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基于现有实验, 本文构建一束弱线性偏振光在平行于传播方向的磁场作用下分裂为两正交偏振光, 当其与三角形三量子点相互作用后形成五能级M型三量子点电磁感应透明介质模型. 随后, 利用多重尺度结合傅里叶积分方法研究体系中的光孤子传播及两孤子间的碰撞特性, 结果发现孤子间的碰撞方式是由其初始相位差所决定. 当孤子间初相位差为0时, 孤子间的碰撞为周期性弹性碰撞; 当初相位差为
$\text{π} /4$ ,$ \text{π} /2$ 和$ \text{π} $ 时, 孤子间会产生排斥作用力而使两孤子分离. 有趣的是, 孤子间的碰撞特征受量子点间的隧穿强度的调控. 当点间隧穿强度的增加, 初相位差为0的孤子间的碰撞周期减小; 而初相位差为$ \text{π} /4$ ,$ \text{π} /2$ 和$ \text{π} $ 时孤子间的排斥力增大. 这为实验上如何操控半导体量子点器件中的孤子动力学提供了一定的理论依据.Experimentally, the triple-quantum-dots system can be produced on a GaAs $ \left[ {001} \right]$ substrate by molecular beam epitaxy or in-situ atomic layer precise etching, thus enabling a triangle triple quantum dot (QD) aligned along the$ \left[ {1\bar 10} \right]$ direction. According to this, we first propose a five-level M-type triple QD electromagnetically induced transparency (EIT) model which consists of a triple QD molecule interacting with a weakly linearly polarized probe field with two orthogonal polarization components under the action of a magnetic field parallel to the light propagation direction. Subsequently, by using the multiple-scale method combined with the Fourier integration method, the propagation characteristics of the optical solitons and the collision characteristics of two solitons in the system are studied. It is shown that the optical solitons can form and propagate stably in this system under the action of quantum inter-dot tunneling coupling whose formation mechanism is different from the soliton-forming mechanism in ultra-cold atomic, single QD, and double QD EIT system. This is because the necessary condition for forming a soliton is to use a strong light beam to modulate a weak light beam, whether it is in an ultra-cold atom system, or a single quantum dot EIT medium or a double quantum dot EIT medium. In a word, the formation of soliton in previous EIT systems needs an additional strong controlling field, while the five-level M-type triple QD EIT system is dependent on the inter-dot tunneling.Since the solitons can propagate stably, the collision properties of the solitons may be studied in this system. Finally, by applying Fourier integration method, it is found that the collision behaviors of two solitons are determined by their initial phase difference. When their initial phase difference is 0, the collision behavior between the solitons is periodic elastic collision. While their initial phase difference is separately $ {\rm{\pi }}/4$ ,$ \text{π}/2$ , and$ \text{π}$ , the collision behaviors exhibit separation phenomenon due to repulsive effect. Interestingly, the collision characteristics of two solitons are controlled by the inter-dot tunneling strength. With the increase of inter-dot tunneling strength, the collision period of two solitons with the initial phase difference of 0 decreases, and the repulsive force of two solitons with the initial phase difference being separately π/4, π/2 and π increases. This provides some theoretical basis for experimentally controlling the soliton dynamical properties in semiconductor quantum dot devices.-
Keywords:
- inter-dot tunneling coupling/
- solition collision behaviors/
- phase difference/
- electromagnetically induced transparency medium
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