}}}^{-1}{\cdot}\text{μeV} $.
图 3 关闭右点间隧穿耦合 (${\text{T}}{{\text{e}}_2} = 0$) 仅开启左点间隧穿耦合情况下, 线性吸收系数$ {K}_{0{\mathrm{i}}} $随失谐$ {{{\varDelta }}}_{{\mathrm{p}}} $的变化情况. 图中所使用的其他参数与图2一致
Fig. 3. In the case that the left (right) inter-dot tunneling coupling is turned on (off), the linear absorption coefficient $ {K}_{0{\mathrm{i}}} $ as a function of the detuning $ {{{\varDelta }}}_{{\mathrm{p}}} $. Other parameters used are the same as the Fig. 2.
图 4 左、右两边两个点间隧穿耦合均开启情况下, 线性吸收系数$ {K}_{0{\mathrm{i}}} $随失谐$ {{{\varDelta }}}_{{\mathrm{p}}} $的变化情况. 图中所使用的其他参数与图2一致
Fig. 4. Under both the left and right inter-dot tunneling coupling are turned on, the linear absorption coefficient $ {K}_{0{\mathrm{i}}} $ as a function of the detuning $ {{{\varDelta }}}_{{\mathrm{p}}} $. Other parameters used are the same as the Fig. 2.
图 5 单点间隧穿耦合下三量子点EIT介质中光孤子的稳定性分析($ {\text{T}}{{\text{e}}_1} = 1\;{\text{meV}} $, $ {\text{T}}{{\text{e}}_2} = 0 $)
Fig. 5. Stability analysis of optical solitons in the three quantum dot EIT medium under the single inter-dot tunneling coupling effect ($ {\text{T}}{{\text{e}}_1} = 1\;{\text{meV}} $, $ {\text{T}}{{\text{e}}_2} = 0 $).
图 8 不同右点间隧穿强度下, 孤子的幅度随左点间隧穿强度Te1的变化
Fig. 8. Amplitude of the solitons as a function of the strength Te1 of the left inter-dot coupling with the different strength of the right inter-dot tunneling coupling.
图 6 双点间隧穿耦合下三量子点EIT介质中光孤子的稳定性分析($ {\text{T}}{{\text{e}}_1} = 1\;{\text{meV}} $, $ {\text{T}}{{\text{e}}_2} = 0.5\;{\text{meV}} $)
Fig. 6. Stability analysis of optical solitons in three quantum dot EIT medium under the two single inter-dot tunneling coupling effect ($ {\mathrm{Te}}_1 = 1\;{\text{meV}} $, $ {\text{T}}{{\text{e}}_2} = 0.5\;{\text{meV}} $).
图 7 不同右点间隧穿强度下孤子的群速度随左点间隧穿强度Te1的变化
Fig. 7. Group velocity of the solitons as a function of the strength Te1 of the left inter-dot coupling with the different strength of the right inter-dot tunneling coupling.
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Google Scholar
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Google Scholar
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